The formula
How to calculate power
Power is the rate at which work is done or energy transferred. The same job done in half the time requires twice the power, which is the distinction between how much and how fast.
For mechanical systems power can also be written as force times velocity, which is often more convenient — a vehicle's power output at a given speed follows directly from the resisting force it overcomes.
What to enter:
- Work done (J)
- Time taken (s)
The result updates on every keystroke. The URL updates too, which makes the filled-in version easy to bookmark or send to someone else.
Units matter more here than the arithmetic itself: the formula assumes a specific set of units for each input, stated next to the field, and converting into those units first is usually the difference between a correct result and one that is wrong by a clean power of ten.
Why power matters
The formula behind power is standard and appears in the same form across textbooks and reference material; what a calculator adds is speed and the ability to see instantly how the result responds to a change in any one of the inputs, which is far slower to do by hand.
This also functions as a reference implementation of the formula itself: where the exact form of an equation is in question, the one used on this page, stated in the formula section above, is the standard version found in the relevant textbooks and reference material.
A formula like this one is rarely the last step in a piece of work — the figure it produces usually feeds into a further calculation, a comparison against a published value, or a write-up that needs to state both the result and how confident it is. Getting this step right the first time, rather than propagating a small arithmetic slip through several more steps, is the main practical reason to check a manual calculation against a tool like this one before building on top of it.
Where a calculation like this one is part of a larger piece of work, it is generally worth running it with a round, easy-to-check set of numbers first — inputs of exactly 1, 10 or 100 — purely to confirm the formula is being applied correctly, before switching to the real measured values the actual result depends on.
Worked example
A concrete run-through, using the values already in the fields:
- Work done: 45,000 J
- Time taken: 60 s
That gives:
- Power: 750 W
- In horsepower: 1.0058 hp
- Energy at that rate for an hour: 0.75 kWh
The figures above are the calculator's own default values, shown purely so the working is visible rather than hidden — the same steps apply exactly to your own numbers, entered in the fields at the top of this page.
Reading the result
Reference points: a person sustains about 100 W of useful output, a kettle draws 3,000 W, a family car peaks around 100,000 W. Cyclists sustaining 400 W for an hour are at professional level.
Where this goes wrong. Power and energy are routinely confused, including on utility bills. A kilowatt is a rate; a kilowatt-hour is an amount. A 2 kW heater running for three hours uses 6 kWh.
A result that is wrong by an exact factor of ten, a hundred or a similar round number is almost always a units error rather than a mistake in the formula itself — checking each input against the unit stated beside it is the fastest way to track it down.
Watts measure the rate of energy use at an instant. Watt-hours measure the total energy used over time. A 100 W bulb burning for ten hours consumes one kilowatt-hour.
745.7 W for mechanical horsepower, the version used for engines. Metric horsepower, common in continental Europe, is 735.5 W.
The headline figure is power. With 45,000 J work done and 60 s time taken, that comes to 750 W. Change any field and the figure moves with it.
Generally, no more than the least precise input justifies — a result reported to six decimal places from inputs measured to two significant figures is implying a precision the calculation does not actually have. The calculator shows full precision so you can round appropriately for your own use.
Yes — the equation shown in the formula section above is the standard form used in textbooks and reference material for this calculation, not a simplified or approximate version.
Yes, in the sense that it applies the correct standard formula and returns an accurate result for the inputs given — but check your own course or publication's requirements for how results should be rounded, presented and referenced, since those conventions vary and are not something a calculator can know on your behalf.