Angle Converter — degrees, radians, gradians & more

How it works

Angles measure rotation, and the SI unit is the radian — the angle subtended by an arc equal in length to the radius. A full circle is 2π radians. The other units are fixed multiples (NIST SP 811):

• 1 degree = π/180 rad ≈ 0.017453 rad, so 180° = π rad and a full turn is 360°.
• 1 gradian (gon) = π/200 rad, dividing a right angle into 100 parts, so 400 gradians make a full turn.
• 1 arcminute = 1/60 degree and 1 arcsecond = 1/60 arcminute — fine divisions used in astronomy and navigation.
• 1 revolution = 2π rad = 360°.

The calculator converts your value to radians and then to the unit you want, so any pairing works the same way.

Worked example

Converting 180 degrees to radians: 180 × π/180 = π ≈ 3.141593 rad. Going the other way, 1 radian ≈ 57.2958°, and 1 revolution = 360°.

Frequently asked questions

How many degrees are in a radian?

About 57.2958. Because a full turn is 2π radians and 360 degrees, one radian equals 360 ÷ (2π) ≈ 57.30 degrees.

How do I convert degrees to radians?

Multiply degrees by π/180 (about 0.017453). So 90° = 90 × π/180 = π/2 ≈ 1.5708 rad.

What is a gradian?

A gradian (or gon) splits a right angle into 100 parts, so a full turn is 400 gradians and 100 gradians = 90 degrees. It is used in some surveying.

What are arcminutes and arcseconds?

Fine subdivisions of a degree: one degree = 60 arcminutes, and one arcminute = 60 arcseconds. They are used to describe small angles in astronomy and navigation.

What is the SI unit of angle?

The radian. It is dimensionless — a ratio of arc length to radius — which is why it appears naturally in trigonometry and calculus.

Why do calculators have degree and radian modes?

Because trigonometric functions expect an angle unit. `sin(30)` is 0.5 if the 30 is degrees, but about −0.988 if it is radians, so pick the mode that matches your input.