# What is the kinetic energy?

Computes kinetic energy from mass and speed (KE = ½ m v²), or the mass or speed from the other two, in metric or US units.

- Page: https://www.acalculator.org/physics/kinetic-energy-calculator
- JSON spec: https://www.acalculator.org/physics/kinetic-energy-calculator.json
- Version: b4dae8df968d

## Default answer

Example with the default inputs (Find Kinetic energy, Mass 2,204.62262184878 lb, Speed 55.9234073013601 mph): A mass of 2,204.62 lb at 55.9234 mph has 312,500 J of kinetic energy.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| find | Find | Which value to work out from the other two. |
| m | Mass | The mass of the moving object. |
| v | Speed | How fast the object moves. |
| ke | Kinetic energy | The kinetic energy of the moving object. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| ke | Kinetic energy (J) | The kinetic energy in joules: ½ × mass × speed². |
| kj | Kinetic energy (kJ) | The same energy in kilojoules. |
| ftlbf | Kinetic energy (ft·lbf) | The same energy in foot-pounds. |
| kcal | Kinetic energy (kcal) | The same energy in kilocalories (food Calories). |
| kg | Mass (kg) | The mass in kilograms: 2 × energy ÷ speed². |
| lb | Mass (lb) | The same mass in pounds. |
| mps | Speed (m/s) | The speed in metres per second: √(2 × energy ÷ mass). |
| kmh | Speed (km/h) | The same speed in kilometres per hour. |
| mph | Speed (mph) | The same speed in miles per hour. |

## Method

KE = ½ × m × v²; m = 2 × KE ÷ v²; v = √(2 × KE ÷ m). Mass in kg and speed in m/s give the energy in joules.

## Assumptions

- Classical (Newtonian) mechanics: the speed is below 10% of the speed of light, where KE = ½ m v² is within about 0.75% of the relativistic value.
- The energy is the translational kinetic energy of the whole object; spin (rotational energy) is not included.
- Units are converted with exact factors: 1 lb = 0.45359237 kg, 1 mph = 0.44704 m/s, 1 km/h = 1/3.6 m/s, 1 ft·lbf = 1.3558179483314004 J, 1 kcal = 4,184 J.

## Worked examples

1. find = energy, m = 80, v = 10 gives ke = 4,000, kj = 4. Source: OpenStax, University Physics Volume 1, §7.2 Kinetic Energy, Example 7.6(a): ½ × 80 kg × (10 m/s)² = 4.0 kJ. https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy.
2. find = energy, m = 1,000, v = 25 gives ke = 312,500, kj = 312.5, kmh = 90. Source: OpenStax, University Physics Volume 1, §7.2 Kinetic Energy (K = ½mv²). https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy.
3. find = energy, m = 0.145, v = 40.2336 gives ke = 117.358836, mps = 40.2336. Source: NIST Handbook 44 Appendix C (1 mi = 1,609.344 m). https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy.
4. find = speed, ke = 1,000, m = 20 gives mps = 10, kmh = 36. Source: OpenStax, University Physics Volume 1, §7.2 Kinetic Energy (K = ½mv², so v = √(2K ÷ m)). https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy.
5. find = mass, ke = 450, v = 3 gives kg = 100, lb = 220.462262. Source: OpenStax, University Physics Volume 1, §7.2 Kinetic Energy (K = ½mv², so m = 2K ÷ v²). https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy.

## FAQ

### What is the formula for kinetic energy?

Kinetic energy is KE = ½ × m × v², where m is the mass and v the speed. With the mass in kilograms and the speed in metres per second, the energy is in joules. An 80 kg runner at 10 m/s has ½ × 80 × 10² = 4,000 J, or 4 kJ.

### How do I find speed from kinetic energy?

Rearrange the formula: v = √(2 × KE ÷ m). A 20 kg object with 1,000 J of kinetic energy moves at √(2 × 1,000 ÷ 20) = √100 = 10 m/s.

### How do I find mass from kinetic energy?

Use m = 2 × KE ÷ v². An object with 450 J of kinetic energy at 3 m/s has a mass of 2 × 450 ÷ 9 = 100 kg.

### What happens to kinetic energy when speed doubles?

It goes up four times, because the speed is squared. A car at 50 mph has four times the kinetic energy it has at 25 mph, which is why braking distance grows so fast with speed.

### Can kinetic energy be negative?

No. The mass is positive and the speed is squared, so kinetic energy is zero for an object at rest and positive for any moving object.

### What units is kinetic energy measured in?

The SI unit is the joule: 1 J = 1 kg·m²/s². The page also shows kilojoules, foot-pounds (1 ft·lbf = 1.3558179483314004 J) and kilocalories (1 kcal = 4,184 J).

### When does KE = ½mv² stop working?

Near the speed of light. Below 10% of light speed the classical formula is within 0.75% of the relativistic value. The page gives no answer at or above 10% of light speed (29,979,245.8 m/s).

## Sources

- OpenStax, University Physics Volume 1, §7.2 Kinetic Energy (K = ½mv², Example 7.6). https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy (retrieved 2026-10-01)
- NIST Handbook 44 (2026), Appendix C, General Tables of Units of Measurement: 1 lb = 0.45359237 kg; 1 mi = 1,609.344 m; 1 ft = 0.3048 m. https://www.nist.gov/document/2026-nist-handbook-44-appendix-c (retrieved 2026-10-01)
- NIST SP 811 (2008), Appendix B.8, Factors for Units Listed Alphabetically (1 kcal (thermochemical) = 4,184 J; 1 ft·lbf ≈ 1.355818 J, exactly 0.3048 m × 0.45359237 kg × 9.80665 m/s² = 1.3558179483314004 J). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-01)