About the Angle Converter
This angle converter switches an angle between degrees, radians, gradians (gons), arcminutes, arcseconds, full turns, milliradians and NATO mils. Enter a value, choose the unit it is in and the unit you need, and you also get the angle written in degrees-minutes-seconds (DMS) and reduced to the 0–360° range.
Students need radians for trigonometry and calculus, surveyors work in gradians or DMS, astronomers in arcminutes and arcseconds, and shooters and optics users in milliradians or mils. Programmers often need radians because most maths libraries expect them.
Every unit is defined as a fixed fraction of a full turn, so conversions are exact apart from the rounding of π. For extremely large angles (beyond about a trillion degrees) the DMS and normalised lines are hidden, because double-precision arithmetic can no longer resolve the leftover fraction of a turn. Note that the NATO mil (6,400 per circle) is slightly different from the true milliradian (about 6,283.2 per circle).
How to use the angle converter
- 1Enter the angle you want to convert (negative values are allowed).
- 2Choose the unit it is in.
- 3Choose the unit you need.
- 4Read the answer, the DMS form and the normalised angle.
Formula and method
A full circle is 360°, 2π radians, 400 gradians, 21,600 arcminutes, 1,296,000 arcseconds or 6,400 NATO mils. The converter changes your angle to degrees and then into the target unit using those ratios, so 1 radian = 180/π ≈ 57.29578° and 1 gradian = 0.9°.
For DMS, the whole-number part is the degrees; the fractional part × 60 gives minutes, and the remaining fraction × 60 gives seconds (rounded to 0.01″ with carrying). The normalised angle is the value reduced into the range 0° to less than 360°.
- deg
- Degrees (360 per full turn)
- rad
- Radians (2π per full turn)
- grad
- Gradians or gons (400 per full turn)
- mil
- NATO mils (6,400 per full turn)
Worked examples
180 degrees in radians
180 × π/180 = π ≈ 3.14159 radians. It is also 200 gradians and exactly half a turn.
One radian in degrees
1 × 180/π = 57.2958°. The fraction 0.2958° × 60 = 17.75′, and 0.7468′ × 60 = 44.81″, giving 57° 17′ 44.81″.
Decimal degrees to DMS
0.5125° × 60 = 30.75′, and 0.75′ × 60 = 45″, so 45.5125° is 45° 30′ 45″ — or 163,845 arcseconds in total.
Angle larger than a full turn
810 ÷ 360 = 2.25 turns. Removing the two whole turns leaves 810 − 720 = 90°.
Frequently asked questions
How do I convert degrees to radians?+
Multiply degrees by π/180 (about 0.0174533). For example, 60° × π/180 = π/3 ≈ 1.0472 radians.
How do I convert radians to degrees?+
Multiply radians by 180/π (about 57.2958). For example, 2 radians × 57.2958 = 114.59°.
What is a gradian?+
A gradian (also called a gon or grade) is 1/400 of a circle, so a right angle is exactly 100 gradians and 1 gradian = 0.9°. It is used mainly in surveying.
How do I convert decimal degrees to degrees, minutes and seconds?+
Keep the whole degrees, multiply the decimal part by 60 for minutes, then multiply the remaining decimal of the minutes by 60 for seconds. 12.345° = 12° 20′ 42″.
Is a mil the same as a milliradian?+
No. A true milliradian is 1/1000 radian, about 6,283 per circle. The NATO mil used on military compasses is 1/6400 of a circle, so each NATO mil is about 1.8% smaller than a milliradian.