Radians to Degrees Calculator with Steps

Convert radians to degrees quickly and accurately with this step-by-step calculator. Learn the conversion formula, see practical examples, and understand when to use radians versus degrees in calculations.

Conversion Formula

The relationship between radians and degrees is defined by the formula:

Degrees = Radians × (180/π)

This formula comes from the fact that a full circle is 360 degrees or 2π radians. Therefore, to convert radians to degrees, you multiply the radian value by 180 and then divide by π.

Inverse Conversion

To convert degrees to radians, use the inverse formula:

Radians = Degrees × (π/180)

How to Use the Calculator

Enter the angle value in radians in the input field.
Click the "Calculate" button to convert the value to degrees.
View the result in the output field.
Use the "Reset" button to clear the calculator.

For best results, enter values with up to 6 decimal places. The calculator will round the result to 4 decimal places.

Worked Example

Let's convert 2 radians to degrees using the formula:

Degrees = 2 × (180/π)

Degrees ≈ 2 × 57.2958

Degrees ≈ 114.5916

So, 2 radians is approximately 114.5916 degrees.

Radians vs Degrees

Both radians and degrees are units of angular measurement, but they are used in different contexts:

Degrees are commonly used in everyday applications, such as measuring angles in geometry, navigation, and temperature scales.
Radians are the standard unit of angular measurement in calculus, physics, and engineering, particularly in trigonometric functions and rotational motion.

Degrees are based on the division of a circle into 360 equal parts, while radians are based on the radius of a circle. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius.

Common Angle Conversions

Here are some common angle conversions between radians and degrees:

Radians	Degrees
0	0
π/6	30
π/4	45
π/3	60
π/2	90
π	180
3π/2	270
2π	360

Frequently Asked Questions

How do I convert radians to degrees?

Multiply the radian value by 180 and then divide by π. The formula is: Degrees = Radians × (180/π).

When should I use radians instead of degrees?

Radians are typically used in advanced mathematics, physics, and engineering, especially in calculus and trigonometric functions. Degrees are more common in everyday applications.

What is the difference between a radian and a degree?

A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. A degree is 1/360th of a full circle.

Can I convert degrees to radians using this calculator?

No, this calculator converts radians to degrees. For degrees to radians conversion, use the inverse formula: Radians = Degrees × (π/180).