Angle Converter
Convert degrees, radians, gradians, arcminutes, arcseconds, turns and mils — for maths, surveying, astronomy and engineering. 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 angle 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 |
|---|---|---|
| 180 ° | 3.1416 rad | degrees to radians |
| 1 rad | 57.2958 ° | radian to degrees |
| 90 ° | 1.5708 rad | degrees to radians |
| 1 rev | 360 ° | turn (revolution) to degrees |
| 100 gon | 90 ° | gradian (gon) to degrees |
| 1 ° | 60 ′ | degree to arcminutes |
| 1 ′ | 60 ″ | arcminute to arcseconds |
| 45 ° | 0.7854 rad | degrees to radians |
| 1 mil | 0.0563 ° | NATO mil (1/6400 turn) to degrees |
| 360 ° | 400 gon | degrees to gradian (gon) |
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
How many degrees is one radian?
57.2958° (180/π).
How many radians is 180 degrees?
π radians ≈ 3.1416.
What is a gradian?
One four-hundredth of a turn (0.9°), used in some surveying and on scientific calculators as "grad".
How many arcseconds are in a degree?
3,600 (60 arcminutes × 60 arcseconds).
What is a mil?
A NATO mil is 1/6,400 of a turn (0.05625°); it is convenient because 1 mil ≈ 1 m at 1,000 m.
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.