Converting Degrees to Radians

This Degree to Radians Converter Calculator helps you to convert an angle in Degree into Radians notation as an output within a fraction of seconds along with an explanation. Just provide the input number in the input field and click on the calculate button provided next to the input field to get the desired result.

Enter Degrees

Converting Degrees to Radians: Are you searching for the easiest ways to convert the Degree to Radians? Then, you have come to the appropriate place where you can find the simplest option to find conversion. You can get the angles in Radians notation for any regular angle in less time by using our free Online Degree to Radians Converter. Also, you can learn how to convert radian to degrees with steps along with a solved example.

What is Degrees to Radians Conversion?

Angles have units for measurement. When measuring angles, degrees and radians are used as units of measurement. Most often, radians are used to measure angles. Here are a few examples: area of a sector of a circle, arc length, and angular velocity. It is recommended to use radians when considering circular paths or components of circular paths. Angles may be expressed in degrees in the problem statement, but we should always convert them into radians before using them.

Degree: An angle is measured by a degree, also referred to as the degree of arc. It is denoted by the symbol (°). A complete rotation is described by an angle measuring 360° and the instrument from which it is measured is called a protractor.

Radians: A radian measures the angle formed at the centre of a circle by an arc whose length equals the radius 'r' of the circle. One complete rotation is equivalent to 2π radians. The measure of one radian is 57.296°. A right angle is π /2 radians, and a straight angle is π radians.

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Degrees to Radians Conversion Formula

To convert degrees to radians, we multiply the angle (in degrees) by π / 180, which is a generalized formula for converting values in degrees to radians.

Radian = Degree x π/180

How to Convert Degrees to Radians Manually?

360 degrees, or 2π radians, are two units of measurement for angles. Thus, 360° and 2π radians are the same numbers when one goes "once around" a circle. Simply follow the steps below to convert degrees to radians.

  • Write down how many degrees you are converting to radians.
  • You need to multiply the number of degrees by π/180. Because 180 degrees equals π radians.
  • Carry out the multiplication process. Do it by multiplying two fractions.
  • Taking each fraction and putting it in the lowest terms will give you your final answer.
  • You can convert the angle measures to radians by writing them down. Then, you're done!

Solved Example on Degrees to Radians Conversion

Example:

Convert 45 degrees to radians.

Solution:

Given, 45 degrees is the angle.

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

= 45 × (π/180)

= π/4

Hence, 45 degrees is equal to π/4 in radian.

Degrees to Radians Chart or Conversion Table

The following table represents the common values of converted degrees to radian units of measurement in terms of π and numeric values. For quick results, also use this converted degree to radian chart. 

Degrees (°) Radians (rad) Radians (rad)
0 rad 0 rad
30° π/6 rad 0.5235987756 rad
45° π/4 rad 0.7853981634 rad
60° π/3 rad 1.0471975512 rad
90° π/2 rad 1.5707963268 rad
120° 2π/3 rad 2.0943951024 rad
135° 3π/4 rad 2.3561944902 rad
150° 5π/6 rad 2.6179938780 rad
180° π rad 3.1415926536 rad
270° 3π/2 rad 4.7123889804 rad
360° 2π rad 6.2831853072 rad

FAQs On Converting Degrees to Radians Calculator with Steps

1. How do you convert degrees to radians?

We will use the equation 1 radian = (180π)° to convert Radians to Degrees. Then, multiply the Degree value to π/180° Radians.

2. What is the formula to convert radians to degrees?

The simple conversion formula of radians to degrees is Degrees = Radians × (180/π)

3. How do you convert from Degree 11 to Radians?

The conversion can be done simply by using the degree to Radian Formula:

Radian = [π/ 180] × Degree

Rad = [π/ 180] × 11 = 0.1919

4. What is meant by 1 radian?

A Radian is a unit of measurement of angle based on the radius of the circle. 1 Radian is about 57.2958 degrees also it is the angle that is formed at the centre of the circle by this arc.