Kinetic Energy Calculator
Solve KE = ½mv² for energy, mass or speed — in joules, kilojoules, calories or kilowatt-hours — with the rearranged formula shown each way.
KE = ½·m·v²
Kinetic energy
Formula used for this direction
KE = ½·m·v²
Your values
m = 1,200 kg, v = 27 m/s
The Squared Term Is Everything
Kinetic energy is the energy a moving object carries by virtue of its motion: KE = ½·m·v². Mass enters linearly, so doubling the mass doubles the energy. Speed enters quadratically, so doubling the speed quadruples it. Almost every surprising consequence of kinetic energy traces back to that asymmetry.
Rearranged, v = √(2·KE ÷ m) recovers the speed an object needs to carry a given energy, and m = 2·KE ÷ v² gives the mass. This calculator solves all three directions.
Worked example — 30 mph versus 60 mph
A 1,200 kg car at 30 mph (13.41 m/s):
KE = ½ × 1200 × 13.41² = 107,900 J (107.9 kJ)
The same car at 60 mph: 431,700 J (431.7 kJ) — precisely 4 times as much energy for twice the speed.
A second example at the opposite extreme. A 4 gram bullet at 900 m/s carries 1,620 J, while a 70 kg person jogging at 5 m/s carries 875 J. The jogger has more total energy — but spread over a body rather than concentrated on a few square millimetres, which is the whole difference between a nuisance and a wound.
Working backwards: 437,400 J in a 1,200 kg car implies a speed of 27 m/s.
Energy of a 1,200 kg Car by Speed
Each row computed with this page's own function. Watch the final column: energy grows far faster than speed.
| Speed | In m/s | Kinetic energy | Relative to 10 mph |
|---|---|---|---|
| 10 mph | 4.47 | 11.99 kJ | 1× |
| 20 mph | 8.941 | 47.96 kJ | 4× |
| 30 mph | 13.41 | 107.9 kJ | 9× |
| 40 mph | 17.88 | 191.9 kJ | 16× |
| 50 mph | 22.35 | 299.8 kJ | 25× |
| 60 mph | 26.82 | 431.7 kJ | 36× |
| 70 mph | 31.29 | 587.5 kJ | 49× |
Keep going
- Potential and kinetic energy trade back and forth in any falling or swinging system, with the total conserved; the potential energy calculator handles the stored half. Potential Energy Calculator
- Rearranging KE = ½mv² for velocity recovers the speed an object needs to carry a given energy; the velocity calculator works in those terms. Velocity Calculator
Frequently Asked Questions
What is the kinetic energy formula?
KE = ½·m·v², where m is mass in kilograms and v is speed in metres per second, giving energy in joules. The half comes from integrating force over distance as an object accelerates from rest — it is not an arbitrary fudge factor.
Why does doubling speed quadruple kinetic energy?
Because velocity is squared. Doubling v multiplies v² by four. This is the single most consequential fact in road safety: a car at 60 mph carries four times the energy of the same car at 30 mph, and all of it has to be absorbed by something in a crash.
Can kinetic energy be negative?
No. Mass is positive and v² is positive regardless of the sign of v, so kinetic energy is always zero or positive. An object moving backwards has negative velocity and negative momentum, but positive kinetic energy — which is one of the clearest practical differences between the two quantities.
How is kinetic energy related to braking distance?
All of it must be dissipated as heat in the brakes and tyres. Since the work done by a constant braking force is F·d, and that must equal ½mv², the stopping distance d scales with v². Doubling speed roughly quadruples the distance needed to stop, before you even add reaction time.
What is a joule, intuitively?
Roughly the energy of a 100 gram apple dropped one metre. It is a small unit for vehicles — a family car at motorway speed carries several hundred kilojoules — and a large one for molecules, which is why chemistry tends to work in kilojoules per mole.
Related Calculators
- Potential Energy Calculator — Energy, Work & Power
- Work Calculator — Energy, Work & Power
- Acceleration Calculator — Motion & Kinematics
- Velocity Calculator — Motion & Kinematics