Angle Converter

Value

From

To

Result

0 rad

Common Angles

Angle Visualization

45°

Acute angle

Trigonometric Values

sin(45°)

0

cos(45°)

0

tan(45°)

0

All Conversions

Degrees45 °

Radians0 rad

Gradians (gon)0 gon

Turns (revolutions)0 turn

Minutes of arc0 '

Seconds of arc0 "

Milliradians0 mrad

Common Angle Conversions

Degrees	Radians	Gradians	Turns
0°	0	0 gon	0
30°	π/6	33.333333 gon	0.083333
45°	π/4	50 gon	0.125
60°	π/3	66.666667 gon	0.166667
90°	π/2	100 gon	0.25
180°	π	200 gon	0.5
270°	3π/2	300 gon	0.75
360°	2π	400 gon	1

About Angle Units

Degrees

The most commonly used unit for measuring angles. A full circle contains 360 degrees. This system originated in ancient Babylon and is used in navigation, geometry, and everyday applications.

Radians

The standard unit in mathematics and physics. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. A full circle is 2π radians (approximately 6.283).

Gradians (gon)

Also known as gons or grades. A full circle contains 400 gradians, making a right angle exactly 100 gradians. This unit is commonly used in surveying and some European countries.

Turns (Revolutions)

A turn represents one complete rotation. One turn equals 360°, 2π radians, or 400 gradians. This intuitive unit is useful for describing rotational motion.

Arc Minutes and Arc Seconds

These are subdivisions of a degree used for precise measurements in astronomy and navigation. One degree equals 60 arc minutes, and one arc minute equals 60 arc seconds.

Milliradians

One milliradian (mrad) is 1/1000 of a radian. Milliradians are commonly used in military applications, surveying, and optics due to their convenient relationship with distance calculations.

Key Conversion Formulas

Degrees to Radians: radians = degrees x (π / 180)
Radians to Degrees: degrees = radians x (180 / π)
Degrees to Gradians: gradians = degrees x (10 / 9)
Degrees to Turns: turns = degrees / 360
Radians to Milliradians: mrad = radians x 1000