Power Calculator

The formula this calculator uses

Power = work / time

W

Work or energy transferred, in joules — the quantity being moved

t

Time taken, in seconds — the interval over which the energy moves

P

Power in watts — one joule per second, the rate of transfer

hp

Horsepower — an alternative unit, equal to 745.6998715822702 W

How to check the result by hand

1. 1

   Put the energy into joules

   Start from the work done or energy transferred, expressed in joules. A kilowatt-hour is 3,600,000 joules, so 0.001 kWh becomes 3600 J. If the figure arrives in another energy unit, convert it to joules first, because the watt is defined against the joule.

2. 2

   Put the time into seconds

   The watt is a joule per second, so the interval must be in seconds, never minutes or hours. Twelve seconds stays 12; twelve minutes would become 720. Dividing by an unconverted time is the error that most often turns a sensible answer into one that is wrong by a factor of sixty.

3. 3

   Divide energy by time to get watts

   3600 J divided by 12 s gives 300 W. This single division is the whole calculation, because power is defined as the rate at which the energy moves. The answer is a rate, so it carries units of joules per second, which are renamed watts for convenience. If the division returns a very small or very large number, that is not a mistake; a torch bulb draws a couple of watts while a power station delivers hundreds of millions, and both are ordinary results of the same formula.

4. 4

   Convert to the unit the context uses

   300 W is 0.3 kW when a kilowatt is more readable, and 0.4023066268785084 hp when horsepower is expected. The same 3600 J is 0.001 kWh, useful when comparing against an energy bill. Each conversion divides by a fixed constant and changes nothing about the underlying rate.

5. 5

   Sanity-check the magnitude and round last

   A domestic appliance should land somewhere between 10 W and 3000 W; a car engine near 100 kW. If the number is far outside its expected band, a unit or a factor of a thousand has slipped. Carry full precision through the division, then round the displayed figure to the accuracy the inputs support.