Work Done Calculator (W = F·d·cos θ)

Compute mechanical work from force, displacement, and the angle between them. Result in joules with calorie and foot-pound conversions.

Inputs

In newtons (N).

Distance moved in metres.

Degrees. Use 0° if the force is in the direction of motion.

Result

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General calculation reads

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How to use this calculator

  • Enter the magnitude of the applied force in newtons.
  • Enter the displacement (distance the object moves) in metres.
  • Enter the angle between the force and the displacement. Use 0° when they point the same way.
  • Read work in joules plus calorie and foot-pound conversions.

About this calculator

Work in physics is the energy transferred when a force moves an object along a displacement. Only the component of force along the direction of motion does work, so the formula carries a cos θ factor. Pushing a crate 10 m with 50 N of horizontal force does 500 J. Carrying it 10 m horizontally while pushing straight up does zero work — the force is perpendicular to the motion. Work is measured in joules (1 J = 1 N·m), the same unit as energy. By the work-energy theorem, the net work done equals the change in kinetic energy of the object.

Frequently asked

Why does carrying a heavy bag horizontally do "no work"?+
You apply an upward force, but the bag moves horizontally. The angle between force and displacement is 90°, and cos 90° = 0, so the mechanical work is zero. Your muscles still expend metabolic energy to hold it, but that is biological — not mechanical work in the physics sense.
What does negative work mean?+
Negative work means the force opposes the motion (90° < θ ≤ 180°). Friction during sliding is the classic example — it removes kinetic energy from the moving object.
How does work differ from torque?+
Work is force × distance along the line of motion. Torque is force × perpendicular distance from a pivot, in N·m, but it represents rotational tendency, not energy. Both share the unit but mean different things.
How is work related to energy?+
They share the same unit (joule). Work done on an object equals the energy transferred to it. The work-energy theorem: W_net = ΔKE.
What is a joule in everyday terms?+
Lifting a 100 g apple 1 metre takes about 1 J. A typical AA battery stores ~10 000 J. A nutritional Calorie (kcal) is 4184 J.

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Force Calculator (F = m·a)
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Compute impulse from force and contact time, or use it to find the change in velocity for a given mass.
Torque Calculator
τ = r × F × sin(θ). Rotational force = lever arm × applied force × angle.

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Scope of Work (SOW)
Docs

Detailed work specification — usually attached to a Master Services Agreement or contract.