Kinetic Energy Formula
Kinetic energy is the energy an object possesses due to its motion. It depends on both mass and the square of velocity — doubling speed quadruples kinetic energy.
Formula
KE = ½ × m × v²
m = mass (kg)
v = velocity (m/s)
KE = Joules (J)Worked Examples
Car: m=1500 kg, v=30 m/s (108 km/h)
KE = 0.5 × 1500 × 900 = 675,000 J = 675 kJ
Tennis ball: m=0.057 kg, v=70 m/s (252 km/h serve)
KE = 0.5 × 0.057 × 4900 = 139.7 J
Bullet: m=0.009 kg, v=900 m/s
KE = 0.5 × 0.009 × 810,000 = 3,645 JWhy Speed Matters More Than Mass
Doubling mass: KE × 2
Doubling speed: KE × 4 (squared relationship)
Car at 60 mph vs 120 mph:
4× the KE → 4× longer stopping distance
(not 2× — this surprises most drivers)Unit Conversions
- 1 J = 1 kg·m²/s²
- 1 kJ = 1000 J
- 1 kWh = 3,600,000 J
- 1 BTU = 1055 J
Calculate kinetic energy: Free Kinetic Energy Calculator
Kinetic Energy Quick-Reference Table
| Object | Mass (kg) | Speed (m/s) | KE (J) |
|---|---|---|---|
| Tennis ball | 0.057 | 50 | 71.25 |
| Baseball pitch | 0.145 | 44 | 140.4 |
| Car at 60 km/h | 1,500 | 16.7 | 209,415 |
| Car at 100 km/h | 1,500 | 27.8 | 579,630 |
| Bullet (rifle) | 0.004 | 900 | 1,620 |
How Kinetic Energy Works
Kinetic energy (KE = ½mv²) describes the energy an object has due to its motion. The key insight is that KE scales with the square of velocity — doubling speed quadruples kinetic energy. This is why highway crashes are so much more destructive than parking-lot fender-benders: a car at 100 km/h carries roughly four times the kinetic energy of the same car at 50 km/h.
In engineering, kinetic energy calculations underpin crashworthiness testing, projectile ballistics, wind turbine power output (wind KE converted to electrical energy), and roller-coaster ride design. In sports science, coaches use KE estimates to quantify the impact forces athletes absorb.
Common Mistakes
- Forgetting to halve: The formula is ½mv², not mv². Always divide the mv² product by 2.
- Unit mismatch: Mass must be in kilograms and speed in metres per second for joules. Convert km/h ÷ 3.6 to get m/s.
- Confusing KE with momentum: Momentum = mv (linear); KE = ½mv². They behave differently in collisions.
Frequently Asked Questions
No. KE = ½mv² — both mass and velocity² are always non-negative, so KE ≥ 0. Negative values in a calculation indicate a sign error in velocity, but since velocity is squared the sign cancels out anyway.
The work-energy theorem states that the net work done on an object equals its change in kinetic energy (W = ΔKE). Applying a 100 N force over 2 m does 200 J of work, which — if no friction is present — becomes 200 J of additional kinetic energy.
In thermodynamics, the temperature of a gas is a direct measure of the average translational kinetic energy of its molecules: KE_avg = (3/2)k_B T, where k_B is Boltzmann's constant. Hotter gas = faster-moving molecules = higher average KE per molecule.