Kinetic Energy Calculator
Calculate kinetic energy, mass, or velocity from the other two quantities and convert the result between common SI, US customary, and electrical-energy units.
KE = ½mv². The calculator uses translational motion and limits velocity to less than 10% of the speed of light, where relativistic corrections remain small.Kinetic energy formulas
For an object of mass m moving at speed v, KE = ½mv². Rearranging gives m = 2KE ÷ v² and v = √(2KE ÷ m). Inputs are converted to kilograms, meters per second, and joules before the selected equation is applied.
Checked examples
| Known values | Calculation | Result |
|---|---|---|
| 1 kg at 10 m/s | KE = ½ × 1 × 10² | 50 J |
| 2 kg at 3 m/s | KE = ½ × 2 × 3² | 9 J |
| 1,000 kg at 72 km/h | 72 km/h = 20 m/s | 200,000 J = 200 kJ |
| 10 lb at 30 mph | Convert mass and speed to SI first | ≈ 407.916 J |
| KE = 100 J; v = 10 m/s | m = 2 × 100 ÷ 10² | 2 kg |
| KE = 450 J; m = 9 kg | v = √(900 ÷ 9) | 10 m/s |
How to use this calculator
- Select kinetic energy, mass, or velocity as the unknown.
- Enter the two known positive quantities.
- Choose the unit beside each quantity, including the desired output unit.
- Calculate to see the result, supporting conversions, momentum, and checked steps.
- Use the mass of the moving object and its speed relative to the chosen reference frame.
Units and limitations
- 1 kJ = 1,000 J; 1 MJ = 1,000,000 J; 1 Wh = 3,600 J; 1 kWh = 3,600,000 J.
- 1 calorie = 4.184 J; 1 kilocalorie = 4,184 J; 1 ft·lbf = 1.355817948 J.
- Velocity is speed magnitude in this scalar calculation; direction does not change kinetic energy.
- Every known input must be finite, greater than zero, and no greater than 10³⁰ in its selected unit.
- Calculated speed must remain below 29,979,245.8 m/s, approximately 10% of light speed. Use relativistic kinetic energy above that range.
- The equation covers translational kinetic energy only. Rotating objects may also have rotational kinetic energy.
Frequently asked questions
Why is velocity squared?
Doubling velocity multiplies kinetic energy by four when mass stays constant, while doubling mass only doubles kinetic energy.
Can kinetic energy be negative?
No. Classical kinetic energy is zero for an object at rest and positive for any nonzero speed.
Is kinetic energy the same as momentum?
No. Momentum is p = mv and includes direction as a vector. Kinetic energy is a scalar proportional to the square of speed.
Does the reference frame matter?
Yes. Speed and therefore kinetic energy depend on the observer’s reference frame.
Related calculators
Use the Scientific Notation Calculator for very large or small values, the Exponent Calculator for squared terms, the Density Calculator to connect mass and volume, the Average Calculator to summarize repeated measurements, or the Pace Calculator for distance, time, and speed.