Kinetic Energy Calculator
Calculate kinetic energy using KE = ½mv². Enter mass and velocity to find energy in joules, kJ, or kWh. Includes speed doubling examples and crash physics.
Kinetic energy is the energy an object possesses due to its motion. The faster an object moves, or the heavier it is, the more kinetic energy it carries — and the more energy is required to stop it.
Kinetic Energy Formula
KE = ½ × m × v²
Where:
- KE = Kinetic energy in joules (J)
- m = Mass in kilograms (kg)
- v = Velocity in metres per second (m/s)
Example: A 1,000 kg car travelling at 14 m/s (50 km/h / 31 mph):
KE = 0.5 × 1,000 × 14² = 0.5 × 1,000 × 196 = 98,000 J = 98 kJ
Why Velocity Matters More Than Mass
The quadratic relationship between speed and kinetic energy is one of the most important concepts in crash physics — and everyday driving.
Because kinetic energy uses v², doubling speed quadruples kinetic energy:
| Speed | KE (1,000 kg car) | Relative to 30 mph |
|---|---|---|
| 30 mph (13.4 m/s) | 89.8 kJ | 1× |
| 60 mph (26.8 m/s) | 359 kJ | 4× |
| 90 mph (40.2 m/s) | 808 kJ | 9× |
| 120 mph (53.6 m/s) | 1,436 kJ | 16× |
A car at 60 mph doesn't just need twice the braking distance of a car at 30 mph — it needs four times the distance. This is the physics behind speed limit enforcement near schools and pedestrian zones.
Kinetic Energy in Real Scenarios
| Object | Mass | Speed | Kinetic Energy |
|---|---|---|---|
| Tennis ball (serve) | 0.058 kg | 70 m/s (252 km/h) | 142 J |
| 70 kg cyclist | 90 kg total | 8 m/s (29 km/h) | 2,880 J |
| 1,000 kg car | 1,000 kg | 14 m/s (50 km/h) | 98,000 J (98 kJ) |
| 40-tonne lorry | 40,000 kg | 25 m/s (90 km/h) | 12,500,000 J (12.5 MJ) |
| Boeing 747 landing | 300,000 kg | 70 m/s (252 km/h) | 735,000,000 J (735 MJ) |
| Meteorite (small) | 1,000 kg | 20,000 m/s | 200,000,000,000 J (200 GJ) |
Energy Unit Conversions
| Unit | Equivalent | When used |
|---|---|---|
| 1 joule (J) | 1 kg·m²/s² | Physics calculations |
| 1 kilojoule (kJ) | 1,000 J | Cars, machinery |
| 1 megajoule (MJ) | 1,000,000 J | Large vehicles, explosions |
| 1 kilowatt-hour (kWh) | 3,600,000 J | Electricity billing |
| 1 calorie (cal) | 4.184 J | Chemistry (not nutrition) |
| 1 kilocalorie (kcal) | 4,184 J | Food/nutrition labelling |
| 1 BTU | 1,055 J | US heating/cooling |
Example: A 1,500 kg car at 100 km/h has KE = 0.5 × 1,500 × 27.78² = 578,750 J ≈ 579 kJ ≈ 0.161 kWh.
That's the same energy as running a 160W light bulb for one hour — consumed entirely in the braking process.
The Work-Energy Theorem
Kinetic energy and the work done by forces are directly related:
Work done (J) = Change in kinetic energy (J)
W = KE_final − KE_initial
Braking example: A 1,200 kg car brakes from 60 mph (26.8 m/s) to 0:
KE_initial = 0.5 × 1,200 × 26.8² = 430,752 J
KE_final = 0
Work done by brakes = −430,752 J
The brakes must absorb 430 kJ — this energy becomes heat in the brake discs and pads.
Kinetic Energy vs Potential Energy
Kinetic energy (motion) and potential energy (position/height) convert into each other in conservative systems:
Potential energy: PE = m × g × h
(where h = height in metres, g = 9.81 m/s²)
A 70 kg person at the top of a 10-metre diving board:
PE = 70 × 9.81 × 10 = 6,867 J
At the water surface (h = 0), all potential energy has converted to kinetic energy:
KE = 6,867 J → v = √(2 × KE ÷ m) = √(2 × 6,867 ÷ 70) = 14 m/s (50.4 km/h)
Frequently Asked Questions
What happens to kinetic energy when an object stops?
Kinetic energy is converted into other forms. In braking: heat in brake pads and discs. In a collision: deformation energy (crumpling metal), sound, and heat. In friction: heat. Energy is never destroyed — it changes form, per conservation of energy.
Does kinetic energy depend on direction?
No. Kinetic energy is a scalar quantity — it has magnitude but no direction. A car moving north at 60 mph and a car moving east at 60 mph have the same kinetic energy, even though their velocities (vector quantities) are different.
Why is there a ½ in the kinetic energy formula?
The ½ comes from the calculus derivation. Force = ma, and kinetic energy is the work done accelerating from rest: KE = ∫F·dx. Substituting F = ma and using the kinematic relationship v² = 2as gives KE = ½mv². The ½ is exact, not an approximation.
What is rotational kinetic energy?
Objects can also have rotational kinetic energy from spinning: KE_rot = ½ × I × ω², where I is the moment of inertia (kg·m²) and ω is angular velocity (rad/s). A spinning flywheel or a rolling tyre has both translational and rotational kinetic energy.
How does aerodynamic drag relate to kinetic energy?
Aerodynamic drag increases with the square of speed (F_drag ∝ v²). Combined with kinetic energy also increasing as v², fuel consumption from drag increases as v³ — which is why driving at 80 mph uses dramatically more fuel than 60 mph. Reducing speed from 80 to 70 mph cuts drag-related fuel consumption by about 30%.
Related Calculators
- Velocity Calculator — calculate speed, distance, or time
- Force Calculator — Newton's Second Law: F = ma
- Free Fall Calculator — velocity and energy from free fall
- Acceleration Calculator — find acceleration from velocity change