Work Calculator

1. Enter two of work, force and distance.
2. Enter the angle between the force and the motion.
3. Leave the one you want to find blank.
4. Read the result and the formula used.

Here is what each result means:

In physics, work is done when a force moves an object through a distance. It equals the force times the distance times the cosine of the angle between them, written W equals F d cos of theta. When the force is in line with the motion, the angle is zero and the cosine is one, so work is simply force times distance.

Only the part of the force along the direction of motion does work, which is why the angle matters. A force at a right angle to the motion does no work at all. Work is measured in joules, the same unit as energy, because doing work transfers energy. This calculator links work, force and distance.

It applies the work formula, using the angle to take the useful part of the force.

1. Take the cosine of the angle to find the useful fraction of the force.
2. For work, multiply force, distance and that cosine.
3. To find force or distance, divide the work by the other two.

Work transfers energy, and doing it over time gives power; the kinetic energy calculator deals with the energy of motion.

A 100 newton force pushes an object 5 meters in the same direction, so the angle is 0.

Calculation: W = F d cos(0) = 100 x 5 x 1 = 500 joules. If the force acted at 60 degrees to the motion, the cosine of 60 is 0.5, so the work would be half as much, 250 joules.

Only the part of the force along the motion counts, set by the cosine of the angle.

A force at a right angle to the motion, like the pull holding a satellite in orbit, does no work even though it acts the whole time.

These related ideas are often mixed up.

Work and energy share the joule as a unit, since doing work moves energy from one place or form to another.

The Force

A larger force in the direction of motion does more work in direct proportion.

The Distance

Moving farther under the same force does more work. No motion means no work, however large the force.

The Angle

The cosine of the angle sets how much of the force is useful. At 90 degrees, none of it does work.

Physics Homework

Find the work done by a force, or solve for the force or distance.

Machines and Lifting

Work out the energy needed to move a load a certain distance.

Understanding Energy Transfer

See how force and distance combine to move energy.

1. Ignoring the Angle

Only the force along the motion does work. Include the cosine when the force is at an angle.

2. Counting Work with No Motion

If nothing moves, no work is done, no matter how hard you push.

3. Confusing Work and Power

Work is force times distance; power is work over time. They are different quantities.

4. Mixed Units

Use joules, newtons and meters for a clean SI result.

5. Wrong Angle Reference

The angle is between the force and the direction of motion, not the vertical.

The formula is exact; only the displayed decimals are rounded.

Work is done when a force moves an object through a distance. It equals the force times the distance times the cosine of the angle between them, and it transfers energy, measured in joules.

Multiply the force by the distance and by the cosine of the angle between them. A 100 newton force moving an object 5 meters in line does 100 times 5 times 1, which is 500 joules.

Only the part of the force along the direction of motion does work. The cosine of the angle picks out that part, so a force at 90 degrees, with a cosine of zero, does no work.

Yes. If the object does not move, or the force is at a right angle to the motion, no work is done, however large the force is.

Divide the work by the distance times the cosine of the angle. Leave the force field blank and enter work, distance and angle to solve for it.

The SI unit of work is the joule, the same as energy, because doing work transfers energy. One joule is one newton of force over one meter in line.

Work is force times distance, the energy transferred. Power is how fast that work is done, work divided by time. They are related but distinct.

Yes. When a force acts opposite to the motion, the angle is more than 90 degrees, the cosine is negative, and the work is negative, meaning it takes energy away.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Work (physics) (Wikipedia).
• Work explained (Maths Is Fun).
• Joule (Wikipedia).