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.
Result
Work done
500.000 J
- cos θ1.0000
- In calories119.503 cal
- In foot-pounds368.781 ft·lb
Step-by-step
- W = F × d × cos(θ).
- cos(0°) = 1.0000.
- W = 50 N × 10 m × 1.0000 = 500.000 J.
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
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.
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