Kinetic Energy Calculator — KE = ½mv²
Calculate kinetic energy from mass and velocity. Understand how speed dominates over mass in KE, with examples from cars, sports, and particle physics.
Here's something that surprises a lot of people: doubling your speed quadruples your kinetic energy. That's not intuitive, but it has enormous real-world consequences — it's why highway crashes are so much more dangerous than parking lot fender-benders, and why speeding is treated so seriously in traffic safety.
The CalcHub kinetic energy calculator makes it easy to see this relationship in action with any mass and velocity values.
The Formula
KE = ½ × m × v²- KE = kinetic energy (Joules, J)
- m = mass (kilograms, kg)
- v = velocity (meters per second, m/s)
Real-World Reference Points
| Object | Mass | Speed | KE |
|---|---|---|---|
| Baseball pitch | 0.145 kg | 40 m/s | ~116 J |
| Cyclist | 85 kg | 8 m/s | ~2,720 J |
| Car at 60 km/h | 1500 kg | 16.7 m/s | ~209,000 J |
| Car at 120 km/h | 1500 kg | 33.3 m/s | ~833,000 J |
How to Use the Calculator
Enter mass (in kg, grams, pounds, or tonnes) and velocity (in m/s, km/h, or mph). The tool handles unit conversion and returns kinetic energy in joules, kilojoules, or calories.
You can also solve backwards: enter KE and mass to find the required velocity, or enter KE and velocity to find mass.
Worked Example
A 0.057 kg tennis ball is served at 200 km/h (55.6 m/s):
KE = 0.5 × 0.057 × 55.6² = 0.5 × 0.057 × 3091.4 = 88.1 J
That's more than enough to cause injury — professional serves have caused wrist and arm fractures when hit at close range.
Why is the formula ½mv² and not just mv²?
It comes from integrating F = ma over distance. When you work through the math of a force accelerating an object from rest, the ½ falls out naturally. It's not a rounding or simplification — it's exact.
Does kinetic energy depend on direction?
No. KE is a scalar quantity. A ball moving at 20 m/s east has the same KE as one moving at 20 m/s west. Direction only matters for vector quantities like momentum.
What happens to kinetic energy when objects collide?
In a perfectly elastic collision, total KE is conserved. In real collisions (inelastic), some KE converts to heat, sound, and deformation. Totally inelastic collisions (objects stick together) lose the maximum possible KE while still conserving momentum.