sailboat displacement ratio

What Is Sail Area Displacement Ratio?

Last Updated by

Gabriel Hannon

August 30, 2022

The sail area-displacement ratio is one of the simplest ways to measure the expected performance and speed of a sailboat.

While there is no single number that can encapsulate the performance of every different type of sailboat, the sail area-displacement ratio, or SA/D, provides a relatively robust way to discuss the relationship between sail power and weight that determines many aspects of a boat’s acceleration, maneuverability and performance capabilities.

This article will discuss the methods of calculating the sail area-displacement ratio, what it tells us about a boat’s performance, how it can be used to compare and categorize different boats, and some of its potential shortcomings. As boat building technology and modeling software advance, there are more significant and complex ways to measure performance characteristics. This is becoming especially prominent with the rise of foiling boats and other non-displacement hull plans. Still, the SA/D is a simple, back-of-the-envelope calculation that you can do to ballpark the performance of a boat.

Over years of racing, working with sailors and suppliers, I know how important it is to have a sense of a boat’s performance abilities. This can mean the difference between a single overnight trip and a long slog through the doldrums. Especially as you go to buy a new boat, having a sense of the performance range that you want and ensuring that the boat you purchase has these characteristics will make your decision much easier.

Table of contents

‍ Calculating the Sail Area-Displacement Ratio

For those of us fortunate (or perhaps unfortunate) enough to have had to memorize the concept of a ratio in the 5th grade, calculating the sail area-displacement ratio is a relatively straightforward endeavor. You need to take a measurement of the sail area, which is generally given in square feet, and a measurement of displacement and divide them. There are, however, light complications with both measurements. Here is the formula, and you can read on in this section if you want to understand the various nuances in the calculation and derivation of it, or skip to the next section if you just want to understand what it means for your boat.

When calculating the sail area, there are different points of view on how to accurately measure effective sail area. As the interactions between mainsail, overlapping or non-overlapping headsails, and off-the-breeze sails are not always the same depending on the point of sail. Because the different setups utilize these areas differently, relative sail plan measurements do not always represent how much sail area is directly being used to power the boat. Comparing the sail area-displacement ratio on a plan with a 150% overlapping genoa or a non-overlapping jib by simple square footage will favor the former, even if they have the same effective power. This doesn’t mean that you can’t use the SA/D to compare boats, but you just want to make sure that both boats are using the same method of measurement and that you account for such sail plan differences. Regardless, the sail area component, which will be the numerator in our ratio, is generally just equal to SailArea(ft2), indicating that it is measured in square feet.

The fundamental value of the denominator is a little bit more mathematically confusing, as it requires some conversions in order to return the final ratio. The displacement of a boat is simply equal to its weight, which can be given in pounds. We want our ratio, however, to be unitless, so we have to do some transformations. First, we realize that a displacement in pounds causes the boat to displace a certain volume of water, which we can measure in cubic feet. A single cubic foot of water weighs approximately 64 pounds, i.e. it has a density of 64 lbs/ft3. Therefore, if we want to determine the cubic footage that a boat of a certain weight displaces, we would have to divide its weight by that density. This gives us a converted value for displacement in cubic feet. Finally, we convert cubic feet to square feet by raising the measurement to the power of 2/3, which leaves us with a ratio of square feet over square feet. With this, we can finally perform our SA/D calculation.

Performance Implications and Categorization

The point of the SA/D is to give you an intuitive sense of how a boat will perform under sail. Sail area is one of the best sailing analogues for horsepower. Still, boats are much more dependent on the costs of these larger sail plans--longer, heavier, wider--and so sail area does not tell you as much about a boat as horepower does about a car. This is why we need to incorporate displacement as a shorthand for how big the boat is, and then use the ratio between the two to discuss performance.

Boat Categories

In general, sail area-displacement ratios float around the high teens. Heavy, casual cruising boats tend to be in the range of 15-16, while high performance racing boats can push over 20. A SA/D of 20 is generally accepted as a cutoff for modern performance cruising and racing hulls.

There are helpful niche-types within this larger range, however, so we will discuss the breakdown of what each ratio range should tell you about a boat in which you might be interested.

<15: Motorsailors and Auxiliary Sailboats

Boats in this range are never meant to operate purely on sail power, and cannot really be expected to make much headway under sail alone. With a good breeze, you can certainly save a little on gas, but you will not be cutting through the harbor with any particular excitement.

15-16: Average offshore cruiser

These boats, while a little bulky, need that bulk to handle the rigors and strains of offshore sailing. This is your first level of acceptable performance for making way under sail power alone.

16-17: Coastal cruiser

Sleeker and with more aggressive sail plans than their offshore counterparts, cruising hills  SA/D range starts pushing you into the sporty range. You can expect decent maneuverability and fresh speeds, but you won’t be breaking and sea-speed records, and you may well want to stay within sight of land.

17-19: Racing yachts

Once you get into the high teens, SA/D figures tend to point towards racing hulls with minimal capabilities for cruising and distance sails. These boats are engineered to go fast, shave off every bit of weight possible, and do everything they can to cut through the water. This means getting slimmer and lighter, both to reduce the displacement, in terms of weight, and the sheer amount of ‘wetted surface’ in the water, which introduces drag. It will be hard to say much about a boat’s relative performance within this range, however, as racing boats tend to have more factors effecting their performance at the slimmest of margins, but this range is, nonetheless, a good indicator that you should not expect to be taking such a boat for a long cruise.

20+: Performance racers, Dinghies, One-Design Sailboats

Once you get into the 20s, you may be presented with one of two options. Either you have made it into high-performance racing mono- and multi-hulls tuned for racing, or you have found your average sail around dinghy. The Laser, the Olympic Class singlehanded sailboat and also one of the most common sailboats in the world, has a SA/D of 47.3 by a quick calculation, but this certainly does not mean that it is the highest performance boat in the world: it just means that it is very light! A J-70, a widely competitive racing monohull has a more reasonable SA/D of 24.7, and is a good example of demonstrating a fast, light, and snappy boat that at least resembles the others on this list.

Shortcomings and Alternatives

As with any attempt to compactify an incredibly complex problem into one or two numbers, the SA/D has its share of shortcomings. In particular, it can tell you very little about how a boat will perform on the racing front and is unlikely to help you truly distinguish between the performance of boats within a small range. A boat with an SA/D of 17.2 may just be a fast cruiser, and the foiling boats used in the America’s Cup may well be so far off the charts that it is not even relevant to measure the SA/D for them (in fact, the AC72’s, by a quick calculation, have an SA/D of 81, which is not even on the charts).

Other measurements of performance have come to prominence in an effort to replace the SA/D. Yacht designers use velocity prediction programs to model the hydrodynamics of hull shapes, weights and sizes against sail plans across various windspeeds. Performance Handicap Racing Fleet (PHRF) ratings are tabulated based on years of empirical data from racing times to give an appropriate handicap for timed races, which does a good job of leveling the playing field across boats and giving you a sense of how fast or slow a boat is in a vacuum. Most boat outside the racing field, however, are not tabulated in such systems. Polars demonstrate the expected speeds for a boat at different wind angles and velocities, though they are dense and hard to read graphics.

So there is no single metric that can be used to determine a boat’s performance. Critics of the sail area-displacement ratio will claim that it is a number that does not tell you anything, especially as it can be manipulated by boatbuilders to sell their newest line even if it is not representative of a boat’s true performance. Still, even if it is not useful at the edges of the competitive racing field or can be subject to questionable sail area accounting, the rough categorization bands are useful for a quick summary of a boat’s fundamental characteristics. You would never buy a car just by reading its horsepower, but it is still good to know it in a pinch.

Happy sailing!

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I have been sailing since I was 7 years old. Since then I've been a US sailing certified instructor for over 8 years, raced at every level of one-design and college sailing in fleet, team, and match racing, and love sharing my knowledge of sailing with others!

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How Sailboats Measure Up

• By By Jeremy McGeary
• Updated: October 17, 2012

Sailboats by the Numbers

Boat reviewers rely on numbers to describe some of the key attributes of their subjects, such as length, beam, draft, and displacement. And while judgments on interior layouts and decor are subjective, these figures describing dimensions are not. There are, however, other numbers commonly cited in spec boxes that can prove more elusive, since they attempt to put a numerical value on how a sailboat might be expected to perform while under way. The commonly used ratios are sail area to displacement (SA/D), displacement to length (D/L), and ballast to displacement (B/D). And though they’re so commonly used that a certain amount of dogma has accrued around them, these figures can, in fact, be misleading, or at least misunderstood. And the result is that a boat can be assigned attributes based on numerical values that don’t take into account how sailboat design has changed over the past several decades.

Here, then, is a look at those ratios, what they attempt to describe, and how they should be interpreted when you go off exploring new and used models. (Click to page 2 for a more in-depth explanation.)

Sail Area/Displacement (SA/D)** An automobile buff seeking a high-performance ride looks for a high power-to-weight ratio and compares the horsepower/curb-weight ratios of different cars. For a sailboat, the SA/D provides the same metric. The horsepower comes from the wind on the sails and is proportional to the sail area; a boat’s weight is its displacement (in pounds, kilograms, or tons).

Initially, the SA/D only really gives a measure of potential acceleration rates (in case any physicists are reading this), but since displacement is a key factor in the resistance a boat encounters when moving through the water, SA/D also has a bearing on potential maximum speed.

The traditional calculation for SA/D compares sail area in square feet to displacement in cubic feet. In the formula, displacement in pounds is divided by 64 (the density of seawater) to obtain cubic feet, which are in turn converted to square feet to make the ratio unit-free.

On a spreadsheet, the formula would be S/(D/64) (2/3).

Nominally, the higher the SA/D, the more lively the boat’s sailing performance. The vessel will accelerate more quickly and have the potential for higher speed. But to be able to compare boats with any degree of precision (or fairness), we have to use similar numbers. The displacement must be in the same condition, either light ship (nothing on board) or fully loaded, and the sail-area measurement must reflect the normal working sail plan. Racing boats have measurement certificates from which these numbers can be reliably extracted. The specifications provided in cruising-boat brochures might not be consistent between builders, but we have to assume they are.

Boats measured in the 1970s and the 1980s for racing under the International Offshore Rule for the most part had SA/Ds between 16 and 17, based on the sum of the mainsail triangle (M = P E/2) and 100-percent foretriangle area (100%FT = I J/2). The measurement system favored small mainsails and large headsails, and since designers of cruising boats stuck close to the IOR sail plan, the IOR value for SA/D became the yardstick. An SA/D above 17 said “fast boat,” and anything below 16 said “slow boat.”

After the IOR fell out of favor, cruising-boat design drifted away from raceboat design, and sail plans began to change. Today, many boats are designed with large mainsails and small jibs, and most builders publish a “total sail area” number that includes the standard jib (often as small as 105 percent) and the roach in the mainsail (which is significantly greater on modern boats with full-battened mainsails than on IOR boats).

These builder-supplied numbers are more readily comparable against competing models, but using them in the SA/D formula makes the boats look “faster” than older models. This is a false comparison, because the sail area used for the older boats doesn’t include the extra area in, say, a 150-percent genoa.

The table “Sailboats by the Numbers” (see page 79) illustrates this. It shows SA/Ds calculated for a selection of modern boats and boats from past eras, all about the same length, using different numbers for sail area. For each model, it shows five SA/Ds. SA/D 1 is calculated using the sail area provided by the builder. SA/D 2 is calculated using M (P E/2) and 100% FT (I J/2). SA/D 3 is calculated using M + 105% jib. SA/D 4 is calculated using M + 135% jib. SA/D 5 is calculated using M + 150% jib. The only SA/D that includes mainsail roach is SA/D 1.

Let’s look at some examples. The 1997 Beneteau Oceanis 411 has a published sail area of 697 square feet on a displacement of 17,196 pounds. That gives an SA/D 1 of 16.7 (the same as SA/D 2), which for decades was considered very respectable for a cruising boat.

In 2012, the current Beneteau Oceanis 41 has a published sail area of 902 square feet (453 mainsail + 449 jib) and a published displacement of 18,624 pounds, to give an SA/D 1 of 20.5. Wow! Super-high performance! But this is for the standard sail area, with the 449-square-foot jib (just about 100% FT and typical of the trend today toward smaller jibs that tack easily). Plug in the calculation using I, J, P, and E and SA/D 2 drops to 18.9 because it doesn’t include mainsail roach, which is about 16 percent of the total published mainsail area.

Go back to the 1997 model, tack on a standard-for-the-day 135-percent genoa, and the SA/D 4 becomes 20.7. (If we added in mainsail roach, typically about 11 percent of base mainsail area before full-battened sails, we’d have 21.4.) The 1997 boat has essentially the same horsepower as the 2012 model.

Looking at current models from other builders, the SA/Ds based on published numbers hover around 20, suggesting that designers agree on the horsepower a cruising sailboat needs to generate adequate performance to windward without frightening anyone.

The two boats in our chart that don’t at first appear to fit this model are the Hunter 39 and the Catalina 385, but they’re not really so far apart.

The Hunter’s SA/D 2 is 16.1. Its standard jib is 110 percent (327 square feet), and the rest of the published sail area is in the mainsail—664 square feet, of which 37 percent is roach!

Catalina is a little more traditional in its thinking. If you add the standard 135-percent genoa, the SA/D becomes 21.2—right in the ballpark. (It’s still there at 19.7 with a 120-percent genoa.)

The table shows that, for boats targeted at the “performance cruising” market, the SA/D numbers using actual sail area lie consistently around the 20 mark. To go above that number, you have to be able to fly that sail area without reefing as soon as the wind ripples the surface. To do that, you have to elevate stability—with broad beam, lightweight (i.e., expensive) construction, deep bulb keels, and fewer creature comforts.

Displacement/Length (D/L)** While sailboat builders and buyers are interested in displacement in terms of weight, naval architects view it as volume; they’re creating three-dimensional shapes. When working in feet, to get a displacement in pounds, they multiply cubic feet by 64, the density in pounds per cubic foot of seawater. (Freshwater boats displace more volume because the density of fresh water is only 62.4.) The D/L ratio is therefore a measure of immersed volume per unit of length—how tubby the hull is below the waterline.

According to conventional wisdom and empirical studies, the lower the D/L, the higher the performance potential. This is mainly due to wavemaking resistance being lower for slender hulls than for tubby hulls.

In the D/L formula, displacement in pounds is divided by 2,240 to convert it to tons to bring the values to manageable numbers, so D/L is displacement in tons divided by .01LWL (in feet) cubed.

In a spreadsheet, the formula would be D/(2240*(.01L)3), where D is the displacement in pounds and L is LWL in feet.

In the early days of fiberglass boats, the Cruising Club of America rule was the principal dictator of boat shapes. Because it was a waterline rule, designers kept waterlines short to keep ratings low and relied on long stern overhangs immersing to add “sailing length” when the boats heeled. Carbon fiber was available only to NASA, and boats had full interiors, so “light displacement” wasn’t really in the cards. A D/L of 300 was considered dashing, even risky. Many still-popular designs from the 1970s and 1980s have D/Ls as high as 400; see the Bounty II.

Fast-forward 40 years. Boats now have plumb bows and plumb sterns and waterlines almost as long as their LOAs—there are no rating penalties on a cruising boat. The boats’ weights haven’t changed much because, although builders try to save weight to save cost, the boats are so much bigger. The hull and deck surface areas are greater, and all that extra internal volume can be filled with furniture. The effect on D/L ratios has been drastic—just look at the table. A D/L ratio above 200 today describes a heffalump.

But do these lower D/Ls actually buy you any more speed? Yes and no.

Yes : Because speed is proportional to the square root of the waterline length. Today’s 40-footer has a much longer waterline than yesterday’s and ought to sail as fast as yesterday’s 50-footer. It might also benefit from reduced resistance due to a smaller cross-sectional area, but it also might have greater wetted-surface drag due to the longer immersed length. When sailing downwind in waves, though, the lower-D/L boat will surf more readily.

No : Because, as we saw above, the power-to-weight ratios (SA/D) of modern boats aren’t effectively any higher, and certainly aren’t in the realm that would allow our cruising sailboats to climb out of the displacement zone and plane. In most conditions, the lower-D/L boat is still trapped in its wave.

In the days of the IOR, a D/L of 250 was still pretty racy; see the 1978 Catalina 38. Today, even a D/L as low as 150 doesn’t make a boat a speedster if it can’t carry the sail area to make it so. To compete at a level with a Volvo 70, look for a D/L of about 40 and an SA/D of 65.

Ballast/Displacement (B/D)** The ballast/displacement ratio is simply the ballast weight divided by the boat’s total displacement. Since ballast is there to give the boat stability, it’s easy to jump to the conclusion that the higher the B/D, the stiffer the boat.

However, B/D doesn’t take into account the location of the ballast.

Take a boat that has a total displacement of 20,000 pounds and put its 8,000 pounds of ballast in the bilge. Now take the same boat and put the 8,000 pounds of ballast 4 feet deeper in a bulb at the bottom of a deep fin keel. Same ballast ratio (0.4), but very different stability.

When looking at B/D, therefore, we must ask about the configuration of the keel: How low is the ballast?

Stability analysis is complex and involves beam, hull cross-section, and length, among other factors, of which B/D is just one.

Since the late 1990s, builders of sailboats intended for sale in the European Union have been required to provide stability data, including a curve of righting arm at angles of heel from 0 to 180 degrees—far more information than anyone can divine from a B/D number and a much more useful measure of a boat’s inclination to stay upside down in the unlikely event (the way most people use their boats) that it exceeds its limit of positive stability.

CW contributing editor Jeremy McGeary is a seasoned yacht designer who’s worked in the naval-architecture offices of David Pedrick, Rodger Martin, and Yves-Marie Tanton and as a staff designer for Camper & Nicholson.

To read the related article, How To: Measure Sail Area, click here.

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The Ballast to Displacement Ratio Explained (with Formula)

Ballast to displacement ratio explained.

The ballast to displacement ratio is one of the ratios sailboat enthusiasts use to quickly compare sailboats. It is simply the percentage of ballast against the displacement of a boat.

What is a good ballast ratio?

Sailboats with a ballast ratio of over .40 are generally stiffer, more stable, and have better handling in rougher conditions. Sailboats with a ratio below .40 will typically be less stable, have a higher heel angle, and be more prone to rolling. However, the ballast ratio doesn't account for other important factors, such as righting moment.

Ballast to displacement ratio formula

The formula for this ratio is:

ballast displacement ratio = ballast / displacement

In other words, it tells you what percentage of the sailboat's weight is in the ballast.

The average value is between 0.35 and 0.45 for cruising boats. This means that on average, 35-45% of the weight of a cruising boat will be carried in the keel ballast .

It is a simple indicator that can give you a rough idea of how stiff and stable the boat will be. However, there are limitations to the use of this number, since the ballast weight doesn't tell the whole story. For example, it doesn't tell you how much righting moment the keel design provides, or how much wetted surface there is - while both of these factors greatly affect handling and stability.

To get a more complete picture of the boat's handling, one should also look at the capsize screening ratio (as explained by Ted Brewer) and the comfort ratio .

How Do Sailboat Keels Work?

In short, a sailboat keel's weight is used to increase displacement and lower the center of gravity, while its surface is used to increase wetted surface. This helps to stabilize the boat, but also provides directional stability. For a more detailed explanation on how sailboat keels work , I recommend reading this article.

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Calculations

Sail area / displacement ratio.

A measure of the power of the sails relative to the weight of the boat. The higher the number, the higher the performance, but the harder the boat will be to handle. This ratio is a "non-dimensional" value that facilitates comparisons between boats of different types and sizes. Read more.

SA/D = SA ÷ (D ÷ 64) 2/3

• SA : Sail area in square feet, derived by adding the mainsail area to 100% of the foretriangle area (the lateral area above the deck between the mast and the forestay).
• D : Displacement in pounds.

Ballast / Displacement Ratio

A measure of the stability of a boat's hull that suggests how well a monohull will stand up to its sails. The ballast displacement ratio indicates how much of the weight of a boat is placed for maximum stability against capsizing and is an indicator of stiffness and resistance to capsize.

Ballast / Displacement * 100

Displacement / Length Ratio

A measure of the weight of the boat relative to it's length at the waterline. The higher a boat’s D/L ratio, the more easily it will carry a load and the more comfortable its motion will be. The lower a boat's ratio is, the less power it takes to drive the boat to its nominal hull speed or beyond. Read more.

D/L = (D ÷ 2240) ÷ (0.01 x LWL)³

• D: Displacement of the boat in pounds.
• LWL: Waterline length in feet

Comfort Ratio

This ratio assess how quickly and abruptly a boat’s hull reacts to waves in a significant seaway, these being the elements of a boat’s motion most likely to cause seasickness. Read more.

Comfort ratio = D ÷ (.65 x (.7 LWL + .3 LOA) x Beam 1.33 )

• D: Displacement of the boat in pounds
• LOA: Length overall in feet
• Beam: Width of boat at the widest point in feet

Capsize Screening Formula

This formula attempts to indicate whether a given boat might be too wide and light to readily right itself after being overturned in extreme conditions. Read more.

CSV = Beam ÷ ³√(D / 64)

The theoretical maximum speed that a displacement hull can move efficiently through the water is determined by it's waterline length and displacement. It may be unable to reach this speed if the boat is underpowered or heavily loaded, though it may exceed this speed given enough power. Read more.

Classic hull speed formula:

Hull Speed = 1.34 x √LWL

Max Speed/Length ratio = 8.26 ÷ Displacement/Length ratio .311 Hull Speed = Max Speed/Length ratio x √LWL

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A Closer Look at the Rationale Behind the Ratios

Sailboat performance varies based on the eye of the beholder. Racers want light-air alacrity and a willingness to plane while cruisers want directional stability and reasonable speed with moderate sail area. A boats design dimensions and a few simple ratios give some hints about these attributes.

Most performance-oriented boat designs focus on around-the-buoy racing; these assume that there will be a large crew to keep sail area and trim optimized and to provide movable ballast and that the boat must cope with windward and leeward legs of a race course. Offshore, point-to-point race boat designs are greatly influenced by racings handicapping rules. In either case, these rules penalize performance, and design factors like ultra-wide beam-intended to leverage crew weight for righting moment-are of little value to shorthanded cruisers. Make sure that the boat youre looking for is fast in the context under which it will be sailed.

The sail area-to-displacement ratio (SA/D) compares energy and resistance-much like a horsepower-to-weight comparison in an automobile. As the SA/D ratio grows higher, so does the vessels potential speed under sail. However, too much sail area and too little righting moment means a very tender boat. Too little sail area and too much displacement means you can brag about carrying full sail in 20 knots, but your boat will move like a sea buoy in 7 or 8 knots of breeze.

The ballast-to-displacement ratio (B/D) of a boat tells you how much secondary righting moment to expect from the keel. The smaller and lighter the vessel, the more important it is for this number to be higher for stability as well as for performance reasons. Bulbs and other keel-tip shapes lower the vessels center of gravity (CG) and can lessen the need for a 40-percent B/D ratio. A deeper draft can also lower the CG and can improve on-the-wind performance.

A boats displacement-to-length ratio (D/L) has a lot to do with the resistance of a hull shape moving through the water, and since skin drag is the big enemy at lower speeds, the D/L ratio tells us a lot about a boats light-air performance. By increasing the boat length and keeping the displacement the same, decreasing displacement, or doing both, the D/L ratio decreases, and the boat will go faster in light air. Wave-making kicks in as the major resistance at higher speeds, and the implications of the D/L ratio lessen.

In a nutshell, when it comes to performance under sail, light displacement is fast; deep-keel boats point higher and sail more efficiently to weather; full, flat sections aft cause a boat to plane sooner; and more sail area delivers more power. When it comes to delivering the goods in an open-ocean context, seakeeping ability is an important factor in performance as is the amount of punishment the boat and crew can endure.

Ordered by sail-area-displacement (SA/D), this table illustrates a progression from a heavy-displacement cruiser (Westsail 32) to a fast and light racer (Farr 400). Note how the designers altered ballast, sail area, and displacement to reach their goals.

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• Boat Displacement

Boat Displacement/Length Ratio & Other Key Performance Indicators

A boat's displacement is defined as the weight of the volume of water displaced by it when afloat. It's normally described in long tons (1 ton = 2,240 lbs) but it can also be stated in cubic feet, with 1 ft 3 = 64lb.

Like hullspeed, displacement doesn't mean much unless compared to waterline length,so you need to take a look at the Displacement/Length Ratio to compare the relative heaviness of boats no matter what their size.

Similarly, sail area doesn't tell you much about a boat's likely performance unless compared to its displacement, which is why we have the Sail Area/Displacement Ratio.

Let's take a look at both of these displacement related ratios in turn...

The Displacement/Length Ratio

Displacement/length categories:.

Under 90 -  Ultralight;

90 to 180  -  Light;

180 to 270  -  Moderate;

270 to 360  -  Heavy;

360 and over  -  Ultraheavy;

The formula for calculating the Displacement/Length Ratio is:

D/(0.01L) 3 , where...

• D is the boat displacement in tons (1 ton = 2,240lb), and 
• L is the waterline length in feet.

An ultra-light racing yacht may have a D/L Ratio of 80 or so, a light cruiser/racer would be around 140, a moderate displacement cruiser be around 230, a heavy displacement boat will be around 320 while a Colin Archer type super- heavy displacement cruiser may boast a D/L ratio of 400+.

As immersed volume and displacement are proportional, a heavy displacement yacht will have to heave aside a greater mass of water than its light displacement cousin.

Or put another way, the lower D/L Ratio vessel will have a lower resistance to forward motion than the higher D/L ratio vessel, and will be quicker as a result.

That's a longwinded way of saying that the greater the mass, the greater the power required to shift it.

That power is of course derived from the force of the wind acting upon the sails, and the greater the sail area the greater the power produced for a given wind strength.

A Few Examples...

The Sail Area/Displacement Ratio

The formula for calculating the Sail Area/Displacement Ratio is:

SA/(DISPL) 0.67 , where...

• SA is sail area in square feet, and
• DISPL is boat displacement in cubic feet

Clearly then, performance is a function of both power and weight, or sail area and displacement.

Sail Area/Displacement ratios range from around 14 for a lightly canvassed motor-sailor to 20 or so for an ocean racer.

Calculating Sail Area

Mainsail Area

Calculating the area of the mainsail is simple. After all, it's just a right-angled triangle so:

Area = (Base x Height)/2 = (Foot x Luff)/2

OK, it won't be spot on if the sail has some roach, but it'll be near enough. Having said that, for a fully-battened, heavily roached sail you could add 10 to 15% to be more accurate.

Foresail Area

The foresail would be just as easy if it exactly fitted the fore-triangle but usually the sail will be high-cut or will overlap the mast - or both.

So the calculation becomes:

Sail Area = (luff perpendicular x luff)/2

For more on this subject, take a look at Understanding Sail Dimensions...

A Final Word on Boat Displacement etc...

So to summarize, the criteria associated with good performance under sail are:

• Boat Displacement: the lower the better, as the power requirement is directly proportional to displacement. Provided, of course, that light displacement doesn't come at the cost of structural integrity;
• Waterline length: the longer the better, as wave-making resistance is inversely proportional to waterline length;
• Wetted area: the less the better, particularly in areas where light airs prevail, as hull drag is directly proportional to wetted area;
• Sail area: the more the better, within reason, as power production is directly proportional to sail area. Having to reef early is much less frustrating than wishing you had an extra metre or so on the mast when the wind falls away.
• For real 'Get Up and Go' a sailboat will have a low Displacement/Length ratio and a high Sail Area/Displacement Ratio .

But performance in an offshore cruising sailboat isn't just about speed. Whilst, as part of the deal for getting their hands on the silverware, a racing crew will cheerfully accept the high degree of attentiveness needed to keep a twitchy racing machine on her feet, a cruising sailor most definitely won't.

For us, a degree of speed will be readily sacrificed for a boat that's easy on the helm, and which rewards its crew with a gentler motion and more comfortable ride.

And whilst talking of comfort, Ted Brewer's  'Comfort Ratio'  has much to do with Boat Displacement.

You might like to take a look at these...

The Righting Moment Is a Key Factor to a Sailboat's Stability

Whilst it's the righting moment that influences a sailboat's static stability, it's the dynamic stability that has the larger affect on seaworthiness. And here's what it means to us

Importance of the Prismatic Coefficient in Sailboat Hull Design

The prismatic coefficient is associated with the fullness of fineness of the ends of a boat's hull, but why is this important and how does it affect performance?

Understanding Sailboat Design Ratios

The formulae for sailboat design ratios are quite complex, but with this tool the calculations are done for you in an instant!

How Gz Curves Reveal the Truth about A Sailboat's Stability

Gz curves are a graphic representation as to how a sailboat's righting moment changes with heel angle, identifying the heel angle at which the boat will capsize rather than come back upright

Some Sailboat Interiors are Not Suitable for Offshore Sailing

Examples of practical sailboat interiors that work for serious offshore sailing, compared with those that are more suited for coastal sailing and marina hopping

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Sail Calculator

Go Directly To The Sail Calculator Here

What Carl’s Sail Calculator Does:

Physicist and sailor Carl Adler developed this online Sail Calculator for comparing sailboats  and its database has grown over a number of years to almost 3000 boats. It should be one of the first places you go on the Web if you want to know the vital statistics about a sailboat, including Length Overall (LOA) , Length on the Waterline (LWL) , Displacement and Sail Area .

The Sail Calculator will also give you valuable performance numbers for any vessel in its database or any numbers you enter, including the Displacement / LWL ratio, Theoretical Limiting Hull Speed, Sail Area / Displacement ratio, Length to Beam ratio, Motion Comfort value, Capsize Screening value, sailing category and Pounds per inch immersion value .

Naval architects use these values when they design a new boat, and from them you can determine a conventional displacement hull boat’s purpose and predict its performance. Note that planing hulls, catamarans and hydrofoil vessels are not defined in the same way. Here’s what the performance numbers mean:

Displacement/LWL ratio – Heavy boats (D/L above about 300) will carry big loads but require plenty of power to drive. Light boats (D/L below about 150) are generally quicker and more responsive but are affected by loading. Most boats have moderate displacement and they compromise the conflicting virtues of the extreme designs. Contemporary racing boats often have D/L ratios well below 100.

Hull Speed – A conventional hull, which moves through the water rather than rising atop it and planing across the surface, is limited in speed by length of the waves it produces; long waves travel faster. This wave length can be calculated and the top speed of the hull predicted. Long boats make long waves.

Sail Area / Displacement ratio – The SA/D ratio is like the power/weight ratio of an automobile. A high SA/D ratio (> about 18) indicates a powerful rig, while a low ratio indicates a more docile boat.

Length / Beam ratio – A long, narrow hull with limited interior space is easier to drive than a short, fat one with plentiful capacity. Compare L/B ratios to gain insight into the purpose of the boat.

Motion Comfort value – Not as widely used as the previous numbers, the Motion Comfort value tries to predict whether a boat has a quick, motion through the waves or a slow, easy motion. Note that some people get more seasick with a slowly rolling motion than a quick, jerky one. Your mileage will vary.

Capsize Screening number – Developed after the Fastnet Race tragedy, the Capsize Screening number is a quick way to judge if a boat is seaworthy. Values below 2.0 are desirable for offshore yachts. Do not put too much faith in the exact number, as it is an approximation only.

Pounds / square inch Immersion – When you load a boat, it sinks deeper into the water. This Immersion value indicates the weight carrying capacity of a vessel.

There is also a Prop Sizing section which will calculate the optimum propeller to use on any displacement-hull boat, based on noted naval architect Dave Gerr’s formulas.

 To The Sail Calculator

19 Comments on “ Sail Calculator ”

I corrected it. Thanks!

S2 7.3 specs from factory brochure (visible at boatbrochure DOT com SLASH products SLASH s2-7-3-meter-brochure the free preview is pretty legible)

LWL is 18.5 not 18.73 Beam is 8.0 not 8.5 Displ is 3250 not 3373 S.A. is 255, not 261

Thank you so much for your work maintaining this web page; it is tremendously valuable resource that I refer to often!

Tom, The Colgate 26 has a sail area different from that published on your calculator. It’s listed as 338 SF per https://www.colgate26.com/specifications/

Chris, Thanks for the note; I’m glad you find the Sail Calculator useful. I’ll change the value on the database on the next update, since your source is probably more accurate. I rarely know what the sources are when a user submits data, so there are definitely errors in there. It’s possible that one of the numbers is based on the 100% foretriangle measurement and the other is with a larger jib, which could be either the working jib or a Genoa. I get this question from time to time and probably should add something to the description about it (www.tomdove/blog/sail-calculator/). –Tom

Hi Tom, thanks for Carl’s calculator alive. I have a Tayana 48 DS and from their website, I get a different sail area. 1316 sq ft vs 1048.

Regards, Chris

Hi Tom, Looking at your specs the Marieholm 26 literature does not match what is posted. There were 3 versions of this boat built with the Marieholm being the middle one. The Folkboat website shows this: loa 25.83, lwl 19.83, beam 7.17, s.a. 280 sq. ft., draft 4′, disp. 4740, ballast 2750. The 1st model was built from wood, the last (3rd) model is called the Nordic Folkboat built from fiberglas but made with lapstrack design to look like wood. It was heavier in weight than the other 2 with less s.a.. Google “Folkboats Around the World” and the info is there on the main page. Hope this helps. Like to see values once new info is inserted. Wish I could figure it myself but not sure how to. Thank you, Sam

Thanks for catching that. I’ll correct it on the next update. — Tom

The Goletta Oceanica De Biot 39 is missing a decimal point in the LWL so it is throwing off all of the calculations.

David, There’s no simple answer to that. If you enjoy sailing the boat, it’s a good one. When you put the numbers into SailCalculator, it will return some basic information that can be very useful, but note that small, lightweight boats like the American 23 are sensitive to loading. The working displacement is actually the “Light Ship” displacement plus the weight of the average crew. Try adding the weights of you and your crew in SailCalculator and see how that affects the performance numbers. The people I have known who have the American 23 like it. It looks like a nice, stable daysailer. Enjoy! — Tom

I have American sailboat 23 ft. sailboat with a displacement 3500 lbs my keel is a 1000 lbs with a beam 7ft and 11 inch just wondering how good is this boat for sailing thanks

Mark, Very interesting. I can see why the Length/Beam ratio at the waterline would be the defining characteristic for hull speed. That can be an evasive number, I think. Multis with very narrow hulls will sink deeper into the water quickly as the boat is loaded, so the LWL/BWL could change dramatically. It seems that you’d have to be careful about specifying the displacement that produces a specific LWL/BWL ratio, don’t you think? Is there an issue of one hull being submerged more than the other when the boat is under sail? This seems especially important in trimarans, which often have one hull flying and the other deeply submerged, but a long, narrow cat would have some of the same response to a breeze. Keep me posted on your thoughts. I think you’ve hit on a key element here. — Tom

Hello, I’m a mechanical engineer and experienced multihull sailor that has long thought multihulls need a better performance parameter for comparison so sales guys can’t hoodwink people! I have some graduate school education from Dr. Marshall Tulin (UCSB) who has published many works regarding high-speed displacement mode for long slender hulls for naval/military applications and I think this work is very applicable to sailing multihulls. The critical parameter as far as hull drag for catamarans is really L/B at the waterline since other parameters as far as hull form go (prismatic coefficient) are generally within a narrow range. It has the benefit of implying displacement and waterline length as well, since a heavy boat must be either fat, or long to carry the displacement. As a result, I’ve been working on a parameter that includes both sail area and L/B at the waterline for performance comparisons. The trouble is Schionning is one of the few designers that cites L/B in all of his designs but it would be an easy measurement to take dockside, when the true displacement isn’t known.

Steve, I’ve never seen that formula but would love to have it. The speed of a multihull is largely a factor of the hull shapes, and most multis are not limited by the “Displacement Hull Speed” that determines the maximum speed of most monohulls. The hulls are generally long and narrow and do not create the speed-limiting waves. There are exceptions, and I think any formula that predicts the speed of a cat or tri would have to incorporate prismatic coefficient (“sharpness”). Most boats are not speed-limited by their sail area.

I’m looking for a formula that predicts potential performance of a cruising catamaran, in teh same way that SA/D does for monohulls. I saw teh formula years ago – it uses sail area and the second power (i.e., the square) of a factor, but I don’t recall anything else. Can you help me? -Steve

Charlie, Thank you for the compliment. I enjoy running the site and meeting so many people who love sailing. Good luck on your boat search; there are many good deals on used, mid-size cruising boats available now in the U.S. because builders flooded the market with 40-footers a few years ago. Now that so many Baby Boomers have finished their lifetime sailing adventures, the boats are for sale.

I’ve just been introduced to your site by a good friend from the US. Im looking for a retirement live aboard that can take me around the world. He gave me a potted history and speaks very highly of Carl Alder in this site in general. What a great tool. I’ll be flying to the states to view some boats that otherwise wouldn’t have even been on my Radar. Thank you Tom, Thank you Carl (Thank you Harvey).

Thanks for keeping Carl’s program alive, Tom. I sent him hundreds of small boat specs over the years and found quite a few errors from other inputs that Carl tried to correct. Between his poor vision, a lot of incorrect input (especially the difference between LOD versus LOA for most people) and the vague info from boat builders it was a long process. People should have supported him with far more donations, he was a good guy. Les Hall, San Antonio

Thanks for catching that, Paul. Yes, that would be a mighty powerful boat. It appears that the displacement should have been 14,500, so I corrected that. The SA/D ratio still looks a bit high, but I don’t know what the submitter used as a source. Enjoy the site and please send any other corrections you see. — Tom

Cavalier 37, LWL=30, Sail Area to Displacement=2314.05 Cant possibly be correct Great calculator, thanks for keeping it available. Cheers

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Displacement-Length Ratio of a Yacht: Skipper´s Basics

• April 27th, 2018
• Yachtmaster

When sailors are talking about their boats they often refer to ratios and numbers. That´s a tendency in human behaviour to try to generalize things to make them comparable. Of course, everybody knows that you cannot really describe apple to pears and so it´s worthless to describe a – let´s say – Seventies IOR-era King´s Cruiser 33 like mine to a modern day cruising yacht but we nevertheless tend to do so.

Why? I guess that´s mostly because of the boating industry and their media assets trying to sell more and more newer products to the sailors, as it is done with all products on all markets. And in order to “explain” why a new boat is definitely better than the old one, you need kind of objective figures to compare what´s otherwise incomparable. These numbers are called “non dimensional” figures as they do not depend on subjective and individual design features of a boat or a hull. The just compare two features, reducing them to light chunks which can be viewed and understood with ease. Like the D/L-ratio.

What does the D/L-ratio tell?

The Displacement-Length-Ratio in general is a non-dimensional number. It sets into relation the displacement of a boat (expressed in pounds) to the length of her waterline (in feet). So, in general, this ratio is looking for the relation between the (heavy?) volume of water being pushed aside by a boat´s hull and the length (and therefore speed potential – see for my article “Hull speed vs. Froude number” here ) of her hull. Sounds fair enough?

The formula is as easy as ABC: Displacement (pounds) divided by 2.240 and then divided by the length of the waterline in feet cubed multiplied by 0,01. There are numerous online DLR-calculators available on the net, just do a quick research in the search engine of your choice. So, in the end this figure can be calculated for every hull afloat and as it is non-dimensional it makes comparable what wasn´t comparable at all: You can now set a Chinese Junk into relation with a high-tech Ocean Racer if you want. But, let´s not doom this calculation as it really offers some nice hints.

Generating and interpreting the D/L-ratio for your boat

First of all, the D/L-ratio of your boat can be set into relation with a general accepted comparison chart allowing a classification of your boat. For example, my dream yachts, the Cigale 16 (read more on this great boat here ) and the Oyster 745 . Both boats, after calculating their D/L-ratios deliver the following numbers: D/LR of the Cigale 16 is 98, the displacement-length-ratio of the Oyster 745 is 193. Looking at the chart now:

We will notice, that the aluminium made Cigale 16 is “light displacement” boat (although advertised as ULDB) and that the Oyster bluewater cruising boat may be classified as a “moderate displacement” boat although widely considered a heavy displacement cruiser. Well, that diversions could have their roots in the numbers you put into the calculation, like the sail area which always should be the mainsail plus a 100% jib. But there are seldom boats equipped with a 100% jib – like the Oyster, where the website states only numbers with a 150% fore sail. For the Cigale 16 the website inly states “upwind sail area” without any further specification. Anyway: Looking at the numbers and the shapes of the hulls you will instantly see the meaning of the D/L-ration by your own eyes: Low number means lighter, high number means heavier.

The lower – the better?

So, the sporty sailor might now be compelled to ask for a boat with the lowest D/L-ratio possible. But this wouldn´t be a wise decision. As pro-sailor Tim Kroeger told me when we were talking about the SA/D-ratio (read about it here ), such a number gives but a slight impression on the real performance and behaviour of a boat. One should not compare boats by anonymised numbers and ratios. Yes, lower means lighter means faster. But have you ever sailed on a Pogo? I have (read it here , here and here ) and it´s great fun of course. But this boat is a mess when it comes to sailing comfort. She is hard bouncing off the water (whilst planning) and kicks your ass constantly. Nothing for a longer cruise. In this case, a higher number with a more seakind behaviour in the waves is much appreciated.

As you know – a boat is always a compromise. Speed is always sacrificed for comfort. Fast sailing always means a considerable concession to sailing quality, seakind motion of the boat, tiring hard bounces, roughest movements in waves (especially in foul weather with much swell). On the other hand, a comforting, relaxing, pleasant movement of a boat (through a V-shaped hull) can only be achieved by a higher displacement and a hull-shape which naturally cannot plane anymore: The boat will be slower. But ask yourself: Do you want to be quickly flying over the waves in a short dash or do you want to sail for days, weeks, months or even years enjoying the world´s oceans – no matter if this is done in 8-knots or 8.5 knots?

By the way, my own boat, the King´s Cruiser 33 has a D/L-ratio of 258. Very pleasant …

Also interesting reads on Skipper´s Basics:

What´s the Sail Area-Displacement Ratio ?

What makes a Yacht seaworthy ?

Hull Speed calculation.

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The Sailboats Calculators below will enable you to calculate the main Sailboat Ratios, using data that you can retrieve from the Boat table or your own data.

We will be adding more calculators along the way and more in-depth explanations of how they work and what they can help you with., hopefully you will enjoy them and find them useful to search or understand the characteristics of your or any given sailboat ..

SA/D range of values

16 to 18 Heavy offshore cruisers 18 to 22 Medium cruisers 22 to 26 Inshore cruisers, racing boats 26 to 30+ Extreme racing boats

Ballast/Displacement:

A Ballast/Displacement ratio of 40 or more translates into a stiffer, more powerful boat that will be better able to stand up to the wind.

Displacement/Length:

The lower a boat’s Displacement/Length (LWL) ratio, the less power it takes to drive the boat to its nominal hull speed.

less than 100 = Ultralight;

100-200 = Light;

200-275 = Moderate;

275-350 = Heavy;

350+ = Ultraheavy;

Comfort Ratio:

This is a ratio created by Ted Brewer as a measure of motion comfort. It provides a reasonable comparison between yachts of similar size and type. It is based on the fact that the faster the motion the more upsetting it is to the average person. Consider, though, that the typical summertime coastal cruiser will rarely encounter the wind and seas that an ocean going yacht will meet.

Numbers below 20 indicate a lightweight racing boat;

20 to 30 indicates a coastal cruiser;

30 to 40 indicates a moderate bluewater cruising boat;

40 to 50 indicates a heavy bluewater boat ;

over 50 indicates an extremely heavy bluewater boat.

Comfort ratio = D ÷ (.65 x (.7 LWL + .3 LOA) x Beam^1.33), where displacement is expressed in pounds, and length is expressed in feet.

Capsize Screening Formula (CSF):

Designed to determine if a boat has blue water capability. The CSF compares beam with displacement since excess beam contributes to capsize and heavy displacement reduces capsize vulnerability. The boat is better suited for ocean passages (vs coastal cruising) if the result of the calculation is 2.0 or less. The lower the better.

Hull Speed Calculator

Hull speed calculator is a simple calculator that determines a vessel’s hull speed based on the length of the vessel’s waterline.

Boat Speed Calculator

The boat speed calculator calculates the top speed of a boat based on the boat’s power and her displacement. If you try to understand how fast a boat can go, this calculator will help you answer that. The boat speed calculator utilizes a constant known as Crouch constant which differs based on the type of the boat.  

FOR MULTIHULLS ONLY:

Bn – bruce number:.

The Bruce Number is a power-to-weight ratio for relative speed potential for comparing two or more boats. It takes into consideration the displacement and sail area of main and jib. 100% fore-triangle only, no overlapping sails.

Chris White, “The Cruising Multihull”, (International Marine, Camden, Maine, 1997), states that a boat with a BN of less than 1.3 will be slow in light winds. A boat with a BN of 1.6 or greater is a boat that will be reefed often in offshore cruising.

Derek Harvey, “Multihulls for Cruising and Racing”, International Marine, Camden, Maine, 1991, states that a BN of 1 is generally accepted as the dividing line between so-called slow and fast multihulls.

BN = SA^0.5/(Disp. in pounds)^.333

Kelsall Sailing Performance (KSP):

Another measure of relative speed potential of a boat. It takes into consideration “reported” sail area, displacement and length at waterline. The higher the number the faster speed prediction for the boat. A cat with a number 0.6 is likely to sail 6kts in 10kts wind, a cat with a number of 0.7 is likely to sail at 7kts in 10kts wind.

KSP = (Lwl*SA÷D)^0.5*.05

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How to Calculate the Displacement to Length Ratio of a Boat

Oct 17, 2019

less than a min

How to calculate the displacement to length ratio of your boat!

The displacement to length ratio of a boat is a good comparing parameter for most boats. It is usually referred to sailing boats and it is also seen with the symbol D/L . Basically it shows how heavy the boat is in comparison to the waterline length. The way it is calculated is through a division of the boat’s displacement measured in long tons which is 2.240, by 0.01 of the the waterline length cubed. This is a non dimensional formula because the displacement is measured in volume as cubit feet of water for example, while the length cubed is also measured in volume. As a result, what you get form a formula is a ratio and not a size in any measurement. All in all this parameter makes it possible to compare how heavy boats are in the water, for their given length.

Based on the displacement to length ratio, boats are categorised as ultra-light, light, moderate, heavy and ultra-heavy. Ultralight boats are the ones that reach a ratio of up to 90. The light boats can reach a ratio from 90 to 180. In addition , the moderate boats are categorised from 180 to 270. The heavy boats are the ones with a ratio of 270 to 360 while the ultra-heavy boats are the ones with a ratio of 360 and higher.

The importance of a displacement to length ratio

All the numbers mentioned in the previous paragraph relate to the displacement to length ratio and are used to compare boats in terms of heaviness and speed. What it means is that if a boat is light compared to the waterline length, is able to achieve a higher speed. This comes as a result of wave making drag. Wave making drag is lower if there is less water to be pushed aside. Speed however cannot be measured and compared through the displacement to length ratio alone. The shape of the hull also is an important factor to take into consideration.

In addition , having a small displacement to length ratio does not mean is the best option for a boat. It is just part of the package. As a rule of thumb, a lower displacement to length ratio means that the boat can become less comfortable when it is out in open sea and the sea has heavy waves. In addition, a boat with a small displacement ratio can be overloaded more easily.

All in all , the displacement ratio is an important parameter to keep into consideration when looking for a boat. However it can become misleading when not seen as part of the package, which is why you need to make sure you put the rest of the parameters such as the ballast ratio and the engine power as comparison points. You can use TheBoatDB to make the comparison process easier by simply putting the parameters you are looking into. Contact us for more information!

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