Degrees to Radians Pi Calculator

Convert degrees to radians with our precise π calculator. Learn the conversion formula, π values in both units, and practical examples.

What is Degrees to Radians?

Degrees and radians are two common units for measuring angles. Degrees are used in everyday contexts like navigation and construction, while radians are more common in advanced mathematics and physics. The key difference is that a full circle is 360 degrees but only 2π radians.

Converting between degrees and radians is essential for working with trigonometric functions, circular motion, and wave equations. Our calculator provides an accurate conversion using the fundamental relationship between these units.

How to Convert Degrees to Radians

To convert degrees to radians, multiply the degree value by π/180. This conversion factor comes from the fact that 180 degrees equals π radians (a straight angle).

radians = degrees × (π / 180)

For example, to convert 90 degrees to radians:

Example

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

Our calculator performs this calculation instantly with precise π values.

π in Degrees and Radians

The value of π (pi) is approximately 3.141592653589793. In degrees, π radians is exactly 180 degrees. This relationship is fundamental to angle measurements.

π radians = 180 degrees

This means that any angle in radians can be converted to degrees by multiplying by 180/π, and vice versa.

Degrees to Radians Formula

The conversion formula from degrees to radians is straightforward:

radians = degrees × (π / 180)

Where:

degrees is the angle measurement in degrees
π is the mathematical constant pi (approximately 3.141592653589793)
radians is the resulting angle measurement in radians

This formula works for any angle measurement, whether positive or negative.

Degrees to Radians Examples

Here are some common degree-to-radian conversions:

Example 1: 45 degrees to radians

45° × (π / 180) = π/4 radians ≈ 0.7854 radians

Example 2: 180 degrees to radians

180° × (π / 180) = π radians ≈ 3.1416 radians

Example 3: 360 degrees to radians

360° × (π / 180) = 2π radians ≈ 6.2832 radians

These examples show how the conversion works for standard angles.

Degrees to Radians Table

Here's a table showing common degree-to-radian conversions:

Degrees	Radians	Radians (Decimal)
0°	0	0.0000
30°	π/6	0.5236
45°	π/4	0.7854
60°	π/3	1.0472
90°	π/2	1.5708
120°	2π/3	2.0944
180°	π	3.1416
270°	3π/2	4.7124
360°	2π	6.2832

This table provides quick reference points for common angle conversions.

FAQ

How do I convert radians to degrees?

To convert radians to degrees, multiply the radian value by 180/π. This is the inverse of the degrees-to-radians conversion.

What is the value of π in degrees?

π radians is exactly 180 degrees. This is the fundamental relationship between these units.

Why do we need to convert between degrees and radians?

Different fields use different units. Degrees are more intuitive for everyday use, while radians are more convenient for advanced mathematics and physics calculations.

What is the difference between a degree and a radian?

A degree is 1/360th of a full circle, while a radian is the angle created by a radius-length arc in a unit circle. This means 360 degrees equals 2π radians.