# How do I calculate power?

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.

- Page: https://www.acalculator.org/physics/power-calculator
- JSON spec: https://www.acalculator.org/physics/power-calculator.json
- Version: 1b3ddbc70ba2

## Default answer

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.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| mode | I know | The two values you know, or a power to convert. |
| e | Energy or work | The energy used or the work done. |
| t | Time | The time the energy is used or the work is done over. |
| v | Voltage | The voltage across the load. |
| i | Current | The current through the load. |
| r | Resistance | The resistance of the load. |
| f | Force | The force pushing or pulling along the motion. |
| s | Speed | The speed along the force. |
| p | Power | A power in any unit, to convert. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| watts | Watts (W) | The power in watts: joules per second. |
| kilowatts | Kilowatts (kW) | The power in kilowatts (1,000 W). |
| horsepower | Horsepower (hp) | The power in mechanical horsepower: 550 ft·lbf/s = 745.69987158227022 W. |
| metricHorsepower | Metric horsepower (PS) | The power in metric horsepower: 75 kgf·m/s = 735.49875 W. |
| btuPerHour | BTU per hour | The power in International Table BTU per hour: 1 BTU/h = 0.29307107017222 W. |

## 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.

## Assumptions

- 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

1. mode = energy, e = 1,500, t = 30 gives watts = 50, kilowatts = 0.05, horsepower = 0.067051, metricHorsepower = 0.067981, btuPerHour = 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.
2. mode = vi, v = 120, i = 10 gives watts = 1,200, kilowatts = 1.2. Source: Electric power P = V × I (NIST SP 330, the SI Brochure, 2019: 1 W = 1 V·A).
3. mode = ir, i = 2, r = 50 gives watts = 200.
4. mode = vr, v = 230, r = 52.9 gives watts = 1,000.
5. mode = fv, f = 444.822162, s = 1.6764 gives horsepower = 1, watts = 745.699872. Source: NIST SP 811 (2008), B.8: horsepower (550 ft·lbf/s) = 745.6999 W.
6. mode = convert, p = 1,000 gives watts = 1,000, horsepower = 1.341022, btuPerHour = 3,412.141633. Source: NIST SP 811 (2008), B.8 (1 hp = 745.69987158227022 W; 1 BTU(IT) = 1055.05585262 J).

## FAQ

### 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.

## Sources

- NIST Special Publication 811 (2008), Guide for the Use of the International System of Units, Appendix B.8: horsepower (550 ft·lbf/s) = 745.6999 W, horsepower (metric) = 735.4988 W, British thermal unit (IT) per hour = 0.2930711 W, pound-force = 4.4482216152605 N. https://www.nist.gov/pml/special-publication-811
- NIST Special Publication 330 (2019), The International System of Units (SI): the watt is one joule per second and one volt ampere. https://www.nist.gov/pml/special-publication-330
- OpenStax, University Physics Volume 1, §7.4 Power (P = W ÷ t, P = F · v). https://openstax.org/books/university-physics-volume-1/pages/7-4-power
- OpenStax, University Physics Volume 2, §9.5 Electrical Energy and Power (P = IV = I²R = V²/R). https://openstax.org/books/university-physics-volume-2/pages/9-5-electrical-energy-and-power