Radians to Degrees: Radians to degrees is a type of transformation used in geometry to convert angle measurements. There are two alternative methods for measuring an angle. Radians and degrees are the two units used to measure angles. Radian is the most commonly used unit in trigonometry. Various angles are measured in radians and then converted to degrees using a formula. This formula is discussed below.

Radians to Degrees Conversion

Two separate ways are used to measure angles. A right angle is split into 90 equal portions, referred to as degrees, in the Sexagesimal System. Each degree is split into 60 equal parts called minutes, which are divided further into 60 equal parts called seconds.

Radians to Degrees Conversion

Degree to Radian conversion can also be learned here.

• 60” = 1 minute (1’)
• 90° = 1 right angle

Radians Definition

Angle subtended to the centre of a circle by radius after a complete rotation is called 2π radians. The angle in radians made by the radius at the circle’s centre is the ratio of the length of an arc to the length of a radius. If the length of the arc is equal to the length of the radius, the angle subtended at the centre is called 1 radian. The unit of a radian is rad. Radian is the SI unit for measuring angles.

Degrees Definition

Angles can also be measured in degrees. One revolution divides the circle into 360 equal parts and each part is equal to a degree. Thus, the angle subtended at the centre of a circle after one complete rotation is 360°. The symbol used to denote degrees is ‘°‘. Degrees is not an SI unit for measuring an angle, but it is the most commonly used unit to measure an angle.

By comparing the measures of an angle for a complete rotation

• 360 Degrees = 2π Radians
• 180 Degrees = π Radians

How to Convert Degrees to Radians?

Value of 180° is equal to π radians. For converting the given angle from degrees to radians, we multiply the value of the angle in degrees by a factor of π/180.

Where the value of π = 22/7 or 3.14

Steps shown below are used for the conversion of angle in degrees to radians.

Step 1: Mark the value of the given angle in degrees

Step 2: Multiply the value obtained from the above step by π/180

Step 3: Solve the expression and rationalize the answer

Step 4: The result obtained is the measure of the angle in radian

Example: Convert 60 degrees to radians.

Solution: 

Given angle is 60 degrees

Angle in Radian = Angle in Degree × (π/180)

= 60 × (π/180)

= π/3

Hence, 60 degrees is equal to π/3 in radian.

Radians to Degrees Formula

Radians to Degrees formula converts the value of angle in radians to degrees. To convert the angle in radians to degrees we multiply the value in radians by 180°/π. Angles are used in two units: degrees and radians, 1 degree is expressed as 1° whereas 1 radian is expressed 1^c or 1 i.e. no unit is also used to express angle in radian. The formula for changing the angle in radians to degrees is:

Angle in Radians × 180°/π = Angle in Degrees

2π radians = 360°

π radians = 180°

1 Radian = 180/π Degrees = 57.296 Degrees

Radians to Degrees Calculator

Radians to Degrees Conversion Table

The table is given below shows the values angle in radian and their respective value in degree.