How this calculator works
As a displacement boat moves, it creates a bow wave and a stern wave. At a certain speed the wavelength matches the waterline length and the boat is effectively trapped between its own waves, so pushing harder mostly makes a bigger wave rather than more speed. That speed is called hull speed. It rises with the square root of the waterline length: double the length and the hull speed increases by about 41 percent. The common constant is 1.34 knots times the square root of the waterline length in feet, which is equivalent to 2.43 knots times the square root of the length in metres.
Formula
Hull speed in knots = 1.34 x square root(waterline length in feet), or 2.43 x square root(waterline length in metres). Waterline length in metres = (hull speed in knots / 2.43)^2. Speed in km/h = knots x 1.852.
Worked example
A 10 m waterline gives 2.43 x square root(10) = 2.43 x 3.162 = 7.68 knots, which is 14.2 km/h. A 30 ft waterline gives 1.34 x square root(30) = 1.34 x 5.477 = 7.34 knots. Working back, a target of 10 knots needs a waterline of (10 / 2.43)^2 = 16.9 m.
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Frequently asked questions
Can a boat go faster than hull speed?
Yes, if it can plane or if it has enough power to climb its own bow wave. Light dinghies, catamarans and powerboats routinely exceed the displacement hull speed. The limit applies to boats that stay supported by buoyancy rather than dynamic lift.
Which length should I use?
Use the waterline length, not the overall length. A long overhang or a bowsprit does not contribute to the wave-making length. Measure where the hull meets the water when the boat is loaded normally.
Why do some references use 1.34 and others 1.51?
The constant depends on the hull form and the Froude number chosen as the limit. 1.34 is the traditional displacement-hull figure. Faster hull forms, such as slender catamarans, can sustain a higher value.
Does hull speed apply to a kayak or a canoe?
Yes, in principle, but these craft are short and light enough that paddlers often exceed the displacement limit for short bursts. The formula still gives a useful estimate of the sustainable cruising speed.