Kinetic Energy Calculator
Solve KE = ½mv² for energy, mass or velocity, with momentum and a curve.
Results update as you type.
About this calculator
Kinetic energy is the energy an object has because it is moving, KE = ½ × m × v², measured in joules. Mass enters linearly but speed is squared, which is the single most important fact about it: doubling the mass doubles the energy, but doubling the speed quadruples it. Choose which quantity to solve for — energy, mass or velocity — and the calculator also returns the linear momentum p = m × v and plots how the energy climbs with speed.
As a worked example, a 2 kg object moving at 3 m/s carries KE = ½ × 2 × 3² = 9 joules and momentum p = 2 × 3 = 6 kg·m/s. Speed it up to 6 m/s and the kinetic energy jumps to ½ × 2 × 36 = 36 J — four times as much for twice the speed — while the momentum only doubles to 12 kg·m/s. Solving in reverse, 9 J in a 2 kg mass implies a speed of √(2 × 9 / 2) = 3 m/s.
The squared-speed relationship explains a lot of the real world: why stopping distances grow so sharply with speed, why a small increase in a car’s velocity greatly raises crash severity, and why wind and water carry so much power at high flow rates. Kinetic energy is central to collisions, ballistics, vehicle safety, roller-coaster design and the energy budgets of everything from pile drivers to turbines.
Frequently asked questions
What is the kinetic energy formula?
Kinetic energy is KE = ½ × m × v², where m is mass in kilograms and v is speed in metres per second. A 2 kg object at 3 m/s has ½ × 2 × 9 = 9 joules.
Why does speed matter more than mass?
Kinetic energy scales with the square of velocity but only linearly with mass, so doubling speed multiplies energy by four while doubling mass only doubles it.
What is the difference between kinetic energy and momentum?
Momentum is p = m × v and scales linearly with speed, while kinetic energy is ½ m v² and scales with speed squared. A 2 kg mass at 3 m/s has 6 kg·m/s of momentum but 9 J of energy; at double the speed momentum doubles but energy quadruples.
How do I find the speed from a known kinetic energy?
Rearrange to v = √(2·KE / m). Set "solve for" to velocity, enter the energy and mass, and the calculator does it — for example 9 J in a 2 kg mass gives √(18 / 2) = 3 m/s.
Why do stopping distances grow so fast with speed?
Brakes remove kinetic energy at a roughly steady rate, and that energy rises with the square of speed. Doubling your speed quadruples the energy to shed, so the braking distance roughly quadruples too.
What units should I use?
Use SI units — mass in kilograms and speed in metres per second — to get energy in joules. If you have km/h, divide by 3.6 to convert to m/s before entering it.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/kinetic-energy/curl
curl "https://calculator.free/api/v1/kinetic-energy/?solve=energy&mass=2&velocity=3"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/kinetic-energy/?" + new URLSearchParams({
"solve": "energy",
"mass": "2",
"velocity": "3"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.