# Centrifuge RCF / RPM Converter

> Converts between rotor speed (rpm) and relative centrifugal force (RCF, in multiples of g) for a given rotor radius with RCF = 1.118 × 10⁻⁵ × r_cm × rpm², solving whichever of the two is not given.

- Calculator id: `centrifuge-rcf-rpm` · Category: Biology, Earth & Space (`science`) · Tool name: `convert_centrifuge_rcf_rpm`
- Canonical page: https://tttkmbb.com/science/centrifuge-rcf-rpm · This document: https://tttkmbb.com/science/centrifuge-rcf-rpm.md · JSON definition: https://tttkmbb.com/science/centrifuge-rcf-rpm.json

## Purpose

Converts between rotor speed (rpm) and relative centrifugal force (RCF, in multiples of g) for a given rotor radius with RCF = 1.118 × 10⁻⁵ × r_cm × rpm², solving whichever of the two is not given.

**Use when:** A protocol specifies a centrifugation force in ×g and you need the rpm for your rotor, or you know the rpm and radius and need the force applied to the sample.

**Do not use when:** You need the centripetal force in newtons on a specific mass (use centripetal-force), or sedimentation times and k-factors of ultracentrifuge rotors.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `rpm` | number | rpm | optional | Revolutions per minute. Give rpm or rcf_g, not both. (> 0, max 200000) |
| `rcf_g` | number | ×g | optional | Force in multiples of standard gravity (×g). Give rcf_g or rpm, not both. (> 0, max 2000000) |
| `radius_cm` | number | cm | required | Distance from the rotor axis to the point of interest in the tube (r_max = bottom of the tube, r_min = top; protocols usually mean r_max or r_average). (> 0, max 100) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `rcf_g` | number | ×g | 1.118 × 10⁻⁵ × radius_cm × rpm². |
| `rpm` | number | rpm | √(rcf_g / (1.118 × 10⁻⁵ × radius_cm)). |
| `radius_cm` | number | cm | Rotor radius the conversion refers to. |
| `angular_velocity_rad_s` | number | rad/s | rpm × 2π / 60. |
| `note` | string |  | Which quantity was solved and how the radius affects the result. |

## Formula

`RCF (×g) = 1.118 × 10⁻⁵ × radius_cm × rpm²; rpm = √(RCF / (1.118 × 10⁻⁵ × radius_cm)); ω = 2π × rpm / 60`

RCF = ω² r / g with g = 9.80665 m/s², which reduces to the 1.118 × 10⁻⁵ constant for r in cm and speed in rpm. Because RCF is proportional to the radius, the same rpm gives different forces at the top and bottom of a tube; use the radius your protocol refers to (usually r_max).

## Data Sources

- Wikipedia – Centrifuge — https://en.wikipedia.org/wiki/Centrifuge (reference, retrieved 2026-09-24)
- Wikipedia – Centrifugation — https://en.wikipedia.org/wiki/Centrifugation (reference, retrieved 2026-09-24)

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/centrifuge-rcf-rpm?radius_cm=…`
- `POST https://tttkmbb.com/api/v1/calculate/centrifuge-rcf-rpm` 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/centrifuge-rcf-rpm · OpenAPI operationId `convert_centrifuge_rcf_rpm` 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": "centrifuge-rcf-rpm", "inputs": {…}}`

## Example

- 3,000 rpm at 10 cm radius: inputs `{"rpm":3000,"radius_cm":10}` → `{"rcf_g":1006.2,"rpm":3000,"angular_velocity_rad_s":314.16}`
- 1,000 ×g needed at 8 cm radius: inputs `{"rcf_g":1000,"radius_cm":8}` → `{"rpm":3344,"rcf_g":1000}`

```
GET https://tttkmbb.com/api/v1/calculate/centrifuge-rcf-rpm?rpm=3000&radius_cm=10
```

## Limitations

You need the centripetal force in newtons on a specific mass (use centripetal-force), or sedimentation times and k-factors of ultracentrifuge rotors. RCF = ω² r / g with g = 9.80665 m/s², which reduces to the 1.118 × 10⁻⁵ constant for r in cm and speed in rpm. Because RCF is proportional to the radius, the same rpm gives different forces at the top and bottom of a tube; use the radius your protocol refers to (usually r_max). All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why do protocols give ×g instead of rpm?**

The force on the sample depends on both speed and rotor radius, so only RCF (×g) is transferable between centrifuges; convert it to rpm with your rotor's radius.

**Which radius should I use?**

The maximum radius (bottom of the tube) is the usual reference for pelleting; some manufacturers quote the average radius. Check the rotor specification sheet.

**Where does 1.118 × 10⁻⁵ come from?**

RCF = ω² r / g with ω = 2π × rpm / 60 and r in metres; converting r to centimetres and dividing by 9.80665 m/s² gives (2π/60)² / (100 × 9.80665) = 1.118 × 10⁻⁵.

## Related

- [Centripetal Force Calculator](https://tttkmbb.com/physics/centripetal-force.md) — Centripetal force and acceleration in newtons and m/s² for a mass at that radius.
- [Hemocytometer Cell Count Calculator](https://tttkmbb.com/science/hemocytometer-count.md) — Count the cells after pelleting and resuspending.
- [Frequency Converter](https://tttkmbb.com/conversion/frequency.md) — Convert rpm to hertz or radians per second.