Free Power Calculator
Calculate mechanical power in watts and horsepower from either work and time (P = W/t) or force and velocity (P = F·v), with the arithmetic shown.
Choose a method, then enter values to compute power. P = W / t or P = F · v.
Power is the rate of doing work: 1 watt = 1 joule per second. Horsepower uses 1 hp = 745.7 W (mechanical). Use SI units throughout: joules, seconds, newtons and m/s.
Quick answer
Mechanical power is the rate of doing work: P = W / t, where W is work in joules and t is time in seconds. For example, 1000 J of work done in 10 s gives P = 1000 / 10 = 100 watts. When motion is steady, you can equivalently use P = F·v (force times velocity); 100 W also equals about 0.134 horsepower since 1 hp = 745.7 W.
Formula & method
Power from work and time
P = W / t
- P — Power (watts, W)
- W — Work or energy transferred (joules, J)
- t — Time interval (seconds, s)
P is power in watts (W), W is work or energy transferred in joules (J), and t is the time in seconds (s). One watt equals one joule per second.
Power from force and velocity
P = F · v
- F — Force in the direction of motion (newtons, N)
- v — Velocity (metres per second, m/s)
For an object moving at constant velocity in the direction of the force, instantaneous power equals force (newtons) times speed (metres per second). F·v in N·m/s is identical to J/s, so the result is again in watts.
Watts to horsepower
hp = P / 745.7
Converts mechanical (imperial) horsepower. 1 hp = 745.7 W (the value used here). The metric horsepower, 1 PS = 735.5 W, differs slightly.
Examples
- Input
- W = 1000 J, t = 10 s
- Result
- P = 100 W ≈ 0.1341 hp
- Why
- P = W / t = 1000 J ÷ 10 s = 100 W. In horsepower: 100 ÷ 745.7 = 0.1341 hp. This is the calculator's default case.
- Input
- W = 90,000 J, t = 60 s
- Result
- P = 1500 W ≈ 2.0115 hp
- Why
- P = 90,000 J ÷ 60 s = 1500 W. Converting: 1500 ÷ 745.7 = 2.0115 hp. So a motor doing 90 kJ of work each minute is a roughly 2 hp motor.
- Input
- F = 600 N, v = 25 m/s
- Result
- P = 15,000 W = 15 kW ≈ 20.1153 hp
- Why
- P = F · v = 600 N × 25 m/s = 15,000 W (15 kW). In horsepower: 15,000 ÷ 745.7 = 20.1153 hp. This is the engine power needed just to overcome a 600 N resistive force at 90 km/h (25 m/s).
- Input
- F = 40 N, v = 7.5 m/s
- Result
- P = 300 W ≈ 0.4023 hp
- Why
- P = F · v = 40 N × 7.5 m/s = 300 W. In horsepower: 300 ÷ 745.7 = 0.4023 hp. A sustained 300 W output is roughly the level of a fit competitive cyclist.
When to use this tool
- Finding the power output of a motor, engine, pump, or person from the work done over a measured time.
- Estimating the steady power needed to move a vehicle or object against a constant resistive force at a known cruising speed (P = F·v).
- Converting a mechanical power figure between watts, kilowatts, and horsepower.
- Checking physics homework or lab results where you need power from energy and elapsed time.
Common mistakes
- Dividing by zero time. Power is undefined when t = 0 s because no duration means no rate; enter a positive, non-zero time.
- Mixing up energy and power. Joules (J) measure total work done; watts (W = J/s) measure how fast it is done. A 100 W device run for 10 s does 1000 J of work, not 100 J.
- Using non-SI units without converting. The formula P = W/t needs joules and seconds, and P = F·v needs newtons and metres per second. Convert kJ→J (×1000), minutes→seconds (×60), and km/h→m/s (÷3.6) first.
- Confusing the two horsepower definitions. This tool uses mechanical horsepower (1 hp = 745.7 W); metric horsepower (PS) is 735.5 W, so the same wattage gives a slightly different hp number.
Frequently asked questions
What is the formula for power?
Power is the rate of doing work: P = W / t, where W is the work or energy in joules and t is the time in seconds, giving power in watts. When an object moves at a steady speed under a force, you can instead use P = F · v (force in newtons times velocity in m/s), which gives the same watts.
How do I convert watts to horsepower?
Divide the power in watts by 745.7. For example, 1000 W ÷ 745.7 = 1.341 hp. This tool reports mechanical (imperial) horsepower, where 1 hp = 745.7 W. If you need metric horsepower (PS), divide by 735.5 instead.
What is the difference between work and power?
Work (in joules) is the total energy transferred when a force moves something. Power (in watts) is how quickly that work is done — joules per second. Doing the same 1000 J in 1 second is ten times more powerful (1000 W) than doing it in 10 seconds (100 W).
When can I use P = F·v instead of P = W/t?
Use P = F · v when an object moves at (roughly) constant velocity and the force acts along the direction of motion — for example a car cruising at a steady speed or a conveyor moving at fixed speed. It gives the instantaneous power. Both formulas agree because force × distance = work, and distance ÷ time = velocity.
Why does the calculator block a time of zero?
Power P = W/t requires dividing by the time, and division by zero is mathematically undefined — a process that takes no time would imply infinite power. Enter any positive time greater than zero (even a small fraction of a second) to get a valid result.
What units does this power calculator use?
It uses SI units: work in joules (J), time in seconds (s), force in newtons (N), and velocity in metres per second (m/s). The output is in watts (W) and is also converted to kilowatts and mechanical horsepower. Convert other units to SI before entering them.
Sources & references
External references open in a new tab. We are independent and not affiliated with these organizations.
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