Kinetic Energy Calculator
Kinetic energy is the energy of motion, KE = ½mv². Pick what you want to solve for, enter the other two quantities in the units you prefer, and read the answer along with the same values in SI units.
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Formula
KE = ½ × m × v²
- Solve for mass:
m = 2 × KE ÷ v² - Solve for speed:
v = √(2 × KE ÷ m)
All inputs are converted to SI first: 1 lb = 0.45359237 kg, 1 mph = 0.44704 m/s, 1 km/h = 1/3.6 m/s, 1 ft·lbf = 1.3558179 J. The formula is the classical one, valid well below the speed of light.
Worked example
A 1,000 kg car travels at 20 m/s (72 km/h).
- v² = 20 × 20 = 400
- KE = ½ × 1000 × 400 = 200,000 J (200 kJ)
- Momentum = 1000 × 20 = 20,000 kg·m/s
Reversing it: 200,000 J with 1,000 kg gives v = √(2 × 200000 ÷ 1000) = 20 m/s.
Frequently asked questions
What is the kinetic energy formula?
KE = ½ × m × v², with mass m in kilograms and speed v in metres per second, giving joules. A 1,000 kg car at 20 m/s has ½ × 1000 × 400 = 200,000 J, or 200 kJ.
Why does doubling speed quadruple the kinetic energy?
Speed is squared in the formula. The same 1,000 kg car at 40 m/s has ½ × 1000 × 1600 = 800,000 J, four times the energy at 20 m/s, which is why braking distance grows so quickly with speed.
How do I find speed from kinetic energy?
Rearrange to v = √(2 × KE ÷ m). With 200 kJ of energy and a 1,000 kg mass, v = √(2 × 200000 ÷ 1000) = √400 = 20 m/s, which is 72 km/h.
How do I convert kinetic energy to foot-pounds?
One foot-pound-force is exactly 1.3558179 joules, so divide joules by 1.3558179. A 150 lb person moving at 10 mph has about 679.9 J, which is 501.4 ft·lbf.
Does this work at very high speeds?
The formula ½mv² is the classical (non-relativistic) one and is accurate for everyday speeds. This calculator accepts speeds up to 30,000 km/s, 10% of the speed of light, where the error is still under about 1%.