Kinetic Energy Calculator
Kinetic energy is the energy an object possesses by virtue of its motion. The formula KE = 0.5 * m * v² was established in classical mechanics and remains exact for objects moving well below the speed of light. Mass (m) is in kilograms, velocity (v) is in metres per second, and kinetic energy is in joules (J). Because KE depends on the square of velocity, small increases in speed produce large increases in energy: doubling speed quadruples kinetic energy. This is why vehicle braking distances grow rapidly with speed, and why high-energy particle colliders require enormous power to achieve small velocity gains near the speed of light. This calculator has two modes. Mode 1 takes mass and velocity and returns kinetic energy in both joules and kilojoules. Mode 2 reverses the equation: given a kinetic energy value and a mass, it finds the velocity needed to achieve that energy using v = sqrt(2 * KE / m). Both modes update in real time as you type. Results are displayed to two decimal places with thousand separators per standard number-formatting practice.
Kinetic energy: -- J (-- kJ)
How kinetic energy is calculated
The kinetic energy formula is derived from the work-energy theorem: the work done by a net force to accelerate an object from rest to speed v equals 0.5 * m * v². This result holds for classical (non-relativistic) mechanics.
KE = 0.5 × m × v²
where KE = kinetic energy (J), m = mass (kg), v = velocity (m/s)
Reverse: find velocity from KE
v = √(2 × KE / m)
where KE = kinetic energy (J), m = mass (kg), v = velocity (m/s)
Worked example (Mode 1)
A 70 kg person running at 10 m/s:
- KE = 0.5 × 70 × 10² = 0.5 × 70 × 100 = 3,500.00 J
- In kilojoules: 3,500 / 1,000 = 3.50 kJ
Worked example (Mode 2)
Find velocity if KE = 3,500 J and mass = 70 kg:
- v = sqrt(2 × 3,500 / 70) = sqrt(100) = 10.00 m/s
Kinetic energy calculator: frequently asked questions
What is kinetic energy?
Kinetic energy (KE) is the energy an object possesses due to its motion. It is defined as KE = 0.5 * m * v², where m is mass in kilograms and v is speed in metres per second. The SI unit is the joule (J). Kinetic energy is always non-negative because v² is always positive.
How does velocity affect kinetic energy?
Kinetic energy is proportional to the square of velocity. Doubling an object's speed quadruples its kinetic energy. This is why high-speed collisions release far more energy than low-speed ones, and why highway safety margins are much tighter than city-speed ones.
What is the work-energy theorem?
The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W = delta_KE = KE_final - KE_initial. This means applying a net force over a distance changes the object's kinetic energy by exactly the amount of work done.
What is the difference between joules and kilojoules?
A joule (J) is the SI unit of energy, defined as one newton-metre (N m) or one watt-second (W s). A kilojoule (kJ) is 1,000 joules. Everyday energies range from millijoules (insect flight) through kilojoules (food calories, where 1 kcal = 4,184 J) to megajoules (vehicle crashes, explosions).
Can kinetic energy be negative?
No. Because kinetic energy depends on v², which is always zero or positive, and mass is always positive, kinetic energy is always zero or positive. A stationary object has zero kinetic energy. The concept of negative energy appears in potential energy and total mechanical energy, not kinetic energy.
Official sources
- NIST SP 330 (2019) "The International System of Units (SI)": NIST SP 330 PDF.
- NIST SI Unit definitions: nist.gov SI units.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology. General information only.