Work Calculator (W = F·d·cos θ)
Work calculator: W = F·d·cos θ. Find the work done by a force, or the force, distance or angle, in joules and other units.
W = F · d · cos θ
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
Mechanical work is the energy transferred by a force acting along a displacement: W = F·d·cos θ, where θ is the angle between the force and the motion.
When the force points along the motion (θ = 0°) all of it does work; at 90° none does. Angles above 90° give negative work, as with friction.
Formula
W = F · d · cos θ
| Symbol | Quantity | Units |
|---|---|---|
| F | Force | N, kN, mN, dyn, lbf, kgf |
| d | Displacement | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
| θ | Angle between force and motion | °, rad, gon, turn, ′, ″, mrad |
| W | Work | J, kJ, MJ, cal, kcal, Wh, kWh, eV, BTU, erg, ft·lbf |
Worked example
Given: F = 10 N · d = 5 m · θ = 60 °
W = F · d · cos θ
Result: W = 25 J
Frequently asked questions
Does carrying a box horizontally do work?
Not against gravity: the lifting force is vertical and the motion horizontal, so θ = 90° and W = 0.
What is one joule?
The work done by a force of 1 N over 1 m.