Kinetic Energy Calculator: KE = ½mv²
Solve kinetic energy, mass or speed with KE = ½mv². Use m/s, km/h or mph and joules, kJ or kWh, and see each step. Free and private, runs in your browser.
Fill in all but one field: the empty field is the one you solve for.
About the Kinetic Energy Calculator
The Kinetic Energy Calculator solves KE = ½ m v² for kinetic energy, mass or speed. Enter any two of Kinetic energy, Mass and Speed and the third appears as you type. The page shows the formula in standard notation, highlights the solved symbol and prints a one-line substitution such as ½ × 1,000 kg × (20 m/s)² = 200,000 J.
Kinetic energy is the energy an object has because it is moving. A faster or heavier object carries more of it, and that energy is what has to be removed to stop the object, which is why braking distances and crash forces grow so quickly with speed.
How to use the kinetic energy calculator
Steps
- Fill in two fields and leave the one you want to find empty.
- Choose units. Energy offers J, kJ, kWh, ft·lbf and cal, mass offers kg, g and lb, and speed offers m/s, km/h, mph, ft/s and knots.
- Read the answer under the formula. Change the unit of the empty field to see it in another unit.
- Press Clear all to reset.
Mass must be greater than zero. Kinetic energy and speed cannot be negative, since energy of motion has no direction, and a message appears beside any field that breaks the rule. With all three fields filled, clear one, and with fewer than two the calculator shows a hint.
Formula
KE is kinetic energy in joules, m is mass in kilograms and v is speed in metres per second. Because speed is squared, doubling the speed multiplies the kinetic energy by four, and tripling it multiplies it by nine.
Worked examples
Example 1: find the energy
A 1,000 kg car travels at 20 m/s. Then KE = ½ × 1,000 × 20² = 200,000 J, which is 200 kJ.
Example 2: find the speed
A 1,000 kg car has 200 kJ of kinetic energy. Its speed is v = √(2 × 200,000 ÷ 1,000) = √400 = 20 m/s.
Example 3: find the mass
An object moving at 10 m/s has 50 J of kinetic energy. Its mass is m = 2 × 50 ÷ 10² = 1 kg.
Example 4: speed in km/h
The same 1,000 kg car at 100 km/h, which is 27.78 m/s, carries about 385.8 kJ, nearly twice the energy it had at 20 m/s (72 km/h).
Why speed matters most
Compare two vehicles. Doubling the mass doubles the kinetic energy, but doubling the speed quadruples it. That squared relationship is the reason a small increase in speed greatly increases stopping distance and crash severity.
Kinetic energy is also related to work. The work done by the net force on an object equals its change in kinetic energy, so it takes 200 kJ of work to bring the car in the first example to rest. Try the Work Calculator to find the force needed over a given distance.
Privacy
Nothing is uploaded; every calculation runs in your browser and never leaves your device.
Related tools
The Momentum Calculator handles p = m × v, the Speed Converter turns km/h into m/s before you start, and the Mass Converter helps with pounds and ounces.
Frequently asked questions
What is the kinetic energy formula?
KE = ½ × m × v², where m is mass in kilograms and v is speed in metres per second. The result is in joules.
How do I calculate kinetic energy?
Enter the mass and the speed and leave kinetic energy empty. A 1,000 kg car at 20 m/s has ½ × 1,000 × 20² = 200,000 J, which is 200 kJ.
How do I find speed or mass from kinetic energy?
Fill in kinetic energy and mass to get speed, v = √(2 × KE ÷ m), or kinetic energy and speed to get mass, m = 2 × KE ÷ v². The same car with 200 kJ has a speed of 20 m/s.
Why does doubling the speed quadruple the energy?
Speed is squared in the formula, so twice the speed gives four times the kinetic energy and three times the speed gives nine times. This is why high speeds make crashes so much more severe.
Which units can I use?
Energy offers J, kJ, kWh, ft·lbf and cal. Mass offers kg, g and lb. Speed offers m/s, km/h, mph, ft/s and knots. Each field converts to SI before calculating.
Can kinetic energy or speed be negative?
No. Speed here is a magnitude, and energy of motion has no direction, so both must be zero or greater. Mass must be greater than zero. A message beside the field explains any problem.
Is anything uploaded?
No. The mass, speed and energy you enter are calculated locally in your browser, and nothing is uploaded, stored or shared with a server, so any private test figures stay on your device.