Convert Degrees to Radians Fraction Calculator

This guide explains how to convert degrees to radians, including the conversion formula, practical examples, and common angle conversions. The calculator on the right provides instant results for your specific values.

How to Convert Degrees to Radians

Converting degrees to radians is a fundamental trigonometry operation. Radians are the standard unit of angular measurement in calculus and higher mathematics, while degrees are more common in everyday contexts.

The conversion process involves multiplying the degree value by π/180. This relationship comes from the fact that a full circle is 360 degrees or 2π radians.

Note: The π (pi) symbol represents the mathematical constant approximately equal to 3.141592653589793.

Conversion Formula

The exact formula for converting degrees to radians is:

radians = degrees × (π / 180)

This formula works for any angle measurement in degrees. The result will be in radians, which is the standard unit for trigonometric functions in calculus.

For fractional degrees, you can apply the same formula. For example, 45.5 degrees would be converted by multiplying 45.5 by π/180.

Worked Example

Let's convert 90 degrees to radians using the formula:

radians = 90 × (π / 180) radians = π / 2 radians ≈ 1.5708

So, 90 degrees is equal to π/2 radians (approximately 1.5708 radians).

This conversion is useful in trigonometry, physics, and engineering where radians are the standard unit for angular measurements.

Common Angle Conversions

Here are some common angle conversions from degrees to radians:

Degrees	Radians	Fraction of π
0°	0	0
30°	π/6 ≈ 0.5236	1/6
45°	π/4 ≈ 0.7854	1/4
60°	π/3 ≈ 1.0472	1/3
90°	π/2 ≈ 1.5708	1/2
180°	π ≈ 3.1416	1
270°	3π/2 ≈ 4.7124	3/2
360°	2π ≈ 6.2832	2

This table shows how common angles relate to both radians and fractions of π, which is particularly useful in trigonometric calculations.

FAQ

Why do we need to convert degrees to radians?

Radians are the standard unit for angular measurement in calculus and higher mathematics. Many trigonometric functions, especially those used in calculus, are defined in terms of radians. Converting degrees to radians allows for consistent calculations across different mathematical contexts.

How do I convert radians back to degrees?

To convert radians to degrees, use the formula: degrees = radians × (180/π). This is the inverse of the degrees to radians conversion formula.

What is the difference between degrees and radians?

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. This makes radians a more natural unit for calculus and trigonometric functions.