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Work Calculator

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Work, in physics, is the energy transferred when a force moves an object along a distance. This calculator uses the formula W = F·d·cosθ, where θ is the angle between the force and the direction of motion. Enter the force in newtons, the distance in metres and the angle in degrees, and the result appears instantly in joules and kilojoules. When the force pushes straight along the motion (θ = 0°), all of it does work; at 90° the force does no work at all, because cos 90° = 0.

How this calculator works

  1. 1

    Enter the force

    Type the magnitude of the force in newtons (N), then the distance the object moves in metres (m).

  2. 2

    Enter the angle

    Type the angle in degrees between the force and the direction of motion. Use 0° when they point the same way.

  3. 3

    Read the work done

    The work is shown in joules and kilojoules, recomputed live from W = F·d·cosθ as you change any input.

The formula

The work done by a constant force is:

W = F · d · cos θ

Where:

  • W = work done, in joules (J)
  • F = magnitude of the force, in newtons (N)
  • d = distance moved, in metres (m)
  • θ = angle between the force and the direction of motion, in degrees (°)

One joule equals one newton-metre (1 J = 1 N·m): the work done when a force of 1 N moves an object 1 m in the force’s direction. The cos θ factor extracts only the part of the force that lies along the motion. When θ = 0° the force is fully effective (cos 0° = 1); at θ = 90° it does no work (cos 90° = 0); beyond 90° the work is negative, meaning the force removes energy (as friction does).

Worked example

You push a 20 kg box across a floor with a 50 N force, dragging it 8 m. The rope is angled 30° above the floor, so only the horizontal component does work along the motion:

W = 50 × 8 × cos 30° = 50 × 8 × 0.8660 ≈ 346.4 J ≈ 0.346 kJ

If you instead pushed perfectly horizontally (θ = 0°): W = 50 × 8 × 1 = 400 J. The 30° tilt costs you about 54 J of useful work.

Reference values

Scenario Force (N) Distance (m) Angle (°) Work
Lifting a 10 kg box 2 m straight up 98.1 2 0 ≈ 196 J
Dragging a sled (rope at 30°) 50 8 30 ≈ 346 J
Pushing a cart horizontally 120 5 0 600 J
Carrying a bag while walking 40 10 90 0 J
Braking force against motion 200 6 180 −1,200 J

Common pitfalls

  • Use the angle between force and motion, not from vertical. A rope pulled 30° above the floor while the box slides along the floor has θ = 30°.
  • At 90° the work is zero. Carrying a bag horizontally does no work on it, even though it feels tiring, the lifting force is perpendicular to the motion.
  • Negative work is real. Friction and braking act opposite to motion (θ = 180°, cos = −1), so they do negative work and take energy out.
  • Force in newtons, not kilograms. To lift a mass m, the force is m × 9.81 N (its weight), not the mass itself.

Frequently Asked Questions

Work is W = F·d·cosθ, where F is the force in newtons, d is the distance moved in metres, and θ is the angle between the force and the direction of motion. The result is in joules (J).

Because cos 90° = 0. When the force is perpendicular to the motion, none of it acts along the direction of travel, so it transfers no energy and does no work, like carrying a bag horizontally.

Yes. When the angle is greater than 90° the cosine is negative, so the work is negative. This happens with friction or braking, where the force opposes the motion and removes energy from the object.

The calculator does not upload a file or call an external physics service. Input values can be sent to this site and carried in funnel URLs so the page can calculate and preserve the chosen settings.

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