Enter the hull coefficient (C) and any two of the following—speed, horsepower, or displacement—into the calculator to estimate the missing variable. This is not a direct unit conversion from horsepower to knots; it is an empirical speed estimate that depends strongly on hull form, propeller/drive efficiency, and conditions.
- 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 following formula is used to estimate speed in knots from horsepower and displacement using an empirical hull coefficient (C). Because hull resistance and propulsion efficiency vary widely, you must choose (or calibrate) C for your boat to get meaningful results.
S = C * (HP / D)^{1/3}Variables:
- S is the speed in knots
- HP is the horsepower (mechanical hp)
- 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 uses a simple cube‑root power-to-weight model with a user-supplied coefficient (C).
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.
- Choose or calibrate the hull coefficient (C) for your boat (for best results, compute C from a known speed point).
- Determine the horsepower (HP) of the vessel (and whether it is given in HP or kW).
- Determine the displacement (D) of the vessel (in lb or kg).
- Calculate the speed estimate using S = C × (HP / D)^{1/3}.
- 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} ≈ 20.10 knots