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.
Australia is fully metric under the National Measurement Act 1960; imperial units appear only in trade with the US and in older documents.
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 Measurement Institute (NMI) — Australia's national measurement authority.
Last checked: September 2026. Conversion factors are fixed by definition and do not change with tax years or regulations.