Degrees to Radians conversion calculator

Enter angle in degrees and press the Convert button (e.g:30°, -60°):

Enter Degrees:		°
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Radians result:
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How to convert degrees to radians

Pi radians are equal to 180 degrees:

π rad = 180°

One degree is equal 0.01745329252 radians:

1° = π/180° = 0.005555556π = 0.01745329252 rad

The angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees:

α_(radians) = α_(degrees) × π / 180°

or

radians = degrees × π / 180°

Example

Convert 30 degrees angle to radians:

α_(radians) = α_(degrees) × π / 180° = 30° × 3.14159 / 180° = 0.5236 rad

Degrees to Radians

In geometry, both degree and radian represent the measure of an angle. One complete anticlockwise revolution can be represented by 2π (in radians) or 360° (in degrees). Therefore, degree and radian can be equated as:

2π = 360°

And

π = 180°

Hence, from the above equation, we can say, 180 degrees is equal to π radian.

Usually, in general geometry, we consider the measure of the angle in degrees (°). Radian is commonly considered while measuring the angles of trigonometric functions or periodic functions. Radians is always represented in terms of pi, where the value of pi is equal to 22/7 or 3.14.

A degree has its sub-parts also, stated as minutes and seconds. This conversion is the major part of Trigonometry applications.

Degree x π/180 = Radian

Radians × 180/π = Degrees

How to Convert Degrees to Radians?

The value of 180° is equal to π radians. To convert any given angle from the measure of degrees to radians, the value has to be multiplied by π/180.

Angle in radian = Angle in degree x (π/180)

Where the value of π = 22/7 or 3.14

Example:

Convert 90 degrees to radians.

Solution: Given, 90 degrees is the angle

Angle in radian = Angle in degree x (π/180)

= 90 x (π/180)

= π/2

Hence, 90 degrees is equal to π/2 in radian.

 

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