Calculate a sailboat’s sail area to displacement ratio (SA/D) from sail area in ft² or m² and displacement in lb or kg, or solve for either one.
Sail Area to Displacement Ratio Formula
SA/D = sail area (ft²) ÷ [displacement (lb) ÷ 64](2/3).
Why the Ratio Uses a Two-Thirds Power
Displacement in pounds is divided by the conventional 64 lb/ft³ seawater basis to express displacement volume in cubic feet. Raising that volume to the two-thirds power gives a square-foot quantity, which can be compared with sail area. The resulting ratio is dimensionless. The model uses the fraction 2/3 rather than the rounded 0.666 sometimes printed in abbreviated formulas. Fractional roots and displayed results are numerical approximations.
Select Consistent Inputs
Enter the sail area for the sail plan and measurement convention you want to compare. A working-sail area, an area based on the foretriangle, and an area including light-air sails are not interchangeable definitions. Use a consistent loaded displacement as well. Crew, stores, water, fuel, and equipment can make sailing displacement different from an empty or brochure specification. Keep those definitions aligned across boats and scenarios.
Solving for Sail Area or Displacement
For a chosen ratio R, required arithmetic sail area is R × (D/64)(2/3). For known area A and ratio R, displacement is 64 × (A/R)(3/2). These are rearrangements of the same comparison, not an instruction to change the rig or ballast. All three quantities must be positive; zero or negative entries do not define a useful inverse relationship.
Worked Example
With 400 ft² of sail area and 8,000 lb displacement, the displacement volume is 8,000 ÷ 64 = 125 ft³. The two-thirds power of 125 is 25, so SA/D = 400 ÷ 25 = 16. Keeping displacement at 8,000 lb and choosing a ratio of 18 gives 450 ft². Keeping area at 400 ft² and choosing 16 returns the original 8,000 lb displacement.
What Added Load Changes
At the same sail area, adding displacement reduces the ratio. The result card shows the ratio after a 10% displacement increase. In the 400 ft² and 8,000 lb example, the new displacement is 8,800 lb and the ratio is about 15.015. That is an algebraic sensitivity comparison. It does not account for changes in trim, wetted area, stability, or the ability to carry the selected sail plan.
Unit Conversions and the Density Convention
Square meters are converted using exactly 0.09290304 m² per square foot. Kilograms use exactly 0.45359237 kg per pound. The tonne option means a metric tonne of 1,000 kg, not a US short ton or an imperial long ton. All inputs then use the same fixed 64 lb/ft³ calculation, so switching unit choices preserves the conventional ratio. This is not a variable-density hydrostatics model for different salinity or temperature.
Interpret the Ratio with the Boat’s Design
A higher ratio indicates more sail area relative to displacement under the selected conventions. It does not, by itself, establish speed, acceleration, light-air ability, stability, or seaworthiness. Hull form, rig efficiency, righting moment, crew, and conditions all affect actual performance. Published comparison bands are broad conventions and can be misleading when applied to dissimilar designs or mixed sail-area definitions. Use the computed ratio as one consistent comparison, alongside the boat’s other information.
Reference Table
| Sail area (ft²) | Displacement (lb) | SA/D ratio |
|---|---|---|
| 400 | 8,000 | 16.000 |
| 450 | 8,000 | 18.000 |
| 400 | 8,800 | 15.015 |
| 800 | 8,000 | 32.000 |
Sources
PHRF Southern California, Calculated Performance Parameters (SA/D formula); Kasten Marine Design, Sail Area Ratios (sail-area definitions and comparison limitations).
