How to use this calculator
- Enter or choose solve for.
- Enter or choose force unit.
- Enter or choose distance unit.
- Enter or choose work unit.
- Enter or choose angle between force and motion.
- The result updates as you type. Use Copy result or Share to keep it.
Method
W = F d cosθ; F = W ÷ (d cosθ); d = W ÷ (F cosθ)
- W
- work in joules (1 ft·lbf = 1.35582 J)
- F
- force in N
- d
- distance moved in m
- θ
- angle between the force and the direction of motion
Worked example
- With the force along the motion, cos 0° = 1.
- d = W ÷ F = 100 ÷ 50 = 2 m.
A 50 N push does 100 J of work after moving its load 2 m.
What the result means
A force at right angles to the motion does no work, which is why carrying a bag across level ground does no mechanical work on it even though your arms tire. Above 90° the work is negative: the force takes energy out, as friction or braking does.
Assumptions and limits
- Constant force and a straight-line displacement.
- For a varying force, add up F·d over small steps (or integrate) instead.
Questions
What is a joule?
The work done by a 1 N force moving its point of application 1 m. Lifting a 100 g apple 1 m takes about 1 J.
How is work related to power?
Power is work per second. Divide the work by the time taken, or use the Mechanical Power Calculator.