This work calculator solves the physics definition of work, W = F × d × cosθ — the energy transferred when a force moves something. Find work, force or distance, with the force’s angle accounted for.
What Is Work in Physics?
In physics, work is energy transferred by a force acting through a distance: W = F × d × cosθ, measured in joules. It is a stricter idea than everyday “effort”: holding a heavy box still does no physical work on the box (no distance), and carrying it level at constant height does none either (force is vertical, motion horizontal, θ = 90°, cosθ = 0). Only the force component along the motion counts. The force itself comes from our Force Calculator; this tool is part of our Physics Calculators collection.
Worked Examples (Verified)
- Pushing a crate: 100 N over 5 m in the push direction → W = 100 × 5 = 500 J.
- Same push at 60° to the motion: only cos60° = half the force counts → 250 J. Angled effort is wasted effort.
- Lifting a 10 kg box 2 m: the force must equal its weight (10 × 9.81 = 98.1 N), so W = 98.1 × 2 ≈ 196 J — now stored as gravitational potential energy.
The Work–Energy Theorem
The net work done on an object equals its change in kinetic energy: Wnet = ΔKE. Push a frictionless crate with 500 J of net work and it gains exactly 500 J of kinetic energy — compute that side with the Kinetic Energy Calculator. Friction complicates the bookkeeping by diverting work into heat, which is why real pushing takes more work than the theorem’s ideal version. Power, the rate of doing work, is simply work ÷ time — the concept behind wattage and horsepower.
Related Tools
- Force Calculator — F = ma
- Kinetic Energy Calculator — where work ends up
- Physics Calculators — the full collection
Frequently Asked Questions
What is the formula for work?
W = F × d × cosθ, where θ is the angle between the force and the direction of motion. When force and motion align, cosθ = 1 and W = F × d.
What is the unit of work?
The joule (J): one newton of force acting through one meter. A kilojoule is 1,000 J; a food Calorie is 4,184 J.
Can work be negative?
Yes — when force opposes motion (θ > 90°), as friction and braking do. Negative work removes kinetic energy from the object.
Why does holding a heavy object do no work?
Because work requires displacement. No movement, no work on the object — your muscles tire from internal processes, not from transferring energy to the box.
What is the difference between work and power?
Work is the total energy transferred; power is how fast (work ÷ time, in watts). Carrying bricks upstairs slowly or quickly does the same work at different power.
Is this work calculator free?
Yes — free, instant, no sign-up. It is the physics work calculator (W = Fd), not an employment or hours calculator.