Convert between degrees, radians, gradians, and turns. Essential for math, engineering, and programming where different angle units are used.
Degrees
180 °
Radians
3.141593 rad
Gradians
200 gon
Turns
0.5 rev
sin(180°)
0
cos(180°)
-1
tan(180°)
-0
0°
Zero
45°
Eighth turn
90°
Right angle
180°
Straight angle
270°
Three-quarter
360°
Full turn
30°
Pi/6
60°
Pi/3
Angles can be measured in several different units. Degrees are the most common in everyday use, dividing a full rotation into 360 parts. Radians are the mathematical standard used in calculus and most programming languages. Gradians are used in surveying. Turns (or revolutions) represent complete rotations and are useful in engineering and physics.
Multiply the number of degrees by π/180 (approximately 0.01745). For example, 90° = 90 × π/180 = π/2 ≈ 1.5708 radians. Most programming languages and scientific calculators use radians for trigonometric functions.
One radian equals approximately 57.2958 degrees. A radian is the angle subtended by an arc equal in length to the radius of the circle. A full circle is 2π radians or 360 degrees.
A gradian (also called a gon or grade) divides a right angle into 100 parts, so a full circle is 400 gradians. Gradians are used in surveying and some European countries. One gradian equals 0.9 degrees.
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