# Frequency Converter

> Converts frequency and rotational speed between hertz (Hz to THz), revolutions per minute, beats per minute, radians per second (angular frequency, ω = 2πf) and degrees per second.

- Calculator id: `frequency` · Category: Unit Conversion (`conversion`) · Tool name: `convert_frequency`
- Canonical page: https://tttkmbb.com/conversion/frequency · This document: https://tttkmbb.com/conversion/frequency.md · JSON definition: https://tttkmbb.com/conversion/frequency.json

## Purpose

Converts frequency and rotational speed between hertz (Hz to THz), revolutions per minute, beats per minute, radians per second (angular frequency, ω = 2πf) and degrees per second.

**Use when:** You need a rate of rotation or oscillation in another unit, e.g. rpm to Hz, GHz to MHz, rad/s to rpm or bpm to Hz.

**Do not use when:** You need wavelength from frequency (use wavelength-frequency), a pendulum's period (use pendulum) or a time interval (use time).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `value` | number |  | required | Amount to convert, expressed in from_unit. |
| `from_unit` | enum: Hz \| kHz \| MHz \| GHz \| THz \| rpm \| bpm \| rad/s \| deg/s |  | required | Unit of the input value. Accepted symbols: Hz, kHz, MHz, GHz, THz, rpm, bpm, rad/s, deg/s; spelled-out names and common abbreviations are accepted too. |
| `to_unit` | enum: Hz \| kHz \| MHz \| GHz \| THz \| rpm \| bpm \| rad/s \| deg/s |  | required | Unit to convert into (same symbols as from_unit). |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `result` | number |  | Converted value expressed in to_unit (rounded to 6 decimals; see result_text for very small or very large values). |
| `result_text` | string |  | The conversion as text with 6 significant figures, e.g. "5 mi = 8.04672 km". |
| `formula` | string |  | Relation used, e.g. "1 mi = 1.609344 km". |
| `factor` | number |  | Multiplier from from_unit to to_unit (result = value × factor); absent for non-linear conversions. |
| `conversion_table` | object |  | The input value expressed in every supported frequency unit (6 significant figures), keyed by unit symbol. |

## Formula

`result = value × factor, factor = (1 from_unit in Hz) / (1 to_unit in Hz)`

1 Hz = 1 cycle per second = 60 rpm = 60 bpm = 2π rad/s = 360 °/s.

## Data Sources

- NIST Special Publication 811 – Guide for the Use of the International System of Units (SI), Appendix B conversion factors — https://www.nist.gov/pml/special-publication-811 (standard, retrieved 2026-09-23)
- BIPM – The International System of Units (SI Brochure, 9th edition) — https://www.bipm.org/en/publications/si-brochure (standard, retrieved 2026-09-23)
- Wikipedia – Conversion of units — https://en.wikipedia.org/wiki/Conversion_of_units (reference, 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/frequency?value=…&from_unit=…&to_unit=…`
- `POST https://tttkmbb.com/api/v1/calculate/frequency` 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/frequency · OpenAPI operationId `convert_frequency` 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": "frequency", "inputs": {…}}`

## Example

- 3000 rpm to hertz: inputs `{"value":3000,"from_unit":"rpm","to_unit":"Hz"}` → `{"result":50,"formula":"1 rpm = 0.01666666667 Hz","conversion_table":{"rad/s":314.159,"kHz":0.05}}`
- 2.4 GHz to MHz: inputs `{"value":2.4,"from_unit":"GHz","to_unit":"MHz"}` → `{"result":2400,"factor":1000,"conversion_table":{"Hz":2400000000,"THz":0.0024}}`

```
GET https://tttkmbb.com/api/v1/calculate/frequency?value=3000&from_unit=rpm&to_unit=Hz
```

## Limitations

You need wavelength from frequency (use wavelength-frequency), a pendulum's period (use pendulum) or a time interval (use time). 1 Hz = 1 cycle per second = 60 rpm = 60 bpm = 2π rad/s = 360 °/s. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**How do rad/s and Hz relate?**

Angular frequency ω = 2πf: 1 Hz = 6.28319 rad/s, and 1 rad/s = 9.5493 rpm.

**Is rpm the same as Hz?**

Both count cycles, per minute versus per second: rpm / 60 = Hz. bpm (beats per minute) converts identically.

## Related

- [Wavelength & Frequency Calculator](https://tttkmbb.com/physics/wavelength-frequency.md) — Wavelength of a wave at this frequency.
- [Angle Converter](https://tttkmbb.com/conversion/angle.md) — Angular units used in rad/s and °/s.
- [Pendulum Period Calculator](https://tttkmbb.com/physics/pendulum.md) — Period and frequency of a pendulum.