Displacement-Length Ratio Calculator
The displacement-length ratio is a long-standing yardstick for how heavy a boat is relative to its waterline length. By dividing displacement in long tons by the cube of one one-hundredth of the waterline length in feet, it produces a dimensionless number that compares fairly across sizes. Light, easily driven hulls score low, while heavy, full-bodied cruisers score high. This calculator converts displacement in pounds to long tons, cubes the scaled waterline length, and returns the ratio along with an indicative band. Use the waterline length, not the overall length, since waterline length governs how the hull moves through the water.
Displacement-length formula
Displacement (long tons) = displacement (lb) / 2240
Scaled length = 0.01 * waterline length (ft)
Displacement-length ratio = displacement (long tons) / (scaled length ^ 3)
A long ton is 2,240 pounds. Cubing the scaled waterline length makes the ratio dimensionless and comparable across boats of different sizes.
Interpreting the ratio
- Below 100 indicates an ultralight, easily driven racing hull.
- Roughly 100 to 200 indicates a light cruiser or performance design.
- Roughly 200 to 300 indicates a moderate cruising displacement.
- Above 300 indicates a heavy traditional or long-distance cruiser.
- Always use waterline length, not overall length, for this ratio.
Displacement-length ratio: frequently asked questions
What is the displacement-length ratio?
The displacement-length ratio expresses how heavy a boat is for its waterline length, in a dimensionless form. It equals the displacement in long tons divided by one one-hundredth of the waterline length in feet, cubed. A low value indicates a light, easily driven hull; a high value indicates a heavy, full-bodied hull.
How is the ratio calculated?
Convert displacement in pounds to long tons by dividing by 2,240. Take the waterline length in feet, multiply by 0.01, and cube the result. Divide the displacement in long tons by that cubed length. The cubing of length makes the comparison fair between boats of very different sizes.
What is a long ton?
A long ton is 2,240 pounds, the traditional British ton used in the original definition of this ratio. It differs from the US short ton of 2,000 pounds and the metric tonne of about 2,205 pounds. The ratio is defined with long tons, so this calculator divides displacement in pounds by 2,240.
What do typical values mean?
As a rough guide, ultralight racing hulls fall below 100, light cruisers around 100 to 200, moderate cruisers 200 to 300, and heavy traditional or long-distance cruisers above 300. These bands are approximate; hull shape, beam, and intended use all matter alongside the single number.
Why use waterline length rather than overall length?
The waterline length is what governs a displacement hull's wave-making and how much water it must push aside, so it is the meaningful length for weight comparisons. Overall length includes overhangs that do not contribute when the boat sits at rest, so the ratio always uses the waterline length.
Official sources
- NIST Digital Library of Mathematical Functions: powers and roots.
- U.S. Coast Guard Navigation Center: vessel and navigation references.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.