A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. There are 2pi radians in a full circle.

Gradians divide a right angle into 100 parts, so a full circle is 400 gradians. They are used in some surveying and engineering contexts.

Why is pi/4 radians equal to 45°?

A full circle is 360° = 2pi radians. So 45° = 45/360 × 2pi = pi/4 radians.

Radian Converter

Convert between degrees and radians. Also shows the angle as a fraction of pi.

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Degrees

deg

Radians

0.78539816

Pi Fraction0.250000

Gradians50.0000

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Radian Conversion

Formulas

Radians = Degrees × pi/180

Degrees = Radians × 180/pi

Common Conversions

DegreesRadiansPi Form 30°0.5236pi/6 45°0.7854pi/4 60°1.0472pi/3 90°1.5708pi/2 180°3.1416pi 360°6.28322pi

Example Calculation

Convert 45° to radians.

01Radians = 45 × pi/180 = pi/4
02= 0.7854 radians
03Gradians = 45 × 10/9 = 50 grad

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Radian Converter

Radian Conversion

Formulas

Common Conversions

Example Calculation

Frequently Asked Questions

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