How do I convert degrees to radians?

Multiply the degree value by pi/180 (about 0.0174533). For example, 90 degrees equals 1.5708 radians, or exactly pi/2.

How do I convert radians to degrees?

Multiply the radian value by 180/pi (about 57.2958). For example, 1 radian equals about 57.3 degrees.

How many radians are in a full circle?

A full circle is 2*pi radians, approximately 6.2832 radians.

A gradian (or gon) divides a full circle into 400 equal parts instead of 360, so a right angle is exactly 100 gradians. It is mainly used in surveying.

What is the difference between arcminutes and arcseconds?

An arcminute is 1/60 of a degree, and an arcsecond is 1/60 of an arcminute, or 1/3600 of a degree. Both are used in astronomy, navigation and optics for measuring very small angles.

What is a reference angle?

A reference angle is the acute angle (between 0 and 90 degrees) formed between the terminal side of an angle and the x-axis. It's used to simplify trigonometric calculations for angles in any quadrant.

What is a coterminal angle?

Coterminal angles share the same terminal side because they differ by a full rotation. You find them by adding or subtracting 360 degrees (or 2*pi radians) from the original angle.

How do I find the complement of an angle?

Subtract the angle from 90 degrees. Complementary angles only exist for angles between 0 and 90 degrees, since the result must also be positive.

Is this angle converter free to use?

Yes, it is completely free, requires no registration, and runs entirely in your browser with no usage limits.

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Angle Conversions

12 units · angle relationships

Angle Converter

Convert instantly between degrees, radians, gradians, arcminutes, arcseconds and more, then find the quadrant, reference, complementary, supplementary and coterminal angle for any value.

12Angle units

360°= 2π radians

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From

deg

To

rad

1.5707963268rad

rad = deg × 0.0174532925

Angle

Unit

Reference angle = 180° − 150° = 30° (Quadrant II)

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Angle concepts & formulas

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Quick conversion table

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Degree	Radian

Angle unit reference

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