Degrees To Radians - Conversion, Formula, Examples - Cuemath

Degrees to Radians

Degrees to radians is a form of conversion used to convert the unit of measurement of angles in geometry. Just like every quantity has a unit of measurement, angles also are measured in different units depending upon the field of application. For measuring the angles, degrees and radians are used as the units of measurement. It is essential for one to know how to convert degrees to radians since most often, radians are used instead of degrees to measure angles.

These are some of the common applications of radian measure: area of a sector of a circle, arc length, and angular velocity. One should essentially use radians when they are dealing with either object moving in circular paths or parts of a circular path. The problem statement can have the angle measured in degrees, but we should always convert the angles in degrees to radians before using them in any calculations. In this article, let's learn about the degrees to radians formula and the conversion table with solved examples.

1.	What is Degrees to Radians Conversion?
2.	Degrees to Radians Formula
3.	How to Convert Degrees to Radians?
4.	Degrees to Radians Conversion Table
5.	FAQs on Degrees to Radians

What is Degrees to Radians Conversion?

The two units of measurement that are used for measuring angles are degrees and radians. We can convert the measure of any angle given in degrees to radians as per our convenience. This conversion can be done following some very basic calculations. Let us understand the concept of both the units and establish a relationship between them.

Degree

A degree, which is referred to as the degree of arc or arc degree, is the unit of measuring a plane angle. It is denoted by the symbol (°). 360° is the angle measure for a complete rotation. A complete rotation is denoted by the angle measuring 360° and the instrument used to measure an angle in degrees is known as the protractor.

Radians

Radian is another unit of measuring an angle in geometry. One radian is the angle that is formed at the center of a circle by an arc whose length is equal to the radius 'r' of the circle. One complete counterclockwise rotation is equal to 2π in radians. The below-given image shows the measure of one radian as 57.296°. Also, a right angle is expressed as π/2 radians, and a straight angle is expressed as π radians.

We can compare the measure of angles for a complete rotation in radian and degrees as,

360 Degrees = 2π Radians 180 Degrees = π Radians

Degrees to Radians Formula

Converting degrees to radians formula is a generalized formula used to convert the given value in degrees to value in radians. We can say that to convert degrees into radians, we multiply the angle (in degrees) by π / 180.

Radians = Degrees × π / 180

Derivation of Degrees to Radians Formula

In terms of degrees, one complete counterclockwise revolution is 360° and whereas in radians, one complete counterclockwise revolution is 2π. These statements can be equated as:

One complete counterclockwise revolution in degrees = 360° One complete counterclockwise revolution in radians = 2π

Degrees to Radians Equation: The relation between degree measure and radian measure can be represented with this equation:

360° = 2π radians.

Hence, 180° = π radians.

We obtain the equation,

1° = (π)/180 radians.

This gives us the formula to make conversions from degrees to radians and vice versa.

Thus, to convert degrees to radians, use this formula = Degree measure × (π/180°). 1° = (π)/180 radians = 0.017453 radians.

To find the value of 1° as explained above, use the π value to be 3.1415926535...

How to Convert Degrees to Radians?

In order to convert degrees to radians manually, we use the formula: Radians = Degrees × (π/180°). We can follow the steps given below to calculate the measure of an angle given in degrees to radians.

• Note down the measure of the angle given in degrees.
• We know, 1°= (π)/180 radians. So, to convert the angle given in degrees to radians we multiply it with π/180°. Angle in Radians = Angle in Degrees × π/180°.
• Simplify the values and express the answer in radians.

Example: Convert 90 degrees to radians.

Solution: 90° = 90° × (π/180°) = π/2.

Degrees to Radians Conversion Table

The below-given table shows the radian values for the corresponding angle measures in degrees. The first table shows the degrees to radians angles conversion from 0° to 90°.

Degree	0°	30°	45°	60°	90°
Radian	0	π/6	π/4	π/3	π/2

The second table shows the degrees to radians angles conversion from 120° to 360°.

Degree	120º	135º	150º	180º	270º	360º
Radian	(2π)/3	(3π)/4	(5π)/6	π	(3π)/2	2π

Degrees to Radians Chart

The below-given chart shows degree measures and their corresponding radian measures. We can also use this chart to convert the degrees to radians to make the calculations easier and faster. In the below-given chart, we can see that 0° equals 0 rad and 360° equals 2π rad

☛Important Notes on Degrees to Radians

Here is a list of a few points that should be remembered while studying degrees to radians:

• Angles are measured in degrees and radians.
• One full revolution is equal to 2π rad (or) 360°.
• 1° = 0.017453 radians and 1 rad = 57.2958°.
• To convert an angle from degrees to radians, we multiply it by π/180°.
• To convert an angle from radians to degrees, we multiply it by 180°/π.

☛Related Articles on Degrees to Radians

Check out the following pages related to degrees to radians:

• Radians to Degree Calculator
• Degrees to Radians Calculator
• Formula For 180 Degree Rotation
• Radians
• Degrees