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Degrees to Radians (° to rad)
Convert degrees to radians: 1 ° = 0.0174533 rad. Exact conversion factor, formula, 22-row table and worked examples, with JSON API and MCP access.
Formula
1 ° = 0.0174533 rad
radians = degrees × 0.01745329252 — reverse: degrees = radians × 57.29577951
The factor is derived from the SI definitions of both units (base unit: rad) as listed in NIST SP 811; results on this page are shown to 6 significant figures, the API returns up to 12.
Worked examples
- 5 ° = 0.0872665 rad
- 12.5 ° = 0.218166 rad
- 100 ° = 1.74533 rad
Degrees to radians conversion table
| Degrees (°) | Radians (rad) |
|---|---|
| 1 | 0.0174533 |
| 2 | 0.0349066 |
| 3 | 0.0523599 |
| 4 | 0.0698132 |
| 5 | 0.0872665 |
| 6 | 0.10472 |
| 7 | 0.122173 |
| 8 | 0.139626 |
| 9 | 0.15708 |
| 10 | 0.174533 |
| 15 | 0.261799 |
| 20 | 0.349066 |
| 25 | 0.436332 |
| 30 | 0.523599 |
| 40 | 0.698132 |
| 50 | 0.872665 |
| 75 | 1.309 |
| 100 | 1.74533 |
| 200 | 3.49066 |
| 250 | 4.36332 |
| 500 | 8.72665 |
| 1000 | 17.4533 |
FAQ
How many radians are in one degree?
1 ° = 0.0174533 rad. 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 degrees to radians?
Multiply the value in degrees by 0.01745329252: radians = degrees × 0.01745329252. For example, 5 ° = 0.0872665 rad.
How do I convert radians back to degrees?
Multiply by the inverse factor 57.29577951 (degrees = radians × 57.29577951), or use the radians-to-degrees page.
Related conversions
Machine access
- API:
GET https://tttkmbb.com/api/v1/convert?value=5&from_unit=deg&to_unit=rad - MCP: server
https://tttkmbb.com/mcp, toolconvert_unitswith{"value":5,"from_unit":"deg","to_unit":"rad"} - Markdown: https://tttkmbb.com/conversion/degrees-to-radians.md · JSON: https://tttkmbb.com/conversion/degrees-to-radians.json (add
?value=for a result) · Units: /api/v1/units?quantity=angle - OpenAPI operationId:
convert_units. Freshness:static. Authentication: none.