Work and Energy Calculator
Work, kinetic energy and potential energy are all measured in joules and convert freely into one another. This calculator handles all three.
Formula
W = F × d · KE = ½mv² · PE = mgh
- Work in joules = force in newtons × distance in metres
- Kinetic energy rises with the square of speed
A 1,200 kg car at 20 m/s holds ½ × 1,200 × 400 = 240,000 J
The Three Formulas
- Work: W = F × d — force times distance moved in the direction of the force
- Kinetic energy: KE = ½mv² — energy of motion
- Gravitational potential energy: PE = mgh — energy of height
All three are in joules. One joule is roughly the work done lifting an apple one metre.
Why Speed Matters More Than Mass
Kinetic energy scales with the square of velocity, which has stark practical consequences.
A 1,500 kg car at 30 m/s carries 675 kJ. The same car at 60 m/s carries 2,700 kJ — four times the energy for twice the speed.
Since braking must dissipate all of it, stopping distance grows with the square of speed too. Doubling your speed roughly quadruples the distance needed to stop.
No Movement, No Work
In physics, holding a heavy box still does zero work, however exhausting it feels. Work requires movement in the direction of the force.
Carrying a box horizontally also does no work against gravity, because the force is vertical and the motion is not. Your muscles burn energy in both cases, but that is biology rather than mechanics.
Quick Reference
| Speed | In km/h | Kinetic energy | Relative |
|---|---|---|---|
| 10 m/s | 36 | 60 kJ | 1× |
| 20 m/s | 72 | 240 kJ | 4× |
| 30 m/s | 108 | 540 kJ | 9× |
| 40 m/s | 144 | 960 kJ | 16× |
Frequently Asked Questions
- What is a joule?
- The work done when a force of one newton moves an object one metre. Roughly the energy needed to lift an apple one metre.
- Why does stopping distance grow so fast with speed?
- Kinetic energy scales with velocity squared. Doubling speed quadruples the energy the brakes must dissipate, so the distance roughly quadruples too.
- Is holding something heavy doing work?
- Not in the physics sense. Work requires movement in the direction of the force, so holding a static load does zero work even though it tires you.
- How are work and energy related?
- Work is energy transferred. Doing work on an object changes its energy, which is why both are measured in joules.