Kinetic Energy Calculator
The energy of a moving object, ½mv², in joules — and why doubling speed quadruples it.
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Your details
Result
- Kinetic energy
- 96,450.62 J
- In kilojoules
- 96.4506 kJ
- At twice the speed
- 385,802.47 J
- Momentum
- 13,888.89 kg·m/s
1000 kg travelling at 13.8889 m/s
Four times the energy — speed enters the formula squared
Grows only in proportion to speed, unlike energy
1000 kg at 13.8889 m/s…
KE = ½ × m × v²
v² = 13.8889² = 192.9012
½ × 1000 × 192.9012
KE = 96,450.62 J
Formula — written step by step
A 1000 kg car at 50 km/h…
KE = ½ × m × v²
v = 50 km/h = 13.888889 m/s
v² = 192.901235
½ × 1000 × 192.901235
KE = 96,450.62 J
m is mass in kilograms and v speed in metres per second. Speed enters squared, which is the single most important fact about the formula: the same car at 100 km/h carries not twice this energy but four times it.
A worked example
Why stopping distance grows so fast
- Mass
- 1500 kg
- Speed A
- 30 km/h — 8.333 m/s
- Speed B
- 60 km/h — 16.667 m/s
- KE at 30 km/h = ½ × 1500 × 8.333² = 52,083 J
- KE at 60 km/h = ½ × 1500 × 16.667² = 208,333 J
- Ratio = 208,333 ÷ 52,083
Four times the energy for twice the speed
Brakes remove energy at a roughly constant rate, so four times the energy takes about four times the distance. This is why urban speed limits drop in steps that look small: the difference between 30 and 40 km/h is far larger in braking distance than the numbers suggest.
How to use this calculator
- Enter the mass and pick its unit — the calculator converts to kilograms internally.
- Enter the speed and pick its unit. Kilometres per hour and miles per hour are converted to metres per second before the formula is applied.
- Read the energy in joules, or kilojoules for larger figures.
- The "at twice the speed" row is there to make the squaring visible rather than something you have to take on trust.
Energy of motion
Kinetic energy is the work needed to accelerate an object from rest to its current speed — and equally, the work that must be done to bring it back to rest. It is given by half the mass times the square of the speed, and comes out in joules when mass is in kilograms and speed in metres per second.
The squared term is what makes the formula worth understanding rather than merely applying. Mass is linear: double it and you double the energy. Speed is not: double it and the energy quadruples.
Why it matters for safety
Braking systems dissipate energy at a roughly constant rate, so stopping distance tracks kinetic energy rather than speed. A car at 100 km/h carries about eleven times the energy it does at 30 km/h, and needs a correspondingly longer distance to shed it.
The same relationship governs collision severity. Impact energy scales with the square of the closing speed, which is why a modest reduction in speed limits produces a disproportionate reduction in serious injuries.
Momentum is not energy
Momentum, p = mv, and kinetic energy, ½mv², describe the same motion but answer different questions. Momentum is what is conserved in a collision; energy is what determines the damage. Momentum is linear in speed, energy quadratic.
This is why a heavy, slow object and a light, fast one can share the same momentum while carrying very different energies. A 1000 kg car at 10 m/s and a 100 kg motorcycle at 100 m/s both have 10,000 kg·m/s of momentum, but the motorcycle carries ten times the kinetic energy.
Formula & methodology
What this calculator assumes
- Translational motion only. A rotating body also stores ½Iω², which requires its moment of inertia and is not included.
- Newtonian, so it is inaccurate at speeds approaching light. The error is under 1% below about 0.1c.
- Speed is relative to a chosen frame. Kinetic energy is frame-dependent and has no absolute value.
Sources
- Young & Freedman, University Physics, 15th edition, Pearson, 2019 — work and kinetic energy.
Energy of a 1500 kg car at different speeds
| Speed | In m/s | Kinetic energy | Relative to 30 km/h |
|---|---|---|---|
| 30 km/h | 8.33 | 52.1 kJ | 1× |
| 50 km/h | 13.89 | 144.7 kJ | 2.8× |
| 70 km/h | 19.44 | 283.6 kJ | 5.4× |
| 100 km/h | 27.78 | 578.7 kJ | 11.1× |
| 130 km/h | 36.11 | 978.0 kJ | 18.8× |
Speed rises by a factor of just over four across this table; energy rises by a factor of nearly nineteen.
Frequently asked questions
Why is kinetic energy proportional to speed squared?
Because it equals the work done accelerating the object, and work is force times distance. At higher speed the object covers more distance while the same force acts, so the energy accumulates faster than the speed rises.
Does this include rotational energy?
No. This is translational kinetic energy only. A rolling wheel also stores energy in its rotation, given by ½Iω², which requires the moment of inertia.
What is a joule?
The SI unit of energy — the work done by one newton acting over one metre. A joule is small: dropping an apple about a metre releases roughly one.
Can kinetic energy be negative?
No. Mass is positive and speed is squared, so the result is always zero or above. An object moving backwards has the same kinetic energy as one moving forwards at the same speed.