Degrees to Radians Converter

To convert a measurement in degrees to a measurement in radians, you can use either the formula radians = degrees × π / 180 or radians = degrees × 0.017453, with the former utilizing π and the latter offering a direct conversion ratio, providing flexibility in calculation.

Enter the angle in degrees below to get the value converted to radians.

How to Convert Degrees to Radians

Understanding the Interface:

Imagine you’re using a converter where you input the angle in degrees to get it converted into radians.

Input:

You input the angle in degrees that you want to convert into radians.

Formula Explanation:

Since π radians are equal to 180°, we use the formula:
Radians = Degrees × (π / 180)
This means the angle in radians is equal to the angle in degrees times π, divided by 180.

Step-by-Step Calculation:

Substitute the angle in degrees into the formula.
Move the degrees to the top of the fraction.
Simplify the fraction and evaluate.

Alternate Formula:

If you don’t want to use π, you can use the conversion ratio: 0.017453 radians/degree.
Radians = Degrees × 0.017453

Example Calculation:

Let’s convert 5 degrees to radians:
Radians = 5° × (π / 180)
Radians = 5 × π / 180
Radians ≈ π / 36
Using the alternate formula:
Radians ≈ 5 × 0.017453 ≈ 0.087266 rad

Understanding Degrees and Radians:

A degree is 1/360th of a circle, whereas a radian is the angle subtended by an arc that is equal in length to the radius of the circle.
Degrees can be represented using symbols like °, arcminutes, and arcseconds.
Radians are unitless and are represented using the symbol rad.

By understanding this conversion, you can easily switch between degrees and radians for various mathematical calculations.