What this calculator does
Power in physics is the rate at which work is done or energy is transferred. The two most common ways to calculate it are from work and time (power equals work divided by time) or from force and velocity (power equals force multiplied by velocity), and both describe the same underlying quantity from different starting information.
The two formulas are really the same relationship viewed differently: work is force applied over a distance, and dividing that distance by time gives velocity, so P = W/t and P = F×v arrive at the same answer whenever they describe the same situation. Which one to use just depends on which numbers you already have.
The formula
For the work-and-time form, divide the total work done, in joules, by the time taken, in seconds, to get power in watts. For the force-and-velocity form, multiply the applied force, in newtons, by the velocity in the direction of that force, in metres per second. Both give the same unit, the watt, which this calculator also converts to kilowatts and horsepower.
| Term | Meaning |
|---|---|
| P | Power, the rate of doing work or transferring energy, in watts (joules per second). |
| W | Work done, in joules. |
| t | Time taken to do that work, in seconds. |
| F | Force applied, in newtons. |
| v | Velocity in the direction of the applied force, in metres per second. |
The inputs explained
| Field | What to enter |
|---|---|
| Calculate from | Choose whether you know work and time, or force and velocity. |
| Work done (J) | The total work done or energy transferred, in joules. |
| Time taken (s) | The time taken to do that work, in seconds. |
| Force applied (N) | The force being applied, in newtons. |
| Velocity (m/s) | The velocity in the direction that force is acting, in metres per second. |
When to use it
Rating a motor or engine from a work task
Knowing how much work a motor needs to complete and in how much time gives the minimum power rating it needs, before any efficiency losses are added.
Estimating power output while cycling or running
A steady force pushing a bike or a load, multiplied by the speed it moves at, gives the mechanical power being delivered, the same approach used behind cycling power meters.
Comparing power to horsepower ratings
Older or automotive specifications are often quoted in horsepower rather than watts; converting a computed power figure into horsepower puts it on the same footing as an engine spec sheet.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How power changes with time at a fixed amount of work
The same 5,000 joules of work, completed over a range of times.
How power changes with velocity at a fixed force
A steady 250 N of force, applied at a range of velocities.
Questions
What is the difference between power and work?
Work (or energy) is the total amount transferred, measured in joules, with no reference to how quickly it happened. Power is the rate at which that transfer occurs, in watts, so the same work done faster means a higher power.
Why do P = W/t and P = F×v give the same answer?
Work equals force multiplied by the distance moved in the direction of that force. Dividing that distance by the time taken gives velocity, so substituting distance ÷ time for velocity turns F×v back into (F×distance)÷t, which is exactly W/t.
How does this relate to torque and rotational power?
For a rotating shaft, power is torque multiplied by angular velocity rather than force multiplied by linear velocity; see the torque and rotational power calculator for that version of the same idea.
How many watts is one horsepower?
One mechanical horsepower is 745.7 watts. A result in watts from either formula here is divided by that figure to give the equivalent horsepower.
For power delivered through a rotating shaft rather than in a straight line, see the torque and rotational power calculator. To relate a power output to body or vehicle weight, see the power-to-weight ratio calculator.