# Radians to Degrees (rad to °)

> Convert radians to degrees: 1 rad = 57.2958 °. Exact conversion factor, formula, 22-row table and worked examples, with JSON API and MCP access.

- Page id: `radians-to-degrees` · Quantity: Angle (`angle`, base unit rad) · Tool: `convert_units`
- Canonical page: https://tttkmbb.com/conversion/radians-to-degrees · This document: https://tttkmbb.com/conversion/radians-to-degrees.md · JSON: https://tttkmbb.com/conversion/radians-to-degrees.json (add `?value=` for a result)

## Formula

- `1 rad = 57.2958 °`
- `degrees = radians × 57.29577951`
- Reverse: `radians = degrees × 0.01745329252`

The factor follows from the SI definitions of both units (NIST SP 811); values below are rounded to 6 significant figures, the API returns up to 12.

## Worked examples

- 5 rad = 286.479 °
- 12.5 rad = 716.197 °
- 100 rad = 5729.58 °

## Conversion table

| Radians (rad) | Degrees (°) |
| --- | --- |
| 1 | 57.2958 |
| 2 | 114.592 |
| 3 | 171.887 |
| 4 | 229.183 |
| 5 | 286.479 |
| 6 | 343.775 |
| 7 | 401.07 |
| 8 | 458.366 |
| 9 | 515.662 |
| 10 | 572.958 |
| 15 | 859.437 |
| 20 | 1145.92 |
| 25 | 1432.39 |
| 30 | 1718.87 |
| 40 | 2291.83 |
| 50 | 2864.79 |
| 75 | 4297.18 |
| 100 | 5729.58 |
| 200 | 11459.2 |
| 250 | 14323.9 |
| 500 | 28647.9 |
| 1000 | 57295.8 |

## API

- `GET https://tttkmbb.com/api/v1/convert?value=5&from_unit=rad&to_unit=deg` → unified JSON envelope with `result.values.result`, `formula`, `factor`, `sources`, `freshness`
- MCP: server `https://tttkmbb.com/mcp`, tool `convert_units` with `{"value":5,"from_unit":"rad","to_unit":"deg"}`
- All angle units: https://tttkmbb.com/api/v1/units?quantity=angle · full converter: [Angle Converter](https://tttkmbb.com/conversion/angle.md)
- Authentication: none. Freshness: `static` (fixed conversion factors).

## FAQ

**How many degrees are in one radian?**

1 rad = 57.2958 °. The factor comes from the SI definitions of both units (NIST SP 811 / BIPM), so it is exact or correct to at least 10 significant figures.

**What is the formula to convert radians to degrees?**

Multiply the value in radians by 57.29577951: degrees = radians × 57.29577951. For example, 5 rad = 286.479 °.

**How do I convert degrees back to radians?**

Multiply by the inverse factor 0.01745329252 (radians = degrees × 0.01745329252), or use the degrees-to-radians page.

## Related conversions

- [Degrees to radians](https://tttkmbb.com/conversion/degrees-to-radians.md) (reverse)
- [Gradians to Degrees](https://tttkmbb.com/conversion/gradians-to-degrees.md)
- [Degrees to Gradians](https://tttkmbb.com/conversion/degrees-to-gradians.md)
- [Turns (revolutions) to Degrees](https://tttkmbb.com/conversion/turns-to-degrees.md)
- [Degrees to Turns (revolutions)](https://tttkmbb.com/conversion/degrees-to-turns.md)
- [Arcminutes to Degrees](https://tttkmbb.com/conversion/arcminutes-to-degrees.md)
- [Degrees to Arcminutes](https://tttkmbb.com/conversion/degrees-to-arcminutes.md)
- [Milliradians to Degrees](https://tttkmbb.com/conversion/milliradians-to-degrees.md)
- [Degrees to Milliradians](https://tttkmbb.com/conversion/degrees-to-milliradians.md)

## 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 2026-09-24)
- BIPM – The International System of Units (SI Brochure, 9th edition) — https://www.bipm.org/en/publications/si-brochure (standard, retrieved 2026-09-24)
- Wikipedia – Conversion of units — https://en.wikipedia.org/wiki/Conversion_of_units (reference, retrieved 2026-09-24)