Turns to Radians Converter
Convert full turns to radians — one turn is exactly 2π radians. Results update as you type; exact factors shown.
One turn (revolution) is 6.2832 radians — see the exact factor, not a rounded rule of thumb.
How the turns 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.
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 |
|---|---|---|
| 0.125 rev | 0.7854 rad | turn (revolution) to radians |
| 0.25 rev | 1.5708 rad | turn (revolution) to radians |
| 0.5 rev | 3.1416 rad | turn (revolution) to radians |
| 0.75 rev | 4.7124 rad | turn (revolution) to radians |
| 1 rev | 6.2832 rad | turn (revolution) to radians |
| 1.5 rev | 9.4248 rad | turn (revolution) to radians |
| 2 rev | 12.5664 rad | turn (revolution) to radians |
| 3 rev | 18.8496 rad | turn (revolution) to radians |
| 5 rev | 31.4159 rad | turn (revolution) to radians |
| 10 rev | 62.8319 rad | turn (revolution) to radians |
| 100 rev | 628.3185 rad | turn (revolution) to radians |
| 1,000 rev | 6,283.1853 rad | turn (revolution) 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
How many radians in a turn?
2π, about 6.2832.
What is half a turn?
π radians, or 180 degrees.
What is a quarter turn?
π/2, about 1.5708 radians.
Why do some people advocate the turn?
Because 2π appears constantly in trigonometry and physics, and counting in turns removes the factor. It is the argument behind τ.
What is 10 turns?
62.83 radians.
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.