How this calculator works
Crouch formula is an empirical planing-hull rule, not a fluid-dynamics simulation. It relates top speed to shaft horsepower and displacement through a constant that describes how efficiently a hull type converts power into speed. Light, fast hulls carry a higher constant; heavy cruisers and passenger vessels carry a lower one. The original relation works in knots, pounds and shaft horsepower, so the calculator converts metric entries before applying it. Propeller selection, hull condition, sea state and loading can all move the real speed away from the estimate.
Formula
S(kn) = C x sqrt(P(hp) / D(lb)). Solve for power as P = D(lb) x (S(kn) / C)^2, and for displacement as D = P(hp) x (C / S(kn))^2. 1 kn = 1.852 km/h, 1 lb = 0.45359237 kg and 1 hp = 745.6999 W.
Worked example
A 2,000 kg planing cruiser with 150 kW of shaft power has 4,409 lb and 201 hp. For an average runabout constant of 150 the speed is 150 x sqrt(201 / 4,409) = 32.0 kn, which is 59.3 km/h or 36.9 mph.
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Frequently asked questions
What does the Crouch constant mean?
It bundles hull form, propeller efficiency and the weight distribution of a class of boats. 150 suits average planing runabouts and cruisers, while racing hulls reach 210 to 250. Use a custom value only when you have a measured speed from a similar boat.
Does this work for displacement hulls?
No. Crouch formula describes planing hulls. A displacement hull is limited by hull speed, roughly 1.34 x the square root of the waterline length in feet, and needs a different method.
Is shaft horsepower the same as engine horsepower?
No. Shaft power is what reaches the propeller after gearbox losses. If you only know engine output, reduce it by the gearbox and shaft efficiency, typically a few percent.
Why is my measured speed lower in rough water?
The formula assumes calm water, a clean bottom and an efficient propeller. Waves, wind, fouling and an overloaded boat all reduce speed at the same power.