Angle Converter
Degrees, radians, gradians, DMS, turns and mils, with trig values.
About this tool
Type an angle in any unit, or paste a degrees-minutes-seconds value such as 12° 34′ 56″. Every other unit updates, along with the angle normalised to 0–360°, its reference angle and its sine, cosine and tangent.
Angle units
A full turn is 360 degrees, 2π radians, 400 gradians or 1 turn. Radians are the natural unit in mathematics and physics: one radian is the angle whose arc equals the radius, about 57.296°, so degrees × π ÷ 180 gives radians. 45° is π/4, about 0.7854 rad, or 50 gradians. Gradians (also called gon) make a right angle exactly 100 and are used in some surveying. For navigation, astronomy and geographic coordinates, degrees are split into 60 arcminutes and each arcminute into 60 arcseconds, written in DMS form: 12.5824° is 12° 34′ 56.6″. Military mils divide a turn into 6,400, so 1 mil subtends about 1 m at 1 km. The tool also normalises any angle to 0–360°, gives its reference angle (the acute angle to the x-axis, used for trig) and its sine, cosine and tangent. Honest limits: some armies use 6,000 or 6,300 mils per turn, and values are rounded to 10 significant figures. The unit circle and the coordinate converter are related.
Frequently asked questions
How do I convert degrees to radians?
Multiply by π ÷ 180. 90° = π/2 ≈ 1.5708 radians.
How many degrees is one radian?
About 57.2958°.
How do I convert decimal degrees to DMS?
The whole number is degrees; multiply the decimal part by 60 for minutes, then multiply that decimal part by 60 for seconds.
What is a gradian?
1/400 of a full turn, so a right angle is 100 gradians.
Is my data sent anywhere?
No. Everything is calculated in your browser, and nothing is stored or sent.