Work And Power Calculator

What the work and power calculator does

Work is how much energy a force transfers. Power is how fast it transfers it. This calculator handles both and the link between them. In its simple mode it relates work, power, and time, so you can find any one from the other two. In its advanced mode it starts from a force, a displacement, and a time, and returns both the work done and the power.

Below is what separates power from work, the equations behind the answers, why power is so often the figure that matters, and a worked example.

How to use it

1. Pick a mode. Simple mode works with work, power, and time. Advanced mode works from force, displacement, and time.
2. Choose what to find and enter the known values, each with its own unit.
3. Press Calculate for the answer, or Reset to clear it.

Power is the rate of doing work

Two engines can do the same total work but be very different machines, because one does it quickly and the other slowly. That difference is power: the rate at which work is done, or equivalently the rate at which energy is delivered. Lifting a load up a flight of stairs takes the same work whether you stroll or sprint, but sprinting takes more power, because the same energy is spent in less time.

So work answers how much, and power answers how fast. A small motor running for a long time can do as much work as a big one running briefly, yet the big motor has far more power. This is why power, not just work, is what we use to rate engines, motors, and appliances, since it tells you what they can deliver at any moment.

The equations it uses

Power P is the work W done divided by the time t it takes:

P = W ÷ t

Rearranged, that gives the work from a power sustained over a time, W = P t, which is the simple mode's two faces. In the advanced mode, the work itself is found from the force F and the displacement d it acts through, and the power follows by dividing by the time:

W = F d and P = F d ÷ t

So from a force, a distance, and a time, the calculator gives both the energy transferred and the rate of transfer. The advanced mode takes the force as acting along the direction of motion.

Why power matters, not just work

The reason power earns its own name is that the world runs on rates. A lift has to raise its load in a reasonable time, not eventually, so it must supply enough power, not merely enough work. A kettle has to boil before you lose patience, which sets the power it draws. The total energy each task needs is fixed by the work, but whether a machine can do it fast enough is a question of power.

This is also why power connects to everyday measures of capability and cost. An engine's horsepower tells you how quickly it can do work, how fast it can accelerate a car or haul a load. And your electricity meter, despite the name, charges by energy, the power drawn multiplied by the time it runs, which is why a powerful appliance left on briefly and a modest one left on for hours can cost the same.

Units and precision

The SI unit of power is the watt, one joule of work per second, and the calculator works in SI internally, converting your entries before computing. Work can be entered and read in joules and a range of other energy units, time from seconds to years, and power in watts, kilowatts, and larger multiples, along with horsepower and British thermal units per hour for familiar comparisons. Some results are shown with many digits, so the precision is in the arithmetic and you can read the unit and rounding that suit you.

A worked example

Suppose a force of 200 N pushes an object 10 metres in 8 seconds, with the force along the direction of motion.

The work done is W = 200 × 10 = 2,000 J. The power is that work spread over the time, P = 2,000 ÷ 8 = 250 W. To put the power in familiar terms, 250 watts is about a third of a horsepower, since one horsepower is roughly 746 watts. Do the same 2,000 J of work in half the time, 4 seconds, and the power doubles to 500 W, even though the work is unchanged.

Questions people ask

What is the difference between work and power?

Work is the total energy transferred by a force. Power is how fast it is transferred, the work divided by the time. Two machines can do equal work while differing greatly in power.

What is the formula for power?

Power equals work divided by time, P = W/t. Equivalently, work equals power times time, W = Pt, and from a force and distance, the work is W = Fd.

What is a watt?

It is the SI unit of power, one joule of work per second. A kilowatt is a thousand watts, and one horsepower is about 746 watts.

Does my electricity bill measure power or energy?

Energy. The bill charges for power multiplied by time, usually in kilowatt-hours. A powerful appliance used briefly can cost the same as a modest one used for much longer.

References

A quick note on where the physics comes from. Work as force times distance, and power as the rate of doing work, are standard mechanics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The joule, the watt, and the other SI units follow the US National Institute of Standards and Technology.

1. OpenStax, University Physics Volume 1, Section 7.4, Power. https://openstax.org/books/university-physics-volume-1/pages/7-4-power
2. HyperPhysics, Georgia State University, Power. http://hyperphysics.phy-astr.gsu.edu/hbase/pow.html
3. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811