Power Calculator
Calculate power, work, or time from the relationship P = W/t. Enter the two known values with units (J or kJ for work; s, min or h for time) and get the third quantity instantly.
Power Calculator Physics
Power Formula
Where:
- \(P\) — power (watts, W)
- \(W\) — work or energy transferred (joules, J)
- \(t\) — time (seconds, s)
The formula expresses power as the rate at which work is done: one watt equals one joule of work performed per second. Rearranging it gives \(W = P \cdot t\) for work and \(t = W / P\) for time.
Power – Calculation Example
Example: a motor performs 100 J of work in 10 seconds. What is its power output?
\[P = \frac{W}{t} = \frac{100\ \text{J}}{10\ \text{s}} = 10\ \text{W}\]
Result: Power = 10 W (these are the calculator's default values, so you can reproduce this result directly).
How to use the calculator
- In the "I want to calculate" dropdown, choose whether you need Power (P), Work (W), or Time (t). The field of the quantity you are solving for is hidden automatically.
- Enter the known Work (W) value and pick its unit: J or kJ.
- Enter the known Time (t) value and pick its unit: s, min, or h.
- When calculating work or time, enter the known Power (P) in watts instead of the hidden field.
- The Result appears immediately, expressed in watts (W), joules or kilojoules (J/kJ), or seconds, minutes, or hours (s/min/h) depending on your unit selections.
What is power in physics?
Power is the rate at which work is done or energy is transferred. While work tells you how much energy is moved, power tells you how fast it happens. Two machines lifting the same load to the same height do identical work, but the one that finishes first delivers more power. The SI unit of power is the watt (W), defined as one joule per second.
The same relationship governs everyday quantities: a 60 W light bulb converts 60 joules of electrical energy into light and heat every second, and a 1000 W kettle transfers 1000 joules per second to the water inside it. Larger power ratings are often given in kilowatts (1 kW = 1000 W) or, for engines, in horsepower (1 hp ≈ 745.7 W).
Because \(P = W/t\) links three quantities, knowing any two determines the third. Dividing work by power tells you how long a process takes; multiplying power by time tells you the total energy consumed — the basis of electricity billing, where 1 kW running for 1 hour equals 1 kilowatt-hour (kWh) of energy.
Assumptions and practical tips
- The calculator assumes constant power over the time interval. If power varies (e.g. an engine revving up), the result is the average power \(P_{avg} = W/t\).
- Work here means net energy transferred in joules. If you know the force and distance instead, first compute \(W = F \cdot d\), then divide by time.
- Unit conversions are handled automatically: kilojoules are converted to joules and minutes/hours to seconds before the calculation, so you can mix units freely.
- Watch out for negative work: if the force opposes the displacement, \(W < 0\) and the resulting power is negative, meaning energy is being absorbed rather than delivered.
- Power ratings on real devices are usually input power; useful output power is lower by the efficiency factor. To account for losses, see the Mechanical Efficiency Calculator.
If your problem starts from motion or forces rather than energy, you may also find the Average Speed Calculator and the Gravitational Force Calculator useful for finding the intermediate quantities, and the Rotational Kinetic Energy Calculator for spinning systems.
Frequently Asked Questions
How do I calculate power by hand without a calculator?
Divide the work done by the time taken: \(P = W/t\). First convert everything to SI units — joules for work and seconds for time — then divide. For example, 600 J of work over 30 s gives \(P = 600/30 = 20\) W. If time is given in minutes, multiply by 60 to get seconds first; for hours, multiply by 3600.
How do I convert between watts, kilowatts, and horsepower?
1 kilowatt (kW) = 1000 W, and 1 horsepower (hp) ≈ 745.7 W (metric hp ≈ 735.5 W). To convert a 150 hp engine to watts, multiply: \(150 \times 745.7 \approx 111{,}855\) W, or about 112 kW. Going the other way, divide watts by 745.7 to get horsepower. Always check which horsepower definition is used, especially with European (metric) engine ratings.
What is a normal power output for a person or a household device?
A person walking generates roughly 100 W, and a trained cyclist can sustain 200–300 W briefly. Household appliances range from about 10 W for an LED bulb to 2000–3000 W for kettles, dryers, and heaters. A typical home draws a few hundred watts on average, peaking at several kilowatts when heavy appliances run together. These are ballpark figures; check the label on your device for its actual rating.
Can power be negative, and what does negative power mean?
Yes. If the force opposes the motion, the work is negative, so \(P = W/t\) is negative too. Physically this means the system absorbs energy instead of delivering it — for example, friction removing energy from a sliding object, or a brake slowing a wheel. The sign tells you the direction of energy flow, not that the calculation is wrong.
What is the difference between power and energy (watts vs. watt-hours)?
Power is a rate (joules per second); energy is a total amount (joules). A 1000 W heater has a fixed power, but the energy it uses depends on how long it runs: \(W = P \cdot t\). Running it for 1 hour consumes \(1000 \times 3600 = 3.6\) million joules, which equals 1 kWh. Electricity bills charge for energy (kWh), not power.
How do I calculate work if I only know force and distance?
Use \(W = F \cdot d\), where \(F\) is the force in newtons and \(d\) is the displacement in meters, giving work in joules. This assumes the force is constant and acts along the direction of motion. Once you have the work, divide by time to get power. For example, a 50 N force over 4 m gives \(W = 200\) J; done in 20 s, the power is 10 W.
What happens if power is not constant over time?
The formula \(P = W/t\) then gives the average power over the interval, not the instantaneous value at any moment. That average is still meaningful and often all you need — a car engine's rated power, for instance, is an average over a test cycle. For instantaneous power you would need \(P = F \cdot v\) with the velocity at that instant, or calculus if force varies with position.