# Kinetic Energy Calculator

> Computes the translational kinetic energy of a moving mass from KE = ½·m·v², reported in joules, kilojoules, kilowatt-hours and kilocalories.

- Calculator id: `kinetic-energy` · Category: Physics (`physics`) · Tool name: `calculate_kinetic_energy`
- Canonical page: https://tttkmbb.com/physics/kinetic-energy · This document: https://tttkmbb.com/physics/kinetic-energy.md · JSON definition: https://tttkmbb.com/physics/kinetic-energy.json

## Purpose

Computes the translational kinetic energy of a moving mass from KE = ½·m·v², reported in joules, kilojoules, kilowatt-hours and kilocalories.

**Use when:** You need the energy of motion of an object of known mass and speed (vehicle, projectile, ball), for example to compare impact or braking energies.

**Do not use when:** Rotation contributes significantly (rotational energy ½·I·ω² is not included), speeds approach the speed of light (relativistic formula needed), or you need energy from height (use potential-energy).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `mass_kg` | number | kg | required | Mass of the moving object in kilograms. (> 0) |
| `velocity_m_s` | number | m/s | required | Speed in metres per second (km/h ÷ 3.6, mph × 0.44704). Limited to 10 % of the speed of light, below which the classical formula is accurate to within 1 %. (min 0, max 30000000) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `kinetic_energy_j` | number | J | KE = ½ × m × v². |
| `kinetic_energy_kj` | number | kJ | Kinetic energy in kilojoules. |
| `kinetic_energy_kwh` | number | kWh | Kinetic energy in kilowatt-hours (J ÷ 3,600,000). |
| `kinetic_energy_kcal` | number | kcal | Kinetic energy in kilocalories (thermochemical, J ÷ 4184). |
| `velocity_km_h` | number | km/h | The input speed in km/h. |

## Formula

`KE = ½ × mass_kg × velocity_m_s²; kJ = J / 1000; kWh = J / 3,600,000; kcal = J / 4184`

## Data Sources

- HyperPhysics – Kinetic energy — http://hyperphysics.phy-astr.gsu.edu/hbase/ke.html (reference, retrieved 2026-09-23)
- Wikipedia – Kinetic energy — https://en.wikipedia.org/wiki/Kinetic_energy (reference, retrieved 2026-09-23)
- NIST Special Publication 811 – Guide for the Use of the SI, Appendix B (conversion factors) — https://www.nist.gov/pml/special-publication-811 (standard, retrieved 2026-09-23)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/kinetic-energy?mass_kg=…&velocity_m_s=…`
- `POST https://tttkmbb.com/api/v1/calculate/kinetic-energy` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/kinetic-energy · OpenAPI operationId `calculate_kinetic_energy` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool: `calculate_kinetic_energy` (dedicated) or `run_calculator` with `{"calculator_id": "kinetic-energy", "inputs": {…}}`

## Example

- 1200 kg car at 25 m/s (90 km/h): inputs `{"mass_kg":1200,"velocity_m_s":25}` → `{"kinetic_energy_j":375000,"kinetic_energy_kj":375,"kinetic_energy_kwh":0.104167,"kinetic_energy_kcal":89.6272,"velocity_km_h":90}`
- 0.145 kg baseball at 40 m/s: inputs `{"mass_kg":0.145,"velocity_m_s":40}` → `{"kinetic_energy_j":116,"kinetic_energy_kj":0.116,"velocity_km_h":144}`

```
GET https://tttkmbb.com/api/v1/calculate/kinetic-energy?mass_kg=1200&velocity_m_s=25
```

## Limitations

Rotation contributes significantly (rotational energy ½·I·ω² is not included), speeds approach the speed of light (relativistic formula needed), or you need energy from height (use potential-energy). All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why does doubling the speed quadruple the energy?**

Kinetic energy scales with the square of speed (v²), which is why braking distance and crash severity rise much faster than speed.

**Does direction matter?**

No. Kinetic energy is a scalar; only the magnitude of the velocity (speed) enters the formula.

## Related

- [Momentum Calculator](https://tttkmbb.com/physics/momentum.md) — Momentum p = m·v of the same object.
- [Potential Energy Calculator](https://tttkmbb.com/physics/potential-energy.md) — Energy stored by height, exchanged with kinetic energy in free fall.
- [Work & Power Calculator](https://tttkmbb.com/physics/work-power.md) — Work needed to produce this energy change.