Work and Energy Calculator — W = Fd Explained
Calculate mechanical work done by a force over a distance. Covers W = Fd, angle of force, work-energy theorem, and practical physics examples.
In physics, "work" has a very specific meaning — one that doesn't match everyday usage. Holding a heavy box still? No work done. Carrying that box horizontally? Also no work (in the physics sense, anyway). Work requires a force in the direction of motion. That's the part people often miss.
The CalcHub work and energy calculator handles work calculations including the angle factor, so you get accurate results even for diagonal forces.
The Formula
W = F × d × cos(θ)- W = work done (Joules, J)
- F = applied force (Newtons, N)
- d = displacement (meters, m)
- θ = angle between force and displacement
Work-Energy Theorem
Work done on an object equals its change in kinetic energy:
W_net = ΔKE = ½mv² − ½mu²This is one of the most powerful relationships in mechanics. If you know how much work was done, you know exactly how much kinetic energy changed — no need to track every intermediate step.
Units at a Glance
| Quantity | Unit | Equivalent |
|---|---|---|
| Work | Joule (J) | N·m |
| Energy | Joule (J) | kg·m²/s² |
| Power | Watt (W) | J/s |
Worked Example
You push a 50 kg crate across a floor, applying 200 N of force at a 30° angle downward from horizontal, over a distance of 8 meters.
W = 200 × 8 × cos(30°) = 200 × 8 × 0.866 = 1385.6 J
If friction does −400 J of negative work over that same distance, net work = 1385.6 − 400 = 985.6 J going into kinetic energy.
Can work be negative?
Absolutely. When force and displacement point in opposite directions, the angle θ > 90°, and cos(θ) is negative. Friction always does negative work because it always opposes motion. Brakes do negative work on a car — removing kinetic energy and converting it to heat.
What's the difference between work and energy?
Energy is a property of a system (it has energy stored or in motion). Work is a process — it's the transfer of energy from one system to another via a force. Doing 100 J of work on a box increases that box's energy by 100 J.
Is work a vector or scalar?
Work is a scalar — it has magnitude but no direction. The dot product in the formula (F·d·cosθ) automatically extracts the scalar component of the force along the displacement.