Kinetic Energy Calculator
Calculate kinetic energy, mass, or velocity using KE = ½mv². Select what you want to solve for, enter the other two values, and choose your preferred units.
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Kinetic Energy
Mass
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What Is Kinetic Energy?
Kinetic energy (KE) is the energy an object possesses because of its motion. Any moving object — a car, a thrown ball, a flowing electron — has kinetic energy. The formula for classical (non-relativistic) kinetic energy is:
KE = ½ × m × v²
where m is the mass in kilograms and v is the velocity in meters per second. The result is in joules (J), the SI unit of energy (1 J = 1 kg·m²/s²).
Notice that kinetic energy depends on the square of velocity — doubling the speed quadruples the kinetic energy. This is why highway collisions are so much more dangerous than low-speed fender-benders.
Energy Units Explained
- Joule (J): SI unit. 1 J = 1 kg·m²/s².
- Kilojoule (kJ): 1 kJ = 1000 J. Used for larger energies (food, chemistry).
- Calorie (cal): 1 cal ≈ 4.184 J. The "small calorie" used in chemistry.
- Kilocalorie (kcal): 1 kcal = 4,184 J. The "food calorie" (written Cal with capital C on nutrition labels).
- Electron-volt (eV): 1 eV ≈ 1.602 × 10⁻¹⁹ J. Used in atomic and particle physics.
Kinetic Energy vs. Potential Energy
Kinetic energy (energy of motion) and potential energy (stored energy due to position or configuration) are the two main forms of mechanical energy. The law of conservation of energy states their sum remains constant in a closed system: as an object falls, potential energy converts to kinetic energy. A roller coaster at the top of a hill has maximum potential energy and minimum kinetic energy; at the bottom, the reverse is true.
For half-life and nuclear decay problems where energy is measured in electron-volts, see our Half-Life Calculator. For chemistry problems connecting energy and molar quantities, the Molar Mass Calculator provides the bridge between grams and moles.
Relativistic Note
The formula KE = ½mv² is a classical approximation valid when v is much less than the speed of light (c ≈ 3 × 10⁸ m/s). At velocities approaching c (like the electron example above), relativistic kinetic energy must be used: KE = (γ − 1)mc², where γ = 1/√(1 − v²/c²). This calculator uses the classical formula only.
Frequently Asked Questions
Can kinetic energy be negative?
No. Mass and the square of velocity are both always non-negative, so kinetic energy is always ≥ 0. An object at rest has zero kinetic energy. Negative energy appears in potential energy (below a reference level) but not in kinetic energy.
How does kinetic energy relate to momentum?
Momentum (p) = m × v. Kinetic energy can be written in terms of momentum as KE = p² / (2m). A heavier object and a lighter object with the same momentum have different kinetic energies — the lighter one has more KE. Conversely, if they have the same KE, the heavier one has more momentum.
What is the kinetic energy of a 1,500 kg car at highway speed?
At 100 km/h (≈ 27.78 m/s): KE = ½ × 1500 × (27.78)² ≈ 578,700 J ≈ 579 kJ. For comparison, that's equivalent to about 138 food calories. The speed-squared relationship means that at 140 km/h the KE is nearly twice as large — which explains why braking distance grows so rapidly with speed.
Why does the formula use ½?
The factor of ½ comes from integrating Newton's second law (F = ma) over displacement to derive the work-energy theorem. When you compute W = ∫F·ds = ∫ma·ds and substitute ds = v·dt, you arrive at W = ½mv² − ½mv₀², the change in kinetic energy.
