What it does
Power is how fast energy is used or work is done. One watt is one joule per second. This calculator covers the five everyday formulas: mechanical power from work and time or from force and speed, and electrical power from voltage, current and resistance. Every answer is shown in watts, kilowatts, horsepower and BTU per hour. If you need to solve for volts, amps or ohms instead, use the Ohm's law calculator.
How it's calculated
P = W ÷ t (work or energy ÷ time)
P = F × v (force × speed, in the direction of the force)
P = V × I = I2 × R = V2 ÷ R (electrical)
P = F × v (force × speed, in the direction of the force)
P = V × I = I2 × R = V2 ÷ R (electrical)
Inputs are converted to SI units first (joules, seconds, newtons, meters per second). The conversions follow NIST SP 811: 1 kWh = 3,600,000 J, 1 ft = 0.3048 m and 1 lbf = 4.448222 N.
Power units
| Unit | In watts |
|---|---|
| 1 kilowatt (kW) | 1,000 W |
| 1 horsepower (550 ft·lbf/s, mechanical) | 745.6999 W |
| 1 metric horsepower (PS) | 735.4988 W |
| 1 electric horsepower | 746 W |
| 1 BTU per hour | 0.2930711 W |
| 1 ft·lbf per second | 1.355818 W |
Values from NIST Special Publication 811. US engine and motor ratings normally use mechanical horsepower; European car specs often use metric PS.
Worked examples
- Lifting: raising a 50 kg load 2 m takes about 50 × 9.80665 × 2 = 980.7 J of work. Doing it in 4 seconds is 980.7 ÷ 4 = 245 W, about 0.33 hp.
- Pulling: a winch pulling with 500 N at 2 m/s delivers 500 × 2 = 1,000 W, or 1.34 hp.
- Electrical: a 120 V appliance drawing 2 A uses 120 × 2 = 240 W. Run for 5 hours, that's 1.2 kWh; the electricity cost calculator turns that into dollars.
Limitations
- W ÷ t gives average power. A motor can briefly peak well above its average.
- F × v assumes the force acts in the direction of motion. If it's at an angle, use the component along the motion (F cos θ).
- The electrical formulas are for DC or purely resistive AC loads. Motors and other inductive loads have a power factor, so V × I overstates the real power.
- Output power is less than input power: a motor rated at 1 hp output draws more than 746 W from the wall.