📐 Angle Converter

Convert an angle between degrees, radians, gradians and full turns.

Value

From Unit

The conversion factors

A full circle is 360 degrees, 2π radians, 400 gradians or 1 turn. Every conversion here is that one statement rearranged, and the converter works internally in degrees:

radians  = degrees × π / 180
degrees  = radians × 180 / π     (1 rad = 57.295779513°)
gradians = degrees / 0.9            (1 grad = 0.9°)
turns    = degrees / 360

So 90 degrees is 90 × π / 180 = 1.570796 radians, which is also 100 gradians and 0.25 of a turn.

Common angles at a glance

Degrees	Radians	Gradians	Turns
30°	π/6 = 0.523599	33.3333	0.08333
45°	π/4 = 0.785398	50	0.125
60°	π/3 = 1.047198	66.6667	0.16667
90°	π/2 = 1.570796	100	0.25
180°	π = 3.141593	200	0.5
270°	3π/2 = 4.712389	300	0.75
360°	2π = 6.283185	400	1

Results are shown to six decimal places, so irrational values such as π/6 arrive rounded rather than exact.

Negative and oversized angles are passed straight through: enter -45 and you get -45, and 450 degrees stays 450 rather than folding back to 90. If you need an angle inside one revolution, take the remainder after dividing by 360 first.

Frequently asked questions

How many radians is 90 degrees?

Exactly pi/2, which is 1.570796 radians to six decimal places. Multiply any degree figure by pi/180 to get radians.

What is 1 radian in degrees?

57.295779513 degrees, or 180/pi. One radian is the angle at which the arc along the circle is the same length as its radius, which is why the number is not round.

What is a gradian used for?

Surveying and some European civil engineering, where a right angle of 100 grad divides more neatly than 90 degrees. A gradian is 0.9 degrees, so 400 of them make a full circle.