Degrees to Radian Converter

Converting degrees to radians is a fundamental skill in mathematics, particularly in trigonometry, calculus, and various fields like physics and engineering. This Degrees to Radian Converter allows you to easily switch between degrees and radians and vice versa.

Degrees to Radian Converter

This calculator converts angles from degree to radian and radian to degree:

180 degree = π radian

1 degree = 0.0174533 radians.

System of Measurement of Angle

Measurement of various types of angles is done in two different systems:

Sexagesimal System

The Sexagesimal System is a system in which a right angle is divided into 90 equal sections, referred to as degrees. Each degree is divided into 60 equal parts known as minutes, which are further divided into 60 equal pieces known as seconds.

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

Radial System

In the Radial system angles are measured in radians which is based on the radius of a circle. In this system, one radian is defined as the angle formed when the arc length is equal to the radius of the circle.

The radial system is commonly used in mathematics, particularly in trigonometry, calculus, and physics, as it provides a direct relationship between angular measurements and arc lengths of circle.

1 Radian = 57.296°

What is Degrees to Radians Conversion?

In mathematics, we need to measure various angles, these angles are measured in basically two units Degree and Radian. So it is necessary to change the degree in radian and vice versa. Degrees to radians angle conversion is the process of changing an angle measured in degrees to its equivalent in radians.

Degrees to Radians Conversion

This can be achieved by using the formula discussed below:

Degrees to Radians Conversion Formula

Degrees to Radians conversion is very important and can be achieved by the angle conversion formulas listed below:

• Degrees × (π/180) = Radians
• Radians × (180/π) = Degrees
• 180 degrees = π radians

How to Convert Degrees to Radians?

Both the degree and the radian in geometry represent the measurement of an angle. 2π (in radians) or 360° can be used to symbolize a complete anticlockwise revolution (in degrees). As a result, the terms degree and radian can be interchanged.

Steps to convert an angle in the degree to radians.

Step 1: Take the numerical value of the given angle in degrees

Step 2: Multiply the numerical value from step 1 by(π/180) as defined in the conversion formula.

Step 3: Rationalize the obtained expression in step 2

Step 4: Result obtained is the required answer in degrees

Example

Convert 270 degrees to radians.

Solution:

Given Angle = 270 degrees

By using the angle conversion formula

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

= 270 × (π/180)

= 2π/3

Hence, 270 degrees is equal to 2π/3 radian.

Degrees to Radians Conversion Table

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

Related Articles:

• Types of angles
• Pair of Angles

Examples on Degrees to Radians Conversion

Example 1: Convert 300° to radians.

Solution: 

We know 180° = π radians = π^c or 1° =  (π/180)^c

Hence, 300° = 300 × π/180 = 5π/3

Thus, 300° = 5π/3 radians

Example 2: Convert 35° to radians.

Solution:

We know 180° = π radians = π^c or 1° =  (π/180)^c

Hence, 35° = 35 × π/180 = 7π/36

Thus, 35° = 7π/36 radians

Example 3: Convert −300° to radians.

Solution:

By using the angle conversion formula

We know 180° = π radians = π^c or 1° = (π/180)^c

Hence, −300° = −300 × π/180 = −5π/3

Thus, −300° = −5π/3 radians

Example 4: Convert 7°30′ to radians.

Solution:

By using the angle conversion formula

We know 180° = π radians = π^c or 1° = (π/180)^c

Hence, 7°30′ = (7 × π/180)^c × (30/60)° = (7½)° × (π/180)^c = (15π/360)^c = π/24

Thus, 7°30′ = π/24 radians

Practice Questions on Degree to Radian Conversion

Question 1: Find the radian measurement for 45 degrees.

Question 2: Find the radian measurement for 180 degrees.

Question 3: Convert 270 degrees to radians.

Question 4: Convert 60 degrees to radians.

Question 5: Convert [Tex]\frac{3\pi}{4} [/Tex]radians to degrees.

Question 6: Convert[Tex] \frac{\pi}{6}​ [/Tex]radians to degrees.

Question 7: Convert [Tex]\frac{2\pi}{3}[/Tex] radians to degrees.

Degrees to Radians Conversion – FAQs

What is the Value of 1 Radian?

The value of π radian = 180 degrees from this 1 radian = 57.296 degree

How to Convert Degrees to Radians?

180 degrees is equal to π radians and so converting degree to radian is given by multiplying π/180 by the value of a degree.

What is the Relation between π Radians and 180 Degrees?

The relation between π radians and 180 degrees is given by π radians is equal to 180 degrees

What is the Value of 1 Degree?

The value of π radian = 180 degrees from this 1 degree = 0.0174533 radians.

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