How do I convert degrees to radians?

Multiply degrees by π/180. For example, 180° × π/180 = π rad.

How do I convert radians to degrees?

Multiply radians by 180/π. For example, π rad × 180/π = 180°.

How do I convert degrees to gradians?

Multiply degrees by 10/9. For example, 90° × 10/9 = 100 grad.

How do I convert gradians to degrees?

Multiply gradians by 0.9. For example, 100 grad × 0.9 = 90°.

> >Angle Converter

Angle Converter

Convert between degrees, radians, gradians, arcminutes, arcseconds, milliradians, revolutions, and compass points. Enter a value and select units to convert instantly.

From

Conversion Result

Degrees (°): 180

Radians (rad): 3.141593

All Conversions

Unit	Value
Degrees (°)	180.000000
Radians (rad)	3.141593
Gradians (grad)	200.000000
Arcminutes (')	10800.000000
Arcseconds (")	648000.000000
Milliradians (mrad)	3141.592654
Revolutions (rev)	0.500000
Points (compass)	16.000000

Common Angle Reference Values

Angle	Value
Full circle	360° = 2π rad = 400 grad
Right angle	90° = π/2 rad = 100 grad
Straight line	180° = π rad = 200 grad
1 radian in degrees	1 rad = 57.2958°
1 degree in radians	1° = 0.0174533 rad
1 arcminute	1' = 1/60° = 0.000291 rad
1 arcsecond	1" = 1/3600° = 4.848e-6 rad
Compass point (N, NE, etc.)	1 point = 11.25°

Related Tools

External Resources

Wikipedia: Angle Wikipedia: Degree (Angle)Wikipedia: Radian NIST Metric Conversions

Frequently Asked Questions

How do I convert degrees to radians?: Multiply degrees by π/180. For example, 180° × π/180 = π rad.
How do I convert radians to degrees?: Multiply radians by 180/π. For example, π rad × 180/π = 180°.
How do I convert degrees to gradians?: Multiply degrees by 10/9. For example, 90° × 10/9 = 100 grad.
How do I convert gradians to degrees?: Multiply gradians by 0.9. For example, 100 grad × 0.9 = 90°.
How do I convert degrees to arcminutes?: Multiply degrees by 60. For example, 1° = 60 arcminutes.
How do I convert arcminutes to degrees?: Divide arcminutes by 60. For example, 60' / 60 = 1°.
How do I convert degrees to arcseconds?: Multiply degrees by 3,600. For example, 1° = 3,600 arcseconds.
How do I convert arcseconds to degrees?: Divide arcseconds by 3,600. For example, 3,600" / 3600 = 1°.
How many degrees are in a radian?: One radian equals approximately 57.2958 degrees.
How many radians are in a degree?: One degree equals 0.0174533 radians (π/180).
What is a gradian?: A gradian divides a right angle into 100 parts. 400 grad = 360° = 2π rad. Used in surveying and engineering.
What is an arcminute?: An arcminute (') is 1/60 of a degree. Used in astronomy, navigation, and shooting.
What is an arcsecond?: An arcsecond (") is 1/3,600 of a degree. Used in astronomy for measuring star positions.
How many arcseconds in a full circle?: There are 1,296,000 arcseconds in a full circle (360° × 60 × 60).
How do I convert milliradians to degrees?: Multiply milliradians by 0.0572958. For example, 1,000 mrad = 57.2958°.
How do I convert degrees to milliradians?: Multiply degrees by 17.4533. For example, 1° = 17.4533 mrad.
What are revolutions?: A revolution is a full 360° rotation. 1 rev = 360° = 2π rad. Used for rotational speed (RPM).
What is a compass point?: A compass point is 1/32 of a full circle = 11.25°. North = 0°, East = 90°, South = 180°, West = 270°.
How do I convert revolutions to degrees?: Multiply revolutions by 360. For example, 0.5 rev = 180°.
How do I convert degrees to revolutions?: Divide degrees by 360. For example, 180° / 360 = 0.5 rev.
How many gradians in a full circle?: There are 400 gradians in a full circle.
How many gradians in a right angle?: There are 100 gradians in a right angle (90°).
What is the SI unit for angle?: The SI unit for angle is the radian (rad). It is defined as the angle subtended by an arc equal in length to the radius.
Why are radians used in calculus?: Radians are natural for calculus because trigonometric functions' derivatives are simpler in radians: d(sin x)/dx = cos x.
How do I convert bearings to degrees?: Bearings are measured clockwise from north. N 45° E = 45°, S 30° E = 150°, S 45° W = 225°, N 60° W = 300°.
How do astronomers measure angles?: Astronomers use degrees, arcminutes, and arcseconds. The Moon is about 0.5° (30 arcminutes) across.
How many milliradians in a degree?: There are approximately 17.4533 milliradians in one degree.
What is the angular resolution of the human eye?: The human eye can resolve about 1 arcminute (1/60°) of angular separation.
How do surveyors use angles?: Surveyors use degrees, minutes, and seconds (DMS format) or gradians. 1° = 60' = 3,600".
How do I calculate arc length from angle?: Arc length = radius × angle (in radians). For 1 radian, arc length = radius.
What is the difference between azimuth and bearing?: Azimuth is measured clockwise from north (0-360°). Bearing uses quadrants (N45°E). Both describe horizontal direction.