Mechanical Power Calculator - Watts from Work and Time

Two winches, one crate, and a factor of four

A 250 kg crate has to go up 3 m. That is 7,354.99 J of work, and no choice of winch will change it. One winch does the lift in 60 s and needs 122.6 W. The other does it in 15 s and needs 490.3 W, four times as much, for a job that is identical at both ends. That gap is what power measures, and it is why a work figure on its own cannot tell you what motor to buy.

A work figure on its own

Tells you what the job costs in total
Cannot size a motor, a cable or a fuse
Cannot be compared against an appliance rating
Says nothing about whether the job is even possible in the time you have

The same figure with a time

Becomes watts, the unit every machine is rated in
Sits directly against a bulb, a kettle or an engine
Scales in exact inverse proportion to the schedule
Divides by an efficiency to give the power actually drawn

Power is work with a clock attached

The formula is P = W ÷ t. One watt is one joule per second, which makes the watt an unusually honest unit: it says out loud that it is a rate rather than an amount. Everything awkward about power follows from that single fact, including the reason a bill is measured in kilowatt hours rather than kilowatts, and the reason a machine rated at 2.2 kW can be described as consuming nothing at all when it is switched off.

Run the crate example through it and the arithmetic is unremarkable: 7,354.99 J divided by 60 s is 122.58 W, which the calculator also reports as 0.16439 hp, 0.16667 PS and 418.27 BTU/h. Lifting a 20 kg case into an overhead bin, worth 235.4 J, in a brisk 2 s comes to 117.7 W. Two very different jobs, near enough the same power, because the second one is small and fast while the first is large and slow.

The same job on seven different schedules

This is the table the tool prints under every result, built from your own two numbers with your own schedule highlighted. The work never changes down the column. Only the clock does, and the power follows it in exact inverse proportion.

Schedule	Time	Power needed	Against 60 s
In a quarter of the time	15.0 s	490.3 W	4.00x
In half the time	30.0 s	245.2 W	2.00x
A quarter faster	45.0 s	163.4 W	1.33x
As entered	1 min	122.6 W	1.00x
Half as long again	1 min 30 s	81.72 W	0.67x
In twice the time	2 min	61.29 W	0.50x
In four times the time	4 min	30.65 W	0.25x

There is a practical rule buried in that column. If a motor is marginal, buying time is far cheaper than buying watts: stretching a lift from 60 s to 90 s, a delay nobody would notice, drops the requirement by a third, from 122.6 W to 81.72 W. Going the other way is brutal. Shaving the same lift to 15 s costs four times the power for three quarters of a minute saved.

What the three fields want

What to solve for - the power, the work or the time. Nothing else appears until this is set, and no option is preselected.
Work unit - joules, kilojoules, megajoules, kilowatt hours or kilocalories, at 3,600,000 J to the kWh and 4,184 J to the kcal.
Time unit - seconds, minutes, hours or days. Answers in the time mode come back both as a plain figure in your chosen unit and broken into days, hours, minutes and seconds.
Power unit - watts, kilowatts, megawatts, mechanical horsepower or metric PS. The two horsepowers are different constants and the tool keeps them apart; the section below explains why that matters.
Work - the total energy the job takes. If you have a force and a distance rather than a work figure, the work calculator will turn them into one.
Time - how long the job takes from start to finish. This is elapsed time, including any part of it where the machine is loafing, which is exactly why the answer is an average.
Power - only when solving for work or time. This is useful power delivered to the load, not the power drawn from the wall.

From a bulb to a locomotive

Watts span seven orders of magnitude between the things people meet in a day, which is why a bare figure needs somewhere to sit. The tool slots your own result into this ladder at the right rung.

Power source	Where the figure comes from	Power
An LED bulb	its rating	10.00 W
A person pedaling steadily	typical sustained output at the pedals	75.00 W
A person climbing stairs	typical short burst	300.0 W
One mechanical horsepower	550 ft lbf per second, by definition	745.7 W
A trained cyclist sprinting	typical peak	1.50 kW
An electric kettle on a 230 V supply	typical rating; a 120 V kettle is limited to about 1.5 kW	2.20 kW
A small car engine, 100 hp	100 x 745.69987 W	74.57 kW
A city bus engine, 300 hp	300 x 745.69987 W	223.71 kW
An electric locomotive	typical continuous rating	5.00 MW

The crate winch at 122.6 W lands between a person pedaling steadily and a person taking the stairs, which is a fair description of the job: one person could do it, slowly, and would rather not. Push the same lift to 15 s and its 490.3 W jumps above the stair-climbing burst and heads for the horsepower line.

Two horsepowers, and the 1.4 percent between them

They are different constants and both are still in use. Mechanical horsepower, the one an English-speaking reader means by hp, is 550 foot pounds-force per second, which works out at 745.69987 W. Metric horsepower, written PS, is 75 kilogram-force meters per second, which is 735.49875 W. European manufacturers quote PS, American ones quote hp, and the gap is 1.4 percent.

That 1.4 percent shows up on a spec sheet. An engine of 100 hp is 74.57 kW, and the same engine advertised in metric units reads 101.39 PS. Nothing was tuned; the number went up because the unit got smaller. This calculator prints both on every result, so a figure taken from one market can be checked against the other without a second conversion.

The answer here is useful power, not power drawn. Real machines waste some of what they take in. Divide the result by the efficiency to size the supply: the crate winch needing 122.6 W at the load draws 153.2 W if it is 80 percent efficient, and the same job done by a person, whose muscles run near 25 percent, costs 490.3 W of metabolic effort.

Every figure here is an average. A lift that starts fast and eases off finishes with the same average power and a much higher peak, and it is the peak that trips a breaker or stalls a motor. Treat the result as the floor a machine has to clear over the whole job, not the largest demand it will ever meet.

What people get wrong about watts

Is a kilowatt hour a unit of power?

No, and the name is the reason everyone thinks it is. A kilowatt is power; a kilowatt hour is a power multiplied by a time, which makes it energy, the same kind of quantity as a joule. One kWh is 3,600,000 J. A meter counts kWh because what you buy is energy, not the rate you take it at.

Why does taking longer need less power for the same job?

Because power is a rate and the job is fixed. Spreading 7,354.99 J over 120 s instead of 60 s halves the demand to 61.29 W, and the crate ends up in exactly the same place having absorbed exactly the same energy. Nothing was saved except the strain on the motor.

Should I use hp or PS?

Whichever the source used. If the figure came off an American brochure or an SAE rating, it is mechanical hp at 745.69987 W. If it came off a European brochure, a German or French car in particular, it is almost certainly PS at 735.49875 W. When a listing gives kW alongside, that settles it: divide the kW by 0.74569987 for hp and by 0.73549875 for PS and see which matches.

Can a person really produce a horsepower?

Briefly, yes, and not for long. A trained cyclist peaks around 1.50 kW for a few seconds, comfortably above the 745.7 W of one horsepower, but sustained output over an hour is closer to 300 W for an athlete and 75 W for the rest of us. James Watt picked the figure to describe what a horse could keep up all day, which is a different question from what anything can do for five seconds.

Does holding something still take power?

Not in this sense. If nothing moves, no work is done, so the work is zero and so is the power however long you hold it. A person holding a weight tires because muscle burns energy maintaining tension, and an electromagnet holding a load draws current the whole time, but neither is doing mechanical work on the object. The energy goes to heat.

What if the power is not constant?

Then this gives the average, which is still the right number for sizing energy and for billing, and the wrong number for sizing a peak. If you need the peak, split the job into stretches where the rate is roughly steady and run each one separately. The highest of those is what the machine has to survive.

Why is BTU per hour on an air conditioner if it is a power?

Because it is a power, despite looking like an energy. A BTU is an energy, so a BTU per hour is an energy per time, the same shape as a watt: 1 W is 3.412142 BTU/h. A unit that reads 12,000 BTU/h is moving heat at about 3.52 kW. The calculator prints BTU/h alongside watts for exactly this comparison.

Related tools

Work Calculator

For the W in this formula when what you have is a force, a distance and an angle - See the calculator

Potential Energy Calculator

For the work in a lift when you have a mass and a height, which is where the crate figure above came from - See the calculator

Kinetic Energy Calculator

For the work needed to bring something up to speed rather than up to a height - See the calculator

Force Calculator

For the force a load actually applies, which is the first number most of these calculations need - See the calculator

Engine Power Calculator

For converting a published engine rating between kW, hp and PS, rather than deriving a power from a job - See the calculator

Electricity Usage Calculator

For the other end of the same relationship, where a rating and a running time turn into kilowatt hours - See the calculator