Newton to Horsepower Calculator
Convert force in newtons and velocity into horsepower.
Power is force times velocity. This calculator converts a force in newtons and a velocity in meters per second into power, expressed in both watts and horsepower.
Newton to Horsepower Formula
How to Use This Calculator
- Enter force in newtons.
- Enter velocity in meters per second.
- Read horsepower, with watts shown too.
Worked Example
Power = Force × Velocity
This is one of the most fundamental relationships in mechanics. A force does work as it moves something, and the rate of that work is power. Push with 5,000 newtons while moving at 20 meters per second and you're producing 100,000 watts — about 134 horsepower. The faster the same force moves, the more power is required, which is why pushing a car slowly is easy but accelerating it hard demands serious power.
Where This Applies
Force-times-velocity power shows up in tractive-effort calculations (the pulling force of a vehicle at a given speed), winch and crane design, linear actuators, and physics problems. If you know the resistance a machine overcomes and how fast it moves, this converts that directly into the horsepower needed.
Power from Force and Speed
| Force (N) | Velocity (m/s) | Power (kW) | HP |
|---|---|---|---|
| 2,000 | 10 | 20 | 26.8 |
| 5,000 | 20 | 100 | 134.1 |
| 10,000 | 15 | 150 | 201.2 |
For the marine version of the same force-to-power problem, including trolling motors rated in pounds of thrust, see thrust to HP.
Getting the Velocity Into Meters Per Second
The formula only works when force is in newtons and velocity is in meters per second. Force is usually already in newtons on a metric specification; velocity almost never is, because vehicles are quoted in km/h and conveyors in meters per minute. Converting first is where most errors enter:
| Speed | Meters per second | MPH equivalent |
|---|---|---|
| 30 km/h | 8.33 | 18.6 |
| 50 km/h | 13.89 | 31.1 |
| 80 km/h | 22.22 | 49.7 |
| 100 km/h | 27.78 | 62.1 |
| 120 km/h | 33.33 | 74.6 |
| 160 km/h | 44.44 | 99.4 |
The conversions worth committing to memory are dividing km/h by 3.6, dividing meters per minute by 60, and multiplying mph by 0.44704. A conveyor quoted at 30 meters per minute is only 0.5 m/s, and entering 30 instead would overstate the power requirement sixty-fold.
Newtons Versus Kilograms-Force
Older metric specifications and a great deal of everyday usage express force in kilograms, which is strictly incorrect — a kilogram is mass, not force. What is meant is kilograms-force, the weight of that mass under standard gravity, and the two differ by a factor of 9.80665.
| Force figure | In newtons | Common source |
|---|---|---|
| 1 kgf | 9.807 N | Older European specifications |
| 10 kgf | 98.07 N | Winch and hoist ratings |
| 100 kgf | 980.7 N | Tow ratings, cable tensions |
| 1 lbf | 4.448 N | Imperial thrust and force ratings |
| 1 tonne-force | 9,807 N | Press and lifting capacities |
Reading a kilogram-force figure as newtons understates the force nearly tenfold, and the resulting power figure will be wrong by the same factor. A specification quoting "500 kg of pull" on a winch means roughly 4,900 newtons, not 500. Where a datasheet is ambiguous, the magnitude usually resolves it — a hand winch rated in hundreds is quoting kilograms-force, while one rated in thousands is quoting newtons.
Three Cases Worked Through
The force-times-velocity relationship covers a wide range of problems that look unconnected. These three all use the identical calculation:
| Situation | Force | Velocity | Power | Horsepower |
|---|---|---|---|---|
| Belt conveyor moving product | 1,200 N | 0.5 m/s | 600 W | 0.80 HP |
| Winch recovering a vehicle | 9,800 N | 0.15 m/s | 1,470 W | 1.97 HP |
| Car overcoming drag at 100 km/h | 550 N | 27.78 m/s | 15,279 W | 20.49 HP |
The third row is worth pausing on, because it explains something about cars that surprises people. Holding 100 km/h on level ground genuinely needs only around 20 horsepower for a typical sedan. Cars carry far more because drag force rises with the square of speed, while the power to overcome it rises with the cube. Double to 200 km/h and you need roughly eight times the power, not twice. That relationship is what the kW to km/h calculator works with directly.
Steady Force Versus Accelerating a Mass
This calculator handles steady-state force at a steady velocity. Accelerating something is a different problem, and using this formula for it'll understate the power required.
When a mass accelerates, the force needed has two parts: whatever resists steady motion — friction, drag, gravity on a slope — plus the mass multiplied by the acceleration rate. A 1,500 kg vehicle accelerating at 2 m/s² needs 3,000 N for the acceleration alone, on top of the several hundred newtons of drag and rolling resistance already present. Power then rises continuously as speed builds, because the same force is being applied at ever-increasing velocity.
The practical rule is that this calculator answers "how much power to keep going at this speed", not "how much power to get up to this speed". For the second question the power-to-weight ratio calculator is the better starting point, since acceleration depends on the ratio of power to mass rather than on force at a single speed.
Frequently Asked Questions
Newtons alone can't convert to horsepower — you need velocity. Power (watts) = force × velocity, then divide watts by 745.7 for horsepower.
Because power is the rate of doing work. A force does no work, and produces no power, unless something is moving, so velocity is required.
A newton is the SI unit of force — the force needed to accelerate one kilogram at one meter per second squared. It's roughly the weight of a small apple.
Force × velocity already gives watts; divide by 1,000 for kilowatts. 100,000 W equals 100 kW.
Yes. Any force and the speed at which it acts gives power. It works for thrust, drawbar pull, or any applied force with a velocity.
Divide by 3.6 to get meters per second, so 100 km/h becomes 27.78 m/s. For a conveyor quoted in meters per minute, divide by 60 instead. Entering 30 meters per minute as 30 m/s would overstate the power sixty-fold, which is the most common error with this calculation.
No, they differ by a factor of 9.80665. One kilogram-force is 9.807 newtons, so a winch quoting 500 kg of pull means roughly 4,900 newtons. Reading kilograms-force as newtons understates the force nearly tenfold and the resulting power figure will be wrong by the same factor.
Around 20 horsepower for a typical sedan, from roughly 550 N of combined drag and rolling resistance at 27.78 m/s. Cars carry far more because drag force rises with the square of speed while the power to overcome it rises with the cube — doubling to 200 km/h needs roughly eight times the power.
No, it covers steady force at steady velocity only. Accelerating adds mass multiplied by acceleration rate on top of the steady resistance, and power then climbs continuously as speed builds. For that question, power-to-weight ratio is the better starting point.