Convert Degrees to Radians Online Calculator

Degrees and radians are two common units for measuring angles. Degrees are widely used in everyday life, while radians are more common in advanced mathematics and physics. This guide explains how to convert between these units and when to use each.

What are Degrees and Radians?

An angle is a measure of rotation between two rays with a common endpoint. The most common units for measuring angles are degrees and radians.

Degrees are based on the division of a circle into 360 equal parts. A full circle is 360 degrees, a right angle is 90 degrees, and a straight line is 180 degrees.

Radians are based on the radius of a circle. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius. A full circle is 2π radians (approximately 6.283 radians).

Degrees are often used in everyday contexts like navigation, while radians are more common in advanced mathematics, physics, and engineering.

How to Convert Degrees to Radians

Converting degrees to radians involves a simple mathematical formula. The key is to understand the relationship between degrees and radians.

A full circle is 360 degrees or 2π radians. Therefore, to convert degrees to radians, you multiply the degree measure by π/180.

Example

Convert 45 degrees to radians:

45° × (π/180) ≈ 0.785 radians

Conversion Formula

Radians = Degrees × (π/180)

This formula works for any angle measurement in degrees. Simply multiply the degree value by π/180 to get the equivalent in radians.

The constant π (pi) is approximately 3.14159265359. For more precise calculations, you can use the π value provided by your calculator or programming language.

Example Conversions

Here are some common degree-to-radian conversions:

Degrees	Radians
0°	0
30°	0.5236
45°	0.7854
60°	1.0472
90°	1.5708
180°	3.1416
270°	4.7124
360°	6.2832

These examples show how degrees and radians relate to each other. Notice that 180° is equal to π radians, and 360° is equal to 2π radians.

Common Uses of Degrees and Radians

Degrees and radians are used in different contexts depending on the application.

Degrees

Navigation (compass bearings)
Temperature measurements (Fahrenheit and Celsius scales)
Everyday measurements (e.g., angles in architecture)
Trigonometry problems in basic math

Radians

Advanced mathematics (calculus, complex analysis)
Physics (rotational motion, wave theory)
Engineering (electrical circuits, signal processing)
Computer graphics (3D modeling, animations)

Understanding when to use degrees and radians is important for accurate calculations in different fields.

FAQ

Why do we need to convert degrees to radians?

Different fields use different units for angles. Degrees are more intuitive for everyday use, while radians are more mathematically convenient for advanced calculations.

Is there a simple way to remember the conversion formula?

Yes! Remember that a full circle is 360 degrees or 2π radians. Therefore, to convert degrees to radians, multiply by π/180.

Can I use this calculator for reverse conversions (radians to degrees)?

Yes, you can use the same formula in reverse: Degrees = Radians × (180/π). Our calculator can handle both conversions.

Are degrees and radians interchangeable?

No, they are not interchangeable. You must convert between them when working with different systems or formulas.