What this calculator does
Work is force multiplied by the distance moved in the direction of that force. The qualification matters: a force at right angles to the motion does no work at all, which is why carrying a heavy box along a level floor does no work on the box in the physics sense however tired you get.
Power is work divided by time, so it describes the rate rather than the total. Two motors can do identical work while one takes ten times as long, and it is the faster one that needs to be ten times more powerful.
The formula
Multiply force by distance and by the cosine of the angle between them, which removes the component of the force that is not acting along the direction of travel. Dividing by time gives power in watts, and applying the efficiency percentage splits that into useful output and waste.
| Term | Meaning |
|---|---|
| Work | Energy transferred by a force acting over a distance, in joules. |
| Power | The rate of doing work, in watts. One watt is one joule per second. |
| Efficiency | The share of energy input that comes out as useful output, with the rest usually lost as heat. |
The inputs explained
| Field | What to enter |
|---|---|
| Force (N) | The force applied, in newtons. |
| Distance (m) | The distance moved, in metres. |
| Angle to the direction of motion (°) | The angle between the force and the direction of motion. Zero means the force acts straight along the motion, which is the usual case. |
| Time taken (s) | The time taken, in seconds, used to convert work into power. |
| Efficiency (%) | The efficiency as a percentage, used to split the work into useful output and losses. |
When to use it
Sizing a motor or winch
The work needed comes from the force and distance, and the time it must be done in sets the power rating required.
Accounting for losses
No machine is perfectly efficient, so the input has to exceed the useful output, and the efficiency figure quantifies the gap.
Pulling at an angle
Dragging something with a rope at an angle wastes part of the effort lifting rather than pulling, and the cosine term captures exactly how much.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much does pulling at an angle cost you?
The same force and distance with the force applied at increasing angles to the direction of motion.
| Angle to motion | Work done | Power |
|---|---|---|
| 0° | 3,000.00 J | 300.00 W |
| 30° | 2,598.08 J | 259.81 W |
| 45° | 2,121.32 J | 212.13 W |
| 60° | 1,500.00 J | 150.00 W |
Questions
Why does carrying something do no work?
Because the force holding it up is vertical while the motion is horizontal, so the angle between them is 90 degrees and its cosine is zero. Your muscles certainly use energy, but none of it is transferred to the box as work in the physics sense.
What is the difference between work and power?
Work is the total energy transferred; power is how fast it is transferred. Lifting the same load up the same stairs is the same work whether you walk or run, but running takes less time and therefore requires more power.
Where does the wasted energy go?
Almost always to heat, through friction in bearings, resistance in windings and air drag. That is why efficiency and cooling tend to be the same engineering problem.
Can efficiency exceed 100 per cent?
No. Output cannot exceed input, so anything above 100 per cent means the input has been measured incorrectly or an energy source has been overlooked. Heat pumps appear to break this rule but do not: they move heat rather than create it, so their coefficient of performance is not an efficiency.
For the force term on its own, see the force, mass and acceleration calculator. For rotational work, see the torque and rotational power calculator.