Angle Converter
Convert angles between degrees, radians, minutes and seconds of arc, gradians, turns and mils.
Change the values and press Calculate to work out your own figures.
Enter an angle, choose its unit and the unit you want. The answer is exact until it is shown, and the same value appears in every other unit.
Show the working
- 1 ° = 0.0174532925199 rad
- 180 × 0.0174532925199 = 3.14159265359 rad
How to use it
Type an angle, choose the unit it is in and the unit you want, then press Calculate. You can type decimals, fractions such as 3/8, mixed numbers such as 1 1/2, very large or small numbers such as 2.5e6, and simple sums such as 2*3. Swap exchanges the two units.
The answer is worked out with exact fractions and only rounded for display, to 12 significant figures. Below it you get the same value in every other unit on the list, and Show the working gives the factor that was used.
Key definitions
1 turn = 360° = 2π rad = 400 gon 1° = 60′ = 3,600″ 1 rad = 180/π ° ≈ 57.29578°
Degrees and radians
A full turn is 360 degrees or 2π radians, so one radian is about 57.2958 degrees. Radians are the natural unit in mathematics and physics because an angle of one radian cuts off an arc as long as the circle's radius.
Minutes and seconds of arc divide a degree like an hour: 60 minutes to a degree and 60 seconds to a minute. They are used for map coordinates and astronomy.
Questions
How many degrees are in a radian?
180/π, about 57.2957795 degrees.
What is a gradian?
One four-hundredth of a turn, so a right angle is 100 gradians. It is also called a gon and is used in some surveying.
Formulas
result = (value × f(from) + o(from) − o(to)) ÷ f(to)
Sources
Limitations
- Only the units listed are supported here; other angle units arrive with later M4 slices.