Common Conversions

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

Degrees

Radians

Action

0°

30°

π/6

45°

π/4

60°

π/3

90°

π/2

180°

270°

3π/2

360°

2π

Understanding Degrees and Radians

Radians are the standard unit of angular measure in mathematics. One radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. Since the circumference equals 2πr, there are 2π radians in a full circle (360°).

Conversion Formula

radians = degrees × (π / 180)

Example Calculations

45° to radians: 45 × (π/180) = π/4 ≈ 0.7854 rad
90° to radians: 90 × (π/180) = π/2 ≈ 1.5708 rad
180° to radians: 180 × (π/180) = π ≈ 3.1416 rad

Why Use Radians?

Radians provide a natural way to describe angles in calculus and physics because they simplify many mathematical expressions. For example, derivatives of trigonometric functions are straightforward when using radians.

Frequently Asked Questions

Why is 180 degrees equal to π radians?

Because the circumference of a circle is 2πr, half a circle (180°) corresponds to π radians based on the arc length formula.

How do I convert negative degrees to radians?

Use the same formula: radians = degrees × (π/180). Negative degrees will result in negative radians.

Can I convert radians back to degrees?

Yes, use the formula: degrees = radians × (180/π).

Degrees to Radians Converter

Menu

Degrees to Radians Converter - Deg to Rad

AI Assistant

Was this tool helpful?