Degrees to Radians Calculator

You can simply convert the measure of angle from degrees to radians with this degrees to radians calculator tool in a matter of seconds.

Degree

One of the measures for measuring the size of an angle, which is the amount of turning, is a degree. A degree is a very little quantity of turning that is 1/360 of a full turn; or a complete turn in size.

A full turn has 360 degrees; we write this as 360° in symbols. A protractor is used to measure angles in degrees.

A soldier quickly learns that a half turn is the same as a “about turn” and is a 180° rotation.

The Babylonians devised this division of a full turn into 360 equal pieces, known as degrees, roughly 3000 years ago, and it is still in use today.

Radian

A radian (rad) is a measurement unit representing the size of an angle. The following is how a radian is defined (see figure a).

Assume we have a circle with a radius of one unit and a centre of ‘O’. As illustrated in the circle on the left-hand side of the picture, a sector ‘AOB’ with an arc length of one unit is drawn. One radian is defined as the angle ‘AOB’.

degrees to radians

Assume that the chord length ‘AB’ is 1 unit instead of the arc length ‘AB’, as stated on the right-hand side of the picture.

Because triangle ‘AOB’ is an equilateral triangle, the angle ‘AOB’ in the circle on the right-hand side of the illustration is 60°.

Degrees to Radians Calculator Use

  • You only need to input the degrees value in the first field to convert degrees to radians.
  • In the second field, the calculator will display the converted value in radians.

Degrees to Radians Conversion Formula

The formula for converting the angle measuring unit from degrees to radians is extremely easy and is shown below:

degrees to radians conversion formula

How to Convert Degrees to Radians

Converting the angle measurement unit from degrees to radians is as easy as pie. If you didn’t believe it before, you will now because we will walk you through the simple steps of converting degrees to radians.

You can use our above calculator to convert the degrees value to radians, or you can use the conversion formula to convert the value yourself.

We’ll go over some of the examples that have been solved so that you can grasp the idea of conversion better.

Example :

1. Use the conversion formula to convert 22 degrees to radians.

Solution :

We will use the above degrees to radians formula to convert the value from degrees to radians.

Formula : Radians = Degrees × (π/180)

Radians = 22 × (π/180)
Radians = 22 × (3.141592654/180)
Radians = 22 × 0.017453292
Radians = 0.383972435 rad.

You can use the calculator above to double-check your answer.

Example :

2. Convert -133 degrees to radians.

Solution :

The angle’s value is now negative. Don’t be confused by the negative symbol. We’ll approach this issue in the same way we approached the previous.

Formula : Radians = Degrees × (π/180)

Radians = -133 × (π/180)
Radians = -133 × (3.141592654/180)
Radians = -133 × 0.017453292
Radians = -2.321287905 rad.

There is no need to verify the solution, but if you are unsure, you can use the above calculator to double-check your answer.