Radians to Degrees Calculator

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

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°.

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.

Radians to Degrees Calculator Use

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

Radians to Degrees Conversion Formula

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

radians to degrees calculator formula

How to Convert Radians to Degrees

The method of converting radians to degrees is quite similar to the process of converting degrees to radians, which we discussed in the last post and which you may read if you’re interested in learning more about.

To save you time, we created a calculator that accomplishes the same work of converting radian values to degrees. You can always use the calculator provided above. However, understanding the math involved in transforming these numbers is always beneficial.

We’ve solved several examples that will undoubtedly assist you in comprehending the conversion process.

Example :

1. Using the radians to degrees formula, convert the angle π/9 rad to degrees.

Solution :

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

Formula : Degrees = Radians × (180/π)

Degrees = Radians × (180/π)
Degrees = (π/9) × (180/3.141592654)
Degrees = 0.34906585 × 57.29577951
Degrees = 19.99999998 ≈ 20°

To double-check your answer, use the calculator above.

Additionally, you can multiply the numbers using our multiplication calculator or you can directly put the values in our fractions calculator to calculate the answer. Just make sure to use the number 3.14 instead of Pi (π). The below image will will help you to carry out the process using fractions calculator.

using fractions calculator for converting radians to degrees

Example :

2. Points A and B are located on the circumference of a circle with centre O. π/2 radian is the measurement of angle AOB. Convert the radians in AOB’s angle measurement to degrees.

Solution :

We’ll apply the same formula to convert the angle values as we did in the first problem.

Formula : Degrees = Radians × (180/π)

Degrees = Radians × (180/π)
Degrees = (π/2) × (180/3.141592654)
Degrees = 1.570796327 × 57.29577951
Degrees = 90°

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