Work Calculator (Physics)
Work is the quiet workhorse of mechanics: it links force and motion to energy, and it is the idea that lets us say precisely how much a push or a pull has actually achieved. In everyday speech we use the word loosely, but in physics work has a strict meaning. Work is done only when a force moves something along the direction of that force, and the amount of work is the force multiplied by the distance multiplied by the cosine of the angle between them. This calculator takes those three inputs, the force in newtons, the distance in metres, and the angle in degrees, and returns the work done in joules and kilojoules so you can read the result at whatever scale suits the problem. The angle is the part people most often overlook. When you push a box straight along the floor the force and the motion point the same way, the angle is zero, the cosine is one, and the work is simply force times distance. But pull a sled by a rope held at an angle and only the part of the force lined up with the motion counts, which is why the cosine appears. Two special cases are worth remembering. When the force is perpendicular to the motion the angle is ninety degrees, the cosine is zero, and no work is done at all. When the angle is greater than ninety degrees the cosine turns negative and the work is negative, meaning the force is removing energy, as friction and braking do. It is built for students, teachers, engineers and anyone checking how much energy a force has delivered.
The formula
Mechanical work is the force multiplied by the distance moved multiplied by the cosine of the angle between the force and the direction of motion. The result is in joules when force is in newtons and distance is in metres.
W = F × d × cosθ
1 kJ = 1,000 J
Worked example
A force of 100 newtons pushes an object 5 metres in the same direction as the force, so the angle is 0 degrees and the cosine is 1. The work is 100 × 5 × 1 = 500 joules, which is 0.5 kilojoules. If the same force acted at 90 degrees to the motion the cosine would be 0 and the work would be 0 joules.
Who this calculator is for
This calculator is for students, teachers, engineers and anyone who needs to find the mechanical work done by a force acting over a distance.
What this calculator assumes
- The force is constant over the distance travelled.
- The angle is measured between the force and the direction of motion.
- Work is zero at 90 degrees and negative when the angle exceeds 90 degrees.
- Results are rounded for display.
Frequently asked questions
What is the formula for mechanical work?
Work is force times distance times the cosine of the angle between them, W = F d cosθ, giving joules when force is in newtons and distance in metres. When the force lines up with the motion the angle is zero and the work is simply force times distance.
Why is work zero when the force is perpendicular to the motion?
At 90 degrees the cosine is zero, so the work is zero. A force at right angles to the motion neither speeds the object up nor slows it down along its path, so it transfers no energy.
Can work be negative?
Yes. When the angle is greater than 90 degrees the cosine is negative, so the work is negative. This happens when a force opposes the motion, such as friction or braking, taking energy out of the object.
How many joules are in a kilojoule?
One kilojoule is one thousand joules. To convert joules to kilojoules, divide by 1,000.
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