Kinetic Energy Calculator
Calculate kinetic energy from mass and velocity using the formula KE = ½mv². Solve for energy, mass, or velocity with instant unit conversions.
Calculate Kinetic Energy (KE = ½mv²)
Calculation Breakdown
KE = ½ × 10 kg × (20 m/s)²
KE = 0.5 × 10 × 400
KE = 2,000 J
Energy Conversions
Input Values
Kinetic Energy of Common Objects
Reference table showing approximate kinetic energy for various objects in motion. The dramatic increase with velocity demonstrates the v² relationship in the formula.
| Object | Mass | Velocity | Kinetic Energy |
|---|---|---|---|
| Walking person (70 kg) | 70 kg | 1.4 m/s | 69 J |
| Running person (70 kg) | 70 kg | 5 m/s | 875 J |
| Baseball pitch | 0.145 kg | 40 m/s | 116 J |
| Tennis serve | 0.058 kg | 60 m/s | 104 J |
| Cycling (person + bike) | 85 kg | 8 m/s | 2,720 J |
| Car at city speed | 1,500 kg | 14 m/s (50 km/h) | 147,000 J |
| Car at highway speed | 1,500 kg | 31 m/s (112 km/h) | 720,750 J |
| Bullet (9mm) | 0.008 kg | 360 m/s | 518 J |
The Kinetic Energy Formula KE = ½mv²
Kinetic energy is the energy an object possesses due to its motion. Every moving object has kinetic energy, from atoms vibrating in a solid to planets orbiting the sun. The formula KE = ½mv² tells us that kinetic energy depends on both mass and velocity, with velocity having a much greater effect because it is squared.
Kinetic Energy Formulas:
- KE = ½mv² (Kinetic Energy = ½ × Mass × Velocity²)
- m = 2KE/v² (Mass = 2 × Energy ÷ Velocity²)
- v = √(2KE/m) (Velocity = Square root of 2 × Energy ÷ Mass)
Why Is Velocity Squared in the Formula?
The velocity squared term (v²) is what makes kinetic energy increase so dramatically with speed. Doubling an object's speed quadruples its kinetic energy. A car traveling at 100 km/h has four times the kinetic energy of the same car at 50 km/h, even though it's only going twice as fast. This explains why high-speed collisions are so much more destructive.
This squared relationship comes from the physics of work and acceleration. When you accelerate an object, you're doing work on it. The faster it's already moving, the more distance it covers while you push it, so more work is done. This results in the energy scaling with velocity squared rather than linearly.
Kinetic Energy vs. Potential Energy
Kinetic energy is energy of motion; potential energy is stored energy due to position or configuration. A ball held high has gravitational potential energy (PE = mgh). When dropped, that potential energy converts to kinetic energy as the ball accelerates. At the bottom, all potential energy has become kinetic energy. This conservation of mechanical energy is a fundamental physics principle.
Units of Kinetic Energy
The SI unit for kinetic energy is the joule (J), equivalent to kg·m²/s². One joule is the energy transferred when a force of one newton moves an object one meter. Other common units include kilojoules (1 kJ = 1,000 J), calories (1 cal ≈ 4.184 J), and foot-pounds (1 ft·lb ≈ 1.356 J). Our calculator converts between all these units automatically.
Real-World Applications
Understanding kinetic energy has practical applications everywhere. Vehicle safety engineers use it to design crumple zones and airbags. Athletes optimize their technique to maximize kinetic energy in sports like baseball and tennis. Energy companies calculate the kinetic energy in wind and water to design efficient turbines. Even understanding why dropping your phone is worse from higher up involves kinetic energy.
For related physics calculations, explore our potential energy calculator for stored energy, velocity calculator for speed calculations, or work calculator for energy transfer.
Last Updated: January 2026 | Reviewed for accuracy