Convert Degrees to Radians Calculator

Convert degrees to radians quickly and accurately with our online calculator. Learn the conversion formula, see examples, and understand the difference between degrees and radians.

What is Degrees to Radians Conversion?

Degrees and radians are two units of measurement for angles. Degrees are commonly used in everyday contexts, while radians are more common in advanced mathematics and physics. The conversion between degrees and radians is essential for many calculations in trigonometry, calculus, and engineering.

Key Conversion Fact

1 degree (°) = π/180 radians (rad)

This relationship comes from the fact that a full circle is 360 degrees or 2π radians. Therefore, the conversion factor is π/180.

How to Convert Degrees to Radians

To convert degrees to radians, multiply the degree value by π/180. Here's the step-by-step process:

Identify the angle in degrees that you want to convert.
Multiply the degree value by π/180.
The result is the equivalent angle in radians.

Conversion Formula

radians = degrees × (π/180)

For example, to convert 90 degrees to radians:

Example Calculation

90° × (π/180) = π/2 ≈ 1.5708 radians

This conversion is useful in many fields, including physics, engineering, and computer graphics.

Degrees vs Radians

Degrees and radians are both units for measuring angles, but they have different scales and uses:

Unit	Full Circle	Common Uses
Degrees (°)	360°	Everyday measurements, navigation, weather
Radians (rad)	2π ≈ 6.2832 rad	Advanced mathematics, physics, engineering

Degrees are more intuitive for everyday use because they divide a circle into 360 equal parts. Radians, on the other hand, are based on the radius of a circle, making them more natural for calculus and trigonometric functions.

Common Angle Conversions

Here are some common angle conversions between degrees and radians:

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

These common conversions are useful for quick reference in various mathematical and scientific applications.

FAQ

What is the difference between degrees and radians?

Degrees divide a circle into 360 equal parts, while radians divide it into 2π parts based on the radius of the circle. Degrees are more intuitive for everyday use, while radians are more natural for advanced mathematics.

How do I convert radians to degrees?

To convert radians to degrees, multiply the radian value by 180/π. The formula is: degrees = radians × (180/π).

Why are radians used in calculus?

Radians are used in calculus because they simplify many mathematical operations, especially those involving derivatives and integrals of trigonometric functions.

What is the value of π used in degree to radian conversion?

The value of π used in the conversion is approximately 3.141592653589793, but you can use a calculator's π function for more precise results.

Can I use this calculator for negative angles?

Yes, the calculator can handle negative angles. The conversion formula works the same way for negative values.