# Centripetal Force Calculator

> Computes the centripetal (centre-seeking) force and acceleration needed to keep a mass moving in a circle of given radius at a given speed, plus the angular velocity, rotation period and rpm.

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

## Purpose

Computes the centripetal (centre-seeking) force and acceleration needed to keep a mass moving in a circle of given radius at a given speed, plus the angular velocity, rotation period and rpm.

**Use when:** You need the force on a car in a bend, a mass on a string, a satellite or a centrifuge sample from mass, tangential speed and radius, or the g-load of circular motion.

**Do not use when:** You know the angular speed (rpm) rather than the tangential speed (compute v = ω·r first), or the motion is not circular at constant speed.

## 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 along the circular path in metres per second. (> 0) |
| `radius_m` | number | m | required | Radius of the circular path in metres. (> 0) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `centripetal_force_n` | number | N | F = m × v² / r, directed toward the centre. |
| `centripetal_acceleration_m_s2` | number | m/s² | a = v² / r. |
| `acceleration_g` | number | g | Centripetal acceleration in multiples of 9.80665 m/s². |
| `angular_velocity_rad_s` | number | rad/s | ω = v / r. |
| `period_s` | number | s | Time for one revolution, 2π r / v. |
| `rpm` | number | rpm | 60 / period. |

## Formula

`centripetal_acceleration = velocity_m_s² / radius_m; centripetal_force_n = mass_kg × velocity_m_s² / radius_m; ω = velocity_m_s / radius_m; period_s = 2π × radius_m / velocity_m_s; rpm = 60 / period_s`

## Data Sources

- HyperPhysics – Centripetal force — http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html (reference, retrieved 2026-09-23)
- Wikipedia – Centripetal force — https://en.wikipedia.org/wiki/Centripetal_force (reference, retrieved 2026-09-23)
- NIST CODATA – standard acceleration of gravity g_n = 9.80665 m/s² — https://physics.nist.gov/cgi-bin/cuu/Value?gn (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/centripetal-force?mass_kg=…&velocity_m_s=…&radius_m=…`
- `POST https://tttkmbb.com/api/v1/calculate/centripetal-force` 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/centripetal-force · OpenAPI operationId `calculate_centripetal_force` 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:  `run_calculator` with `{"calculator_id": "centripetal-force", "inputs": {…}}`

## Example

- 1200 kg car at 20 m/s in a 50 m bend: inputs `{"mass_kg":1200,"velocity_m_s":20,"radius_m":50}` → `{"centripetal_force_n":9600,"centripetal_acceleration_m_s2":8,"acceleration_g":0.8158,"angular_velocity_rad_s":0.4,"period_s":15.708,"rpm":3.8197}`
- 0.5 kg on a 0.75 m string at 3 m/s: inputs `{"mass_kg":0.5,"velocity_m_s":3,"radius_m":0.75}` → `{"centripetal_force_n":6,"centripetal_acceleration_m_s2":12,"angular_velocity_rad_s":4,"period_s":1.5708,"rpm":38.1972}`

```
GET https://tttkmbb.com/api/v1/calculate/centripetal-force?mass_kg=1200&velocity_m_s=20&radius_m=50
```

## Limitations

You know the angular speed (rpm) rather than the tangential speed (compute v = ω·r first), or the motion is not circular at constant speed. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**What provides the centripetal force?**

Whatever real force points toward the centre: friction for a car in a bend, tension for a string, gravity for a satellite. If that force cannot reach the required value the object leaves the circle.

**Is centrifugal force the same thing?**

Centrifugal force is the apparent outward force felt in the rotating frame; it has the same magnitude as the centripetal force but is not a real force in an inertial frame.

## Related

- [Force Calculator](https://tttkmbb.com/physics/newtons-second-law.md) — Newton's second law in general.
- [Acceleration Calculator](https://tttkmbb.com/physics/acceleration.md) — Linear acceleration from velocity change.
- [Circle Calculator](https://tttkmbb.com/geometry/circle.md) — Circumference of the circular path.