The kinetic energy formula
Kinetic energy is the energy of motion: KE = ½·m·v², where m is mass in kilograms and v is velocity in meters per second. A 10 kg mass at 5 m/s has ½ × 10 × 25 = 125 J. Because velocity is squared, doubling the speed quadruples the energy. Find the speed first with the velocity calculator.
The formula comes from the work needed to accelerate an object from rest. Force multiplied by distance, worked through the equations of motion, collapses neatly to one-half mass times speed squared — and that same quantity is what must be removed again to bring the object back to a stop.
How to use this calculator
Enter the mass in kilograms and the velocity in meters per second. The result is in joules (J), the SI unit of energy. One joule is the work done by a force of one newton over one meter. Energy is always positive regardless of direction.
Kinetic energy is a scalar, so a negative velocity gives exactly the same answer as the matching positive one — the squaring removes the sign. That is the key difference from momentum, which keeps its direction. Use the momentum calculator when direction matters.
Why speed matters so much
The v² term is why high-speed impacts are so dangerous — a car at 40 m/s carries four times the kinetic energy it has at 20 m/s. Kinetic energy connects to force through work and motion; you can explore forces with the force calculator.
The same squaring explains braking distances. Stopping takes work, and work is force times distance, so twice the speed needs roughly four times the distance to shed the energy.
Frequently asked questions
- How do I calculate kinetic energy?
- Multiply one-half by mass and by velocity squared: KE = ½·m·v². For 10 kg at 5 m/s it is 125 J.
- What unit is kinetic energy measured in?
- Joules (J) in SI units, where 1 J = 1 kg·m²/s².
- Why is velocity squared in the formula?
- Because energy grows with the square of speed — doubling speed gives four times the kinetic energy.
- Can kinetic energy be negative?
- No. Mass is positive and velocity is squared, so kinetic energy is always zero or positive.
- What if my speed is in km/h or mph?
- Convert it to metres per second first, or the answer will be badly wrong. Divide km/h by 3.6, or multiply mph by 0.44704. Mass must likewise be in kilograms.