Degrees To Radians

Degrees to Radians conversion is useful for measuring and converting angles in different units. Degrees and Radians are used to measure an angle. A complete revolution is represented by 2π (in radians) or 360° (in degrees). Thus, the degree to radian identity can be represented as:

π radian = 180 degree

Measurement of various types of angles is done in two different systems. Sexagesimal System is a system in which a right angle is divided into 90 equal sections, which are 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

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 degree in radian and vice versa. This can be achieved by using the formula discussed below, Also for Radian to Degree formula click here,

Degrees to Radians Formula

Degrees to Radians conversion is very important and can be achieved by the 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)

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

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

                           = 270 x (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.

Angle in degree	Angle in radian
0°	0
30°	π/6
45°	π/4
60°	π/3
90°	π/2
180º	π
270º	(3π)/2
360º	2π

Solved Examples on Degrees to Radians

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:

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:

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

FAQs on Degrees to Radians

Question 1: What is the value of 1 radian?

Answer:

The value of π radian = 180 degrees from this 1 radian = 57.298 degree

Question 2: How to convert degrees to radians?

Answer:

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.

Question 3: What is the relation between π radians and 180 degrees?

Answer:

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

Question 4: What is the value of 1 degree?

Answer:

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