🏋️ Work Done Calculator (W = Fd cos θ)

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0° = force along the motion; 90° = at right angles.
Work done (J)
500
Work done (kJ)
0.5
cos θ
1

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📘 About the Work Done

In physics, work is done when a force moves something. The amount of work is the force times the displacement in the direction of the force: W = Fd cos θ. This work done calculator gives the answer in joules.

Only the part of the force along the motion does work. Carrying a bag horizontally at steady speed does no work on the bag (θ = 90°), and friction does negative work (θ = 180°).

🧮 Formula

Work done
W = F d cos θ
Force along the motion
W = F × d

Where

  • W = work (J)
  • F = force (N)
  • d = displacement (m)
  • θ = angle between the force and the displacement
1 joule is the work done when a 1 N force moves its point of application 1 m in the direction of the force.

✏️ Worked examples

Pushing a box 10 m

You enter
Force (F)50 N
Displacement (d)10 m
Angle between force and motion (θ)0 degrees
You get
Work done (J)500
Work done (kJ)0.5
cos θ1

Pushing with 50 N along the floor for 10 m does 500 J of work.

Try this example →

Pulling a suitcase at 60°

You enter
Force (F)50 N
Displacement (d)10 m
Angle between force and motion (θ)60 degrees
You get
Work done (J)250
Work done (kJ)0.25
cos θ0.5

Pulling at 60° to the ground does only 250 J of useful work.

Try this example →

🧭 How to use this calculator

What you enter

  • Force (F) (N)
  • Displacement (d) (m)
  • Angle between force and motion (θ) (degrees)0° = force along the motion; 90° = at right angles.

What you get

  • Work done (J)
  • Work done (kJ)
  • cos θ

💡 Positive, zero and negative work

  • θ between 0° and 90°: positive work (the force speeds the object up).
  • θ = 90°: zero work (e.g. the Moon's orbit, carrying a bag level).
  • θ between 90° and 180°: negative work (e.g. friction, brakes).

❓ Frequently asked questions

What is the formula for work done?

W = F × d × cos θ, where θ is the angle between the force and the displacement.

What is the SI unit of work?

The joule (J), equal to 1 N·m.

When is work done zero?

When there is no displacement, or when the force is at 90° to the motion.

Is work a vector?

No. Work is a scalar: it has size but no direction.