What is being measured?
An angle can be represented in radians, degrees or turns. Trigonometric formulas must use the angular convention expected by the function.
Convert compatible measurements of the same quantity. A unit conversion does not infer a new physical property.
Meaning of °
degrees uses the symbol ° in this library and measures angle. Under the stated reference convention, 1 ° = approximately 0.0174532925199 rad. This equivalence changes how a known value is written. It does not increase measurement accuracy or establish whether a measurement is appropriate to a real application.
Conversion method
Multiply the value by the source factor (0.017453292519943295), then divide by the target factor (1). The factor ratio expresses the same angle measurement in the other unit.
Worked example
For a known value of 10 °, the reference conversion gives 0.174532925199 rad. Converting that result back gives approximately 10 °. This reverse check helps catch a reversed factor, but matching round-trip arithmetic alone does not independently verify a source definition.
Common reference values
| Input (°) | Reference equivalent (rad) |
|---|---|
| 1 | 0.0174532925199 |
| 5 | 0.0872664625997 |
| 10 | 0.174532925199 |
| 25 | 0.436332312999 |
| 50 | 0.872664625997 |
| 100 | 1.74532925199 |
Compare one ° with other units
| Target unit | Equivalent of 1 ° | Definition guide |
|---|---|---|
| radians (rad) | 0.0174532925199 | Read definition |
| gradians (gon) | 1.11111111111 | Read definition |
| turns (rev) | 0.00277777777778 | Read definition |
| arcminutes (′) | 60 | Read definition |
| arcseconds (″) | 3600 | Read definition |
Precision and common mistakes
- Keep the source and target quantity consistent. A matching symbol is not enough to establish a compatible definition.
- Record the original measurement precision. Showing twelve significant digits in a table does not make a rounded input more precise.
- Check symbol capitalization, prefixes and any regional convention in the source. Use the displayed unit definition rather than a similarly named unit.
- Factors involving repeating fractions or π use finite numerical precision. Round the final answer to the precision justified by your input.
Use a working converter
- Angle converter
- Degrees to gradians converter
- Degrees to arcminutes converter
- Degrees to arcseconds converter
- Degrees to turns converter
- Degrees to radians converter
Source and verification scope
Examples and tables are computed from the versioned unit definitions used by the linked converters. The source access dates appear below. Computandum is independent of the cited organizations; a citation does not mean that a publisher endorses this page or an actual project.
Sources
- NIST / BIPM: NIST: unit conversion factors ↗ · 2026-10-08