Angle converter
Convert between angle units: degrees, radians, gradians, turns, arcminutes, arcseconds, milliradians and both the NATO 6400 and Soviet 6000 mil, with a 0–360° normalised angle and a degrees-minutes-seconds breakdown.
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Angle input
Enter a value and pick its unit; every other unit is converted below in one go.
Result
All units
1803.1415932000.5108006480003141.59265432003000180°180° 0′ 0″What this tool does
- Bridge the degrees/radians gap in code: trigonometry wants radians while drawings give degrees, and one input shows both at once.
- Work with mils in surveying or aiming: convert between the NATO 6400 and Soviet 6000 systems, or straight back to degrees.
- Turn a decimal angle into degrees, minutes and seconds (12.3456° → 12°20′44.16″) or merge DMS back into a decimal value.
- Normalise compass or rotation angles: -90° becomes 270°, which removes negative-angle special cases.
Example
Input
Angle value 180, source unit “Degrees (°)”
Output
Degrees 180, radians 3.141593, gradians 200, turns 0.5, arcminutes 10800, arcseconds 648000, milliradians 3141.592654, mil (NATO) 3200, mil (Soviet) 3000, normalised 180°, DMS 180° 0′ 0″
180° is exactly half a turn, so the radian value is π ≈ 3.141593, the NATO mil value is 6400/2 = 3200 and the Soviet mil value is 6000/2 = 3000.
Frequently asked questions
How do degrees and radians relate?
π radians equal 180°, so 1° = π/180 ≈ 0.0174533 rad and 1 rad ≈ 57.29578°. The converter always goes through degrees, which is why any pair of units can be converted in a single step.
Why are there two mil systems?
A mil is a full circle divided into equal parts for aiming and range estimation, but the number of parts differs: NATO countries use 1/6400 of a turn while Russia uses 1/6000. Both are close to one milliradian (1/6283.19 of a turn), yet the numbers are not interchangeable, so they are listed separately.
Where are gradians and turns used?
Gradians (also called gon) split a right angle into 100 parts, so a full turn is 400 — common in European surveying and civil engineering. A turn is simply one full rotation, which is often clearer than degrees when animating rotation.
What about negative or over-360° angles?
Conversion is unrestricted: -90° is -1.570796 rad. On top of that the tool shows a “normalised to 0–360°” row that adds whole turns to land in [0, 360), so -90° becomes 270° and 370° becomes 10°.
Are the arcseconds rounded?
Yes — seconds keep 6 decimal places and the carry is handled properly: 12.99999999999° shows as 13° 0′ 0″ rather than 12° 59′ 60″.
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