Power is the rate at which work is done or energy changes form. Two people who climb the same staircase do the same work against gravity, but the one who gets to the top faster delivers more power. This calculator solves P = W/t for power, work (or energy) or time, and converts the answer between watts, horsepower, BTU per hour and other units.
How to use the power calculator
- Under Solve for, choose Power, Work / energy or Time.
- Enter Work or energy (W) in J, kJ, MJ, cal, kcal, Wh, kWh, BTU, ft·lbf, eV or erg.
- Enter Time (t) in seconds, milliseconds, minutes, hours or days.
- When solving for energy or time, enter Power (P) in W, kW, MW, mW, hp (mechanical), PS (metric horsepower), BTU/h, ft·lbf/s or kcal/h.
- Choose the output unit under Show the result in. The result also gives the energy used per hour in kWh and what the power could lift at 1 m/s: how many kilograms it could raise one meter every second if nothing were lost.
Power formula
Rearranged for the other unknowns:
Time must be greater than zero. When solving for time, the power cannot be zero, the energy cannot be zero, and the two must share a sign. The result is an average over the interval; a sprinter or an engine can briefly exceed it.
Worked example: 18 kJ in 12 seconds
A machine does 18 kJ of work in 12 s.
Convert the energy: 18 kJ = 18,000 J.
Power: P = 18,000 J ÷ 12 s = 1,500 W = 1.5 kW.
In other units: about 2.01 hp, 5,118 BTU/h or 1,106 ft·lbf/s.
Kept up for an hour, that is 1.5 kWh, and with no losses it could lift about 153 kg by one meter every second.
That is roughly what a hair dryer draws on its high setting. For a human comparison, a 75 kg person running up 3 m of stairs in 4 s does 75 × 9.80665 × 3 ≈ 2,206 J of work, or about 552 W (0.74 hp).
Watts, horsepower and BTU per hour
| Unit | Watts | Where you see it |
|---|---|---|
| watt (W) | 1 | SI unit: one joule per second |
| kilowatt (kW) | 1,000 | Motors, cars outside the US, solar panels |
| horsepower (hp) | 745.69987 | US engines; defined as 550 ft·lbf/s |
| metric horsepower (PS) | 735.49875 | European car specs; 75 kgf·m/s |
| BTU per hour | 0.29307107 | Furnaces, air conditioners |
| ft·lbf/s | 1.3558179 | US mechanical engineering |
| kcal per hour | 1.1622222 | Exercise and metabolism |
Air-conditioner ratings in BTU/h describe the heat moved, not the electricity drawn. A 12,000 BTU/h unit moves about 3,517 W of heat, but because it pumps heat rather than making it, its electrical draw is usually well under half of that.
Energy versus power: kWh and kW
A kilowatt measures how fast energy flows; a kilowatt-hour measures how much has flowed. Multiplying power by time converts one into the other. Solve for work with P = 1.5 kW and t = 2 h, and the calculator returns 3 kWh. Solve for time with W = 1 kWh and P = 1,500 W, and you get 2,400 s, which is 40 minutes. Mixing the two up is the most common error in reading electricity bills and battery specs: a 10 kWh battery stores energy, while a 5 kW inverter limits how fast that energy can come out.
Power for moving objects: P = Fv
When a force keeps something moving at a steady speed, the work done each second is the force times the distance covered in that second, so P = Fv. A car needing 600 N of push at 27.8 m/s (100 km/h) demands about 16.7 kW, or 22.4 hp, at the wheels. Aerodynamic drag grows roughly with the square of speed, so the power to beat it grows with the cube: driving 20% faster takes about 73% more power against drag.
Related calculators
Work out the energy side first with the work calculator. For electrical power from voltage and current, use the Ohm’s law calculator, and to switch between power units, the power converter.
Frequently asked questions
What is the formula for power?
Power is work or energy divided by the time it takes: P = W ÷ t. One watt is one joule per second. Doing 18 kJ of work in 12 s takes an average of 1,500 W, or 1.5 kW.
How many watts are in one horsepower?
One mechanical horsepower is 550 ft·lbf/s, about 745.7 W. The metric horsepower (PS), common in European car specifications, is slightly smaller at 735.49875 W. The calculator offers both, labeled hp and PS.
What is the difference between kW and kWh?
A kilowatt is a rate, like miles per hour; a kilowatt-hour is an amount, like miles. A 1.5 kW pool pump running for 2 hours uses 1.5 × 2 = 3 kWh. Electricity bills charge for kWh, while appliance labels list watts or kilowatts.
How do I find the power needed to move something at a steady speed?
Multiply the force needed to keep it moving by its speed: P = Fv. A car that needs 600 N to overcome drag and rolling resistance at 100 km/h (27.8 m/s) needs about 16.7 kW, or 22.4 hp, delivered to the wheels.
Can power be negative?
The calculator accepts negative work and power to describe energy flowing out, such as brakes absorbing a car's motion. Time must always be positive, so when solving for time the work and the power must have the same sign.