Calculate estimated boat speed in knots, MPH, or km/h from horsepower, displacement, and a hull coefficient, or solve for power, weight, or coefficient.
- All Unit Converters
- CC to HP Calculator
- WHP to HP Calculator
- HP to Amps Calculator
- HP to Torque Calculator
- HP to Joules Calculator
- HP to kg Calculator
- HP to GPH Calculator
HP to Knots Formula
The calculator offers two empirical models. For a planing hull, the Crouch estimate is V(kn) = C × √[shaft hp / loaded weight (lb)]. The broad preset coefficients 150, 190, 210, 220 and 230 use this knots convention, as described by naval architect Eric Sponberg. Calibrate C from comparable measured performance where possible. The separate cube-root model below also requires its own calibrated coefficient.
Variables:
- S is the speed in knots
- HP is the total shaft power in mechanical horsepower, measured on the same basis as the coefficient calibration
- D is the displacement (boat weight) in pounds
- C is an empirical hull/efficiency coefficient (calibrate from known performance when possible)
To estimate the speed in knots, divide the horsepower by the displacement in pounds, take the cube root of the result, and multiply by the hull coefficient C.
Note: The constant 1.34 is commonly used in a different rule of thumb for displacement-hull “hull speed”: Hull speed (kn) ≈ 1.34 × √(LWL in feet). That hull-speed rule depends on waterline length, not horsepower and displacement.
| Knots (kn) | Miles per hour (mph) | Kilometres per hour (km/h) |
|---|---|---|
| 1 | 1.151 | 1.852 |
| 2 | 2.302 | 3.704 |
| 3 | 3.452 | 5.556 |
| 4 | 4.603 | 7.408 |
| 5 | 5.754 | 9.260 |
| 6 | 6.905 | 11.112 |
| 7.5 | 8.631 | 13.890 |
| 8 | 9.206 | 14.816 |
| 10 | 11.508 | 18.520 |
| 12 | 13.809 | 22.224 |
| 15 | 17.262 | 27.780 |
| 18 | 20.714 | 33.336 |
| 20 | 23.016 | 37.040 |
| 25 | 28.769 | 46.300 |
| 30 | 34.523 | 55.560 |
| 35 | 40.277 | 64.820 |
| 40 | 46.031 | 74.080 |
| 45 | 51.785 | 83.340 |
| 50 | 57.539 | 92.600 |
| 60 | 69.047 | 111.120 |
| * Rounded to 3 decimals. Conversion factors: 1 kn = 1.150779 mph = 1.852 km/h. | ||
What is HP to Knots?
“HP to Knots” is commonly used to refer to estimating a boat’s speed (in knots) from its available horsepower and displacement (weight). Horsepower is not directly convertible to knots; any speed estimate must assume a relationship between power and resistance, which varies with hull type, loading, trim, sea state, and propulsive efficiency. This page offers a Crouch planing estimate and a separate cube-root power-to-weight model. Each coefficient has its own unit and power convention; neither establishes a safe speed, load capacity or guaranteed performance.
How to Calculate HP to Knots?
The following steps outline how to estimate the speed in knots from horsepower and displacement using the formula above.
- Select the model and calibrate its coefficient (C) from a known speed, shaft power and loaded weight for comparable conditions. Crouch and cube-root coefficients are not interchangeable.
- Determine total shaft power and its unit. Engine brake power requires an appropriate drivetrain-loss adjustment before using a shaft-power calibration.
- Determine the displacement (D) of the vessel (in lb or kg).
- For the cube-root option, use S(kn) = C × (HP / D)^{1/3}. For Crouch, use S(kn) = C × √(HP / D). Both formulas here use mechanical shaft hp and loaded pounds internally.
- After inserting the values and calculating the result, compare with known performance and adjust C if needed.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Hull Coefficient (C) = 70 (example value)
Horsepower (HP) = 500
Displacement in pounds (D) = 20000
Estimated Speed (S) ≈ 70 × (500 / 20000)^{1/3} ≈ 20.47 knots (illustrative cube-root coefficient, not a Crouch preset)
