Hong Life CalculatorsUnderstanding the boat speed calculator — concept and principle
How fast will a planing boat go with a given engine? Naval architects use Crouch's formula for a quick estimate from horsepower, loaded weight and a hull constant. This calculator gives the estimated top speed in mph, knots and km/h, the weight per horsepower and the power needed to reach a target speed.
How it is calculated
Speed (mph) = C × √(hp ÷ lb)
Required hp = lb × (S ÷ C)²
- hp is the power delivered at the propeller shaft; lb is the total loaded weight in pounds (kg are converted with 1 lb = 0.45359237 kg).
- C is the hull constant: about 180 for typical modern planing hulls, 190 for light efficient runabouts and 200 or more for long, narrow hulls with flat running surfaces.
- 1 mile = 1.609344 km; 1 knot = 1.852 km/h.
The principle
When a boat planes, it rides on top of the water rather than pushing through it, and the drag it must overcome grows roughly with the square of speed. Power is drag times speed, so power grows faster than speed, and the required power per pound rises roughly with speed squared in this simple model. Rearranging gives speed proportional to the square root of power per pound. The hull constant C lumps together everything else about the hull's efficiency: shape, length, running surface and propeller. It is empirical, which is why calibrating it with a known speed of your own boat improves accuracy.
Worked example
Default inputs: 3,000 lb, 150 hp, hull constant 180, target 45 mph.
- hp ÷ lb = 150 ÷ 3,000 = 0.05; √0.05 = 0.2236.
- Speed = 180 × 0.2236 = 40.2 mph.
- In other units: 35 knots, 64.8 km/h.
- Weight per horsepower = 3,000 ÷ 150 = 20 lb/hp; hull constant used = 180.
- Power for 45 mph = 3,000 × (45 ÷ 180)² = 3,000 × 0.0625 = 188 hp.
| Total boat weight, loaded | Estimated top speed (mph) |
|---|---|
| 750 | 80.5 |
| 1,500 | 56.9 |
| 2,250 | 46.5 |
| 3,000 | 40.2 |
| 3,750 | 36 |
| 4,500 | 32.9 |
| 6,000 | 28.5 |
How to read the result
The formula shows the law of diminishing returns: going 12% faster in this example needs about 25% more power. Adding weight such as passengers, fuel and gear lowers speed noticeably. Shaft horsepower is a little less than the engine's rated horsepower because of gearbox losses, so use realistic figures. The formula applies only to planing boats; displacement hulls are limited by hull speed and do not follow it.
Common mistakes
- Using dry weight instead of fully loaded weight.
- Using engine rated power when shaft power is lower.
- Applying Crouch's formula to displacement boats such as trawlers or sailboats.
- Assuming the hull constant without checking against a known speed.
Frequently asked questions
What hull constant should I use?
Start with 180 for a typical planing hull and adjust it to match a known speed.
Does doubling horsepower double speed?
No. Speed rises with the square root of power, so double power gives about 41% more speed.
Why use shaft horsepower?
Gearbox and drive losses mean less power reaches the propeller than the engine produces.
Sources: D. Gerr, The Propeller Handbook (International Marine), chapter 2 (Crouch's planing speed formula)