How do I calculate power?
Pick what you know, type the two values in any unit, and the power calculator shows the power in watts, kilowatts, horsepower, metric horsepower and BTU per hour. Pick “A power, to convert” to convert between those units.
- Watts (W)
- 50
The power is 50 W, which is 0.067051 hp.
- Kilowatts (kW)
- 0.05
- Horsepower (hp)
- 0.067051
- Metric horsepower (PS)
- 0.067981
- BTU per hour
- 170.607082
Watts (W): 50. The power is 50 W, which is 0.067051 hp.
How to calculate
Computes power from energy and time, voltage and current, current and resistance, voltage and resistance, or force and speed, or converts a power, in watts, kilowatts, horsepower, metric horsepower and BTU per hour.
Example with the default inputs (I know Energy and time (P = E ÷ t), Energy or work 1,500 J, Time 30 s): The power is 50 W, which is 0.067051 hp.
Method: P = E ÷ t; P = V × I; P = I² × R; P = V² ÷ R; P = F × v. 1 hp = 550 ft·lbf/s; 1 PS = 75 kgf·m/s; 1 BTU/h = 1055.05585262 J ÷ 3,600 s.
- Power is the average over the time: the energy or work divided by the time.
- The electrical modes are for DC or for AC in phase (a resistor): V and I are steady or RMS values.
- Force and speed point the same way.
Worked examples
Each example is checked against the calculator on every build.
- I know Energy and time (P = E ÷ t), Energy or work 1,500 J, Time 30 s gives Watts (W) 50, Kilowatts (kW) 0.05, Horsepower (hp) 0.067051, Metric horsepower (PS) 0.067981, BTU per hour 170.607082.Source: NIST SP 811 (2008), B.8: 1 hp = 550 ft·lbf/s = 745.699872 W, 1 PS = 735.49875 W, 1 BTU(IT)/h = 0.2930711 W
- I know Voltage and current (P = V × I), Voltage 120 V, Current 10 A gives Watts (W) 1,200, Kilowatts (kW) 1.2.Source: Electric power P = V × I (NIST SP 330, the SI Brochure, 2019: 1 W = 1 V·A)
- I know Current and resistance (P = I² × R), Current 2 A, Resistance 50 Ω gives Watts (W) 200.
- I know Voltage and resistance (P = V² ÷ R), Voltage 230 V, Resistance 52.9 Ω gives Watts (W) 1,000.
- I know Force and speed (P = F × v), Force 444.8 N, Speed 1.676 m/s gives Horsepower (hp) 1, Watts (W) 745.699872.Source: NIST SP 811 (2008), B.8: horsepower (550 ft·lbf/s) = 745.6999 W
- I know A power, to convert, Power 1.341 hp gives Watts (W) 1,000, Horsepower (hp) 1.341022, BTU per hour 3,412.141633.Source: NIST SP 811 (2008), B.8 (1 hp = 745.69987158227022 W; 1 BTU(IT) = 1055.05585262 J)
How it works
| You know | Power |
|---|---|
| Energy E and time t | P = E ÷ t |
| Voltage V and current I | P = V × I |
| Current I, resistance R | P = I² × R |
| Voltage V, resistance R | P = V² ÷ R |
| Force F and speed v | P = F × v |
| A power in any unit | converted |
The calculator works in SI units (joules, seconds, volts, amperes, ohms, newtons, metres per second, watts) and shows the power in five units, each by an exact size:
- 1 kW = 1,000 W
- 1 hp (mechanical) = 550 ft·lbf/s = 550 × 0.3048 m × 4.4482216152605 N per second = 745.69987158227022 W
- 1 PS (metric horsepower) = 75 kgf·m/s = 75 × 9.80665 = 735.49875 W
- 1 BTU/h = 1,055.05585262 J ÷ 3,600 s = 0.29307107017222… W
Input units are exact too: 1 kWh = 3,600,000 J, 1 cal = 4.184 J, 1 BTU = 1,055.05585262 J, 1 ft·lbf = 0.3048 × 4.4482216152605 J, 1 lbf = 4.4482216152605 N, 1 kgf = 9.80665 N, 1 mph = 0.44704 m/s, 1 km/h = 1,000/3,600 m/s, 1 knot = 1,852/3,600 m/s.
Exact arithmetic. Each value is read as the exact decimal you typed, in the unit you typed it in; the page stores it in the SI unit and reads it back as the decimal with the fewest significant digits, in one of the box's units, that gives the same stored number; on a tie, the unit listed first in the box's unit menu wins. Every step is exact, so 100 lbf at 5.5 ft/s is exactly 1 hp.
Rounding. Each result shows with at most 6 decimals (6 significant figures below 0.0001), rounded half up from its exact value, with trailing zeros left off. A result shown with 15 or more significant digits (a very large value with its decimals) can differ from the exact value in its last shown digit, because the page keeps results as 64-bit floating-point numbers, which hold about 16 significant digits.
Assumptions
- The power is the average over the time.
- Electrical values are DC, or AC RMS values in phase (a resistive load).
- The force points along the motion.
- Each value is from 0.000000001 to 1,000,000,000,000 in its SI unit.
Worked examples by hand
1,500 J in 30 s. 1,500 ÷ 30 = 50 W = 0.05 kW = 50 ÷ 745.69987 = 0.067051 hp = 0.067981 PS = 50 ÷ 0.29307107 = 170.607082 BTU/h.
120 V and 10 A. 120 × 10 = 1,200 W = 1.2 kW.
2 A through 50 Ω. 2² × 50 = 200 W.
230 V across 52.9 Ω. 230² ÷ 52.9 = 52,900 ÷ 52.9 = 1,000 W.
100 lbf at 5.5 ft/s. 100 × 5.5 = 550 ft·lbf/s = 1 hp exactly = 745.699872 W.
1 kW. 1.341022 hp, 3,412.141633 BTU/h.
Other questions people ask
What is the formula for power?
Power is energy per unit time: P = E ÷ t. One watt is one joule per second. Doing 1,500 J of work in 30 s is 1,500 ÷ 30 = 50 W. For a moving object, the power is the force times the speed along it: P = F × v.
How do I calculate electrical power?
Multiply the voltage by the current: P = V × I. A 120 V appliance drawing 10 A uses 1,200 W. With Ohm’s law (V = I × R) the same power is I² × R or V² ÷ R: 2 A through 50 Ω is 200 W, and 230 V across 52.9 Ω is 1,000 W.
How many watts are in one horsepower?
One mechanical horsepower is 550 foot-pounds-force per second, exactly 745.69987158227022 W (about 746 W). One metric horsepower (PS) is 75 kilogram-force metres per second, exactly 735.49875 W. So 1 kW is 1.341 hp or 1.360 PS.
How do I convert watts to BTU per hour?
One International Table BTU is exactly 1,055.05585262 J, so 1 BTU per hour is 1,055.05585262 ÷ 3,600 = 0.29307 W, and 1 W is 3.41214 BTU/h. A 1,000 W heater gives out 3,412 BTU per hour.
What is the difference between power and energy?
Energy is an amount (joules, kilowatt hours); power is how fast it is used (watts, kilowatts). A 1,000 W heater running for 3 hours uses 1,000 × 3 = 3,000 Wh = 3 kWh of energy. Type 3 kWh and 3 h here to get back 1,000 W.
Is this the same as the Ohm’s law calculator?
The electrical modes use the same laws, but this page gives the power only, in five units, and also works from energy and time or from force and speed. To find the missing voltage, current or resistance, use the Ohm’s law calculator.