Angle converter
Degrees, radians, gradians.
1 degree = 0.017453 radians
How it’s calculated
rad = ° × 0.01745329252
- Multiply the value in degrees by 0.01745329252.
- To go back, divide by 0.01745329252 (or multiply by 57.29577951).
- 1 ° = 0.01745329252 rad · 1 rad = 57.29577951 °
Show worked solutionFactor, unit cancellation and rounding, step by step
Find the conversion factor
By definition 1 rad = 57.2957795130823 °. Source: NIST SP 811 / Handbook 44; BIPM SI Brochure (9th ed.) (SI prefixes and accepted units).
Multiply by the factor written as a fraction
Put ° in the denominator so it cancels, leaving rad.
Calculate (unrounded)
Round the answer
Rounded to 5 significant figures.
Answer: 0.017453 rad
1 ° in other units
Batch convert ° → rad
- 1 ° = 0.017453 rad
- 5 ° = 0.087266 rad
- 10 ° = 0.17453 rad
- 25 ° = 0.43633 rad
Common angle conversions
Angle units and exact definitions
| Unit | System | Definition |
|---|---|---|
| Degree (°) | other | 1 ° = 0.01745329252 rad |
| Radian (rad) | SI (metric) | Base unit |
| Gradian (gon) | other | 1 gon = 0.01570796327 rad |
| Arcminute (′) | other | 1 ′ = 0.0002908882087 rad |
| Arcsecond (″) | other | 1 ″ = 0.000004848136811 rad |
| Turn (tr) | other | 1 tr = 6.283185307 rad |
| Milliradian (mrad) | SI (metric) | 1 mrad = 0.001 rad |
Degrees to radians conversion table
| Degrees (°) | Radians (rad) |
|---|---|
| 0.1 ° | 0.0017453 rad |
| 0.5 ° | 0.0087266 rad |
| 1 ° | 0.017453 rad |
| 2 ° | 0.034907 rad |
| 3 ° | 0.05236 rad |
| 4 ° | 0.069813 rad |
| 5 ° | 0.087266 rad |
| 6 ° | 0.10472 rad |
| 7 ° | 0.12217 rad |
| 8 ° | 0.13963 rad |
| 9 ° | 0.15708 rad |
| 10 ° | 0.17453 rad |
| 15 ° | 0.2618 rad |
| 20 ° | 0.34907 rad |
| 25 ° | 0.43633 rad |
| 30 ° | 0.5236 rad |
| 40 ° | 0.69813 rad |
| 50 ° | 0.87266 rad |
| 75 ° | 1.309 rad |
| 100 ° | 1.7453 rad |
| 250 ° | 4.3633 rad |
| 500 ° | 8.7266 rad |
| 1,000 ° | 17.453 rad |
Frequently asked questions
Which angle units can I convert?
degrees (°), radians (rad), gradians (gon), arcminutes (′), arcseconds (″), turns (tr), milliradians (mrad).
How accurate are the results?
Every unit is stored with its exact defining factor (NIST SP 811, NIST Handbook 44 or the BIPM SI Brochure). Calculations use double-precision arithmetic and are rounded only for display, to 5 significant figures by default (trailing zeros dropped, so 1 km shows as 1000 m). You can choose Auto (up to 10 digits), fixed decimals or more significant figures, or switch to scientific or engineering notation.