About the Kinetic Energy Calculator
Kinetic energy is the energy an object has because it is moving. A rolling ball, a flying bullet, a speeding car and the wind all carry kinetic energy, and it has to go somewhere when they stop — into heat, sound, or the work of bending and breaking things. It depends on the object's mass and, even more strongly, on its speed.
This kinetic energy calculator finds kinetic energy from mass and speed, or works backwards to the mass or speed for a given energy. Masses can be in kilograms, grams, tonnes, pounds or ounces, and speeds in m/s, km/h, mph, ft/s or knots. It shows the energy in joules, kilojoules, kilowatt-hours and kilocalories, gives the object's momentum, and shows how the energy would change at double or half the speed.
How to Use the Kinetic Energy Calculator
Choose Find energy, Find mass or Find speed.
Enter the known values and choose their units.
Choose the energy unit for the answer or for the energy you enter.
The Formula
KE = ½ × m × v²
rearranged:
m = 2 KE ÷ v² v = √(2 KE ÷ m)
KE in joules (J), m in kilograms (kg), v in metres per second (m/s)Step-by-Step Examples
A car at 50 km/h. A 1,500 kg car at 50 km/h, which is 13.889 m/s:
KE = ½ × 1,500 × 13.889² = 144,680 J ≈ 144.68 kJThe same car at 100 km/h (27.778 m/s):
KE = ½ × 1,500 × 27.778² = 578,700 JDoubling the speed has multiplied the energy by four.
A bullet. A 10 g bullet at 400 m/s:
KE = ½ × 0.01 × 400² = 800 JSpeed from energy. An object of 0.01 kg with 800 J of energy moves at √(2 × 800 ÷ 0.01) = 400 m/s.
A sprinter. A 70 kg runner at 10 m/s has ½ × 70 × 10² = 3,500 J, about 0.84 kcal.
Why Speed Matters So Much
Because kinetic energy depends on the square of speed, small increases in speed make a large difference. Going from 50 to 60 km/h raises a car's energy by 44 percent; going from 50 to 100 km/h quadruples it. Brakes must remove all of that energy to stop the car, so braking distance also rises with the square of speed — which is why speed limits are lower where people are likely to step into the road, and why crashes at higher speeds are so much more severe. Mass matters too, but only in direct proportion: a car twice as heavy at the same speed has twice the energy.
Kinetic Energy and Work
The work–energy theorem says the work done on an object by the net force equals its change in kinetic energy. To bring a 1,500 kg car from rest to 50 km/h, the engine and tyres must do at least 144,680 J of work on it, more in practice because of air resistance, rolling resistance and drivetrain losses. To stop it, the brakes must do the same amount of negative work, turning the energy into heat in the discs and pads.
Kinetic and Potential Energy
Kinetic energy often trades places with potential energy. A ball thrown upwards slows as its kinetic energy turns into gravitational potential energy; at the top it is momentarily still, and on the way down the potential energy turns back into motion. A pendulum swings back and forth between the two, and a roller coaster converts the potential energy of its first hill into speed. In each case, apart from losses to friction and air resistance, the total stays the same — the principle of conservation of energy.
Kinetic Energy and Momentum
Kinetic energy and momentum both describe motion but behave differently. Momentum, m × v, grows in direct proportion to speed and has a direction; kinetic energy, ½mv², grows with the square of speed and has no direction. A light, fast bullet and a heavy, slow lorry can have similar momentum but very different energies. In collisions, momentum is always conserved, while kinetic energy usually is not, because some of it is converted into heat, sound and deformation.
Units of Energy
The joule is the SI unit: the kinetic energy of a 2 kg mass moving at 1 m/s. Larger amounts use kilojoules and megajoules. The kilowatt-hour, 3.6 million joules, is used for electricity, and the kilocalorie, 4,184 joules, for food energy. The calculator converts between them so that you can compare the energy of a moving object with everyday quantities.
Rotational Kinetic Energy
Spinning objects also carry kinetic energy, even if they are not moving from place to place. A spinning flywheel, a turning wheel or the rotating Earth all store energy in their rotation. A rolling wheel has both kinds at once, which is why a rolling ball accelerates down a slope more slowly than a sliding block would on a frictionless surface.
Understanding Your Result
The headline is the kinetic energy, mass or speed you asked for.
The energy in other units line gives the energy in J, kJ, kWh and kcal.
The mass, speed and momentum line restates the values in SI units, with momentum.
The speed matters line shows the energy at double and half the speed.
When Should You Use This Calculator?
Use it for physics homework on energy and motion.
Use it to see how speed affects braking and crash energy.
Use it to compare the energy of vehicles, projectiles and athletes.
Common Mistakes
Forgetting to square the speed. KE uses v², not v.
Using km/h directly. Convert to m/s by dividing by 3.6; the calculator does it for you.
Using grams for kilograms. The formula needs mass in kilograms for joules.
Leaving out the half. Kinetic energy is ½mv², not mv².