This kinetic energy calculator solves KE = ½mv² for any one unknown — kinetic energy, mass or velocity. Choose what to find, enter the other two values, and get the answer in joules with unit conversions.
What Is Kinetic Energy?
Kinetic energy is the energy an object has because it is moving. Anything in motion — a thrown ball, a moving car, flowing water, a spinning turbine — carries it, and it must go somewhere when the object slows down (brakes turn it into heat; a hydroelectric dam turns it into electricity). This calculator is part of our Physics Calculators collection; for electrical energy instead, see the Ohms Law Calculator.
The Kinetic Energy Formula
KE = ½ × m × v² — half the mass times the velocity squared, in joules when mass is in kilograms and velocity in meters per second.
Worked example (verified): a 1,000 kg car at 20 m/s (72 km/h, about 45 mph): KE = ½ × 1000 × 20² = 200,000 J = 200 kJ. Solving backwards works too: an object with 5,000 J of kinetic energy and a mass of 10 kg is moving at √(2×5000÷10) = 31.62 m/s.
The Squared Velocity Is the Whole Story
- Double the mass → double the energy. Double the velocity → four times the energy.
- That is why highway crashes are so much deadlier than parking-lot bumps: 60 mph carries 4× the energy of 30 mph, and braking distances scale the same way.
- It is also why wind turbines love windy sites: wind power scales even faster (with v³ through the air’s mass flow).
- Speed conversions: m/s × 3.6 = km/h; m/s × 2.237 ≈ mph.
Everyday Kinetic Energies
| Object | Mass | Speed | KE |
|---|---|---|---|
| Baseball pitch | 0.145 kg | 40 m/s | 116 J |
| Sprinter | 70 kg | 10 m/s | 3,500 J |
| Family car at 45 mph | 1,000 kg | 20 m/s | 200,000 J |
| Family car at 90 mph | 1,000 kg | 40 m/s | 800,000 J |
Related Tools
- Ohms Law Calculator — voltage, current, resistance, power
- Density Calculator — mass, volume and density
Frequently Asked Questions
What is the SI unit of kinetic energy?
The joule (J): 1 J = 1 kg·m²/s². Enter mass in kg and velocity in m/s and the result is in joules.
Why is velocity squared in the formula?
Because work = force × distance: accelerating an object over the distance it takes to reach speed v accumulates energy proportional to v². Energy is also frame-dependent — velocity is measured relative to something, usually the ground.
Can kinetic energy be negative?
No. Mass is positive and v² is always ≥ 0, so KE runs from zero (at rest) upward.
How do I find velocity from kinetic energy?
v = √(2·KE ÷ m). Choose “Velocity” in the solve-for menu above.
What is rotational kinetic energy?
For spinning objects, KE = ½·I·ω², with moment of inertia I and angular velocity ω — a cousin formula this translational calculator does not cover.
Is this kinetic energy calculator free?
Yes — free, instant, no sign-up.