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 UK is metric for most trade and science but keeps miles, pints, stone and mpg (with the imperial gallon) in daily life.
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 Physical Laboratory (NPL) — United Kingdom's national measurement authority.
Last checked: September 2026. Conversion factors are fixed by definition and do not change with tax years or regulations.