Work Calculator

What is work in physics?

In physics, work is the energy transferred when a force moves an object through a distance. It is not the everyday sense of effort: holding a heavy box still does no physical work, because nothing moves. Only the part of the force pointing along the direction of motion counts, which is what the cosine term captures.

Here F is the force, d is the distance moved, and θ is the angle between the force and the direction of motion. Work is measured in joules.

How to use this calculator

1. Enter the force value, usually in newtons, into the force field.
2. Enter the distance moved in meters.
3. Enter the angle \(\theta\) between the force and the direction of motion, if the calculator asks for it.
4. Click calculate to get the work in joules.

The formula explained

The formula \(W = F \times d \times \cos\theta\) computes work done by a constant force over a straight-line distance. It adjusts the force by \(\cos\theta\) so only the forward component of the force counts.

• W = work done, in joules \(\text{J}\)
• F = force applied, in newtons \(\text{N}\)
• d = distance moved, in meters \(\text{m}\)
• \(\theta\) = angle between the force and the direction of motion

Step by step method

1. Write down the values for \(F\), \(d\), and \(\theta\).
2. Find \(\cos\theta\). If \(\theta = 0^\circ\), then \(\cos\theta = 1\).
3. Multiply \(F\) by \(d\) and then by \(\cos\theta\).
4. State the answer in joules \(\text{J}\).

Worked example

Problem. A worker pushes a crate with a force of \(50\,\text{N}\) over a distance of \(4\,\text{m}\) at an angle of \(0^\circ\) to the direction of motion. Find the work done.

1. Use the formula \(W = F \times d \times \cos\theta\).
2. Substitute the values, \(W = 50 \times 4 \times \cos 0^\circ\). Since \(\cos 0^\circ = 1\), this becomes \(W = 50 \times 4 \times 1\).
3. Calculate \(W = 200\,\text{J}\).

Tips and common mistakes

• If the force is perpendicular to the motion, then \(\theta = 90^\circ\) and \(\cos 90^\circ = 0\), so the work is \(0\).
• Make sure distance is in meters and force is in newtons before calculating, so the result is in joules.

Frequently asked questions