Degrees to Radians Converter
Convert degrees to radians — multiply by π and divide by 180. Results update as you type; exact factors shown.
One degree is 0.0175 radians — see the exact factor, not a rounded rule of thumb.
How the degrees to radians converter works
Angles convert through the radian. A full turn is 2π radians = 360° = 400 gon = 6,400 NATO mils. A degree is 60 arcminutes, an arcminute 60 arcseconds.
The US uses customary units (US gallon, short ton, °F) in daily life; NIST SP 811 gives the exact SI factors.
Common angle conversions
| From | To | Units |
|---|---|---|
| 1 ° | 0.0175 rad | degree to radians |
| 15 ° | 0.2618 rad | degrees to radians |
| 30 ° | 0.5236 rad | degrees to radians |
| 45 ° | 0.7854 rad | degrees to radians |
| 60 ° | 1.0472 rad | degrees to radians |
| 90 ° | 1.5708 rad | degrees to radians |
| 120 ° | 2.0944 rad | degrees to radians |
| 180 ° | 3.1416 rad | degrees to radians |
| 270 ° | 4.7124 rad | degrees to radians |
| 360 ° | 6.2832 rad | degrees to radians |
| 720 ° | 12.5664 rad | degrees to radians |
| 0.5 ° | 0.0087 rad | degrees to radians |
Units in this converter and their exact factors
| Unit | Symbol | One unit in radians |
|---|---|---|
| degree | ° | 0.0174532925 radian |
| radian | rad | 1 radian |
| gradian (gon) | gon | 0.0157079633 radian |
| arcminute | ′ | 0.0002908882 radian |
| arcsecond | ″ | 0.0000048481 radian |
| turn (revolution) | rev | 6.2831853072 radian |
| NATO mil (1/6400 turn) | mil | 0.0009817477 radian |
FAQFrequently asked questions about angle conversion
What is the formula?
radians = degrees × π ÷ 180.
What is 180 degrees in radians?
Exactly π, about 3.14159.
What is a radian?
The angle where the arc length equals the radius — about 57.3°.
Why do calculators need radians?
Because calculus assumes them: the derivative of sin x is cos x only when x is in radians.
What is 90 degrees?
π/2 radians, about 1.5708.
Where these figures come from
- BIPM — The International System of Units (SI Brochure, 9th edition) — definitions of the base and derived units.
- NIST Special Publication 811 — Guide for the Use of the International System of Units — the exact conversion factors used here.
- National Institute of Standards and Technology (NIST) — United States's national measurement authority.
Last checked: September 2026. Conversion factors are fixed by definition and do not change with tax years or regulations.