What power means
Power is how quickly energy is used or work is done. Lifting a box onto a shelf takes the same work whether you do it slowly or quickly, but doing it in half the time takes twice the power. The SI unit is the watt: one joule per second.
There are two everyday ways to calculate it. If you know the total energy and the time, divide. If something is being pushed or pulled along at a steady speed, multiply the force by the speed.
The formula
P = F × v F = P ÷ v v = P ÷ F
1 hp = 745.7 W 1 kWh = 3,600,000 J
Use joules, seconds, newtons and meters per second to get watts. 1 km/h = 1 ÷ 3.6 m/s, 1 mph = 0.44704 m/s and 1 lbf = 4.448222 N.
Example: 30 kJ of work in one minute
An electric winch does 30 kJ of work in 1 minute (the default values).
| Step | Result |
|---|---|
| Convert: 30 kJ = 30,000 J, 1 min = 60 s | |
| P = 30,000 ÷ 60 | 500 W (0.5 kW) |
| In horsepower: 500 ÷ 745.7 | 0.6705 hp |
| Energy if it ran for an hour: 0.5 kW × 1 h | 0.5 kWh |
Example: force and speed
A car needs about 500 N of force to overcome air drag and rolling resistance at a steady 100 km/h. Switch the formula to force and speed to see this one.
| Step | Result |
|---|---|
| Speed in m/s: 100 ÷ 3.6 | 27.78 m/s |
| P = 500 × 27.78 | 13,889 W (13.89 kW) |
| In horsepower: 13,889 ÷ 745.7 | 18.63 hp |
Real cars have much bigger engines than this because they need extra power to accelerate and climb hills.
Common mistakes
- Confusing kW and kWh. kW is power (a rate); kWh is energy (an amount). A 2 kW heater uses 2 kWh each hour.
- Leaving time in minutes or hours. Joules per minute aren't watts. Convert time to seconds first.
- Mixing horsepower types. Mechanical hp (745.7 W) and metric PS (735.5 W) differ by about 1.4%.
- Using P = F × v for accelerating objects. It gives the power at that instant. If the speed is changing, the power changes too.
Frequently asked questions
What is the formula for power?
Power is the rate of doing work: P = W ÷ t, energy in joules divided by time in seconds, giving watts. For something moving at a steady speed against a force, P = F × v, force in newtons times speed in meters per second.
How many watts is one horsepower?
One mechanical (imperial) horsepower is 745.7 watts, so 1 kW is about 1.341 hp. Metric horsepower (PS), used in some European car specs, is slightly smaller at about 735.5 W.
What is the difference between power and energy?
Energy is the total amount of work done, in joules or kilowatt-hours. Power is how fast it's done, in watts. A 100 W bulb left on for 10 hours uses 1 kWh of energy; a 1,000 W heater uses the same 1 kWh in just one hour.
Where does P = F × v come from?
Work is force times distance, and power is work per unit time. So P = F × d ÷ t, and distance divided by time is speed, giving P = F × v. It's handy for vehicles: the engine power needed at a steady speed equals the drag and rolling resistance times the speed.
How much power can a person produce?
A fit adult can sustain around 100 to 250 W on a bike for an hour, and trained cyclists more. Short sprints can reach well over 1,000 W for a few seconds, which is more than 1 horsepower.
Rates and figures last checked October 2026.
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