Angle Converter
Convert angles between degrees, radians, gradians, turns, arcminutes, arcseconds, DMS text and mils (NATO 6400, milliradian); normalised, with sin/cos/tan.
The angle in every unit, its degrees-minutes-seconds form, the value reduced to [0, 360) and (−180, 180], and sine, cosine and tangent.
Example: 405.5° is 7.077 rad, 450.56 gon, 1.126 turns and 45.5° after a full turn; 12°34′56.7″ is 12.5824°; 1600 NATO mils is exactly 90°.
Every unit is
a fraction of a turn.
The definitions, how DMS text is read and written, the two mils, and normalisation.
Definitions
One full turn is 360 degrees, 2π radians, 400 gradians (gon), 21 600 arcminutes and 1 296 000 arcseconds; the milliradian is a thousandth of a radian (6283.2 per turn) and the NATO mil is defined as 1/6400 of a turn — a rounding of the milliradian that armies adopted for artillery. Conversion is value ÷ (units per turn) × (target units per turn).
Degrees, minutes, seconds
DMS text is read in the common spellings — 12°34'56.7", 12 34 56.7, 12d 34m 56.7s, 12:34:56.7, with a leading sign or a trailing N/S/E/W — and minutes or seconds of 60 or more are rejected. Output DMS carries the seconds to two decimals and carries over at 60.
Normalisation and trigonometry
Angles beyond a turn are reduced into [0, 360) and into the signed range (−180, 180]; sine, cosine and tangent are computed on the radian value, with tangent left undefined where the cosine is zero. Older mil systems (6000, 6300 per turn) are not included. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- 1 turn = 360° = 2π rad = 400 gon = 21 600′ = 1 296 000″; NATO mil = 1/6400 turn; milliradian = 1/1000 rad; DMS parsed as degrees + minutes/60 + seconds/3600
Last reviewed 21 September 2026. How results are checked: How we verify.