Degrees to Radians Calculator in Pi

Convert degrees to radians in terms of π with our precise calculator. Learn the conversion formula, see examples, and understand radians in terms of π.

Conversion Formula

The relationship between degrees and radians is defined by the formula:

radians = degrees × (π/180)

This formula converts degrees to radians by multiplying the degree value by π divided by 180. The constant π (pi) is approximately 3.14159265359.

For example, to convert 90 degrees to radians:

90° × (π/180) = π/2 radians

This means 90 degrees is equal to π/2 radians.

How to Use the Calculator

Enter the degree value you want to convert in the input field.
Click the "Calculate" button to perform the conversion.
The result will be displayed in radians, both as a decimal and in terms of π.
Use the "Reset" button to clear the input and results.

The calculator provides both the decimal approximation and the exact value in terms of π for better understanding.

Examples

Example 1: Convert 45 degrees to radians

Using the formula:

45° × (π/180) = π/4 radians

45 degrees is equal to π/4 radians, which is approximately 0.7854 radians.

Example 2: Convert 180 degrees to radians

Using the formula:

180° × (π/180) = π radians

180 degrees is equal to π radians, which is approximately 3.1416 radians.

Example 3: Convert 30 degrees to radians

Using the formula:

30° × (π/180) = π/6 radians

30 degrees is equal to π/6 radians, which is approximately 0.5236 radians.

Common Angles in Degrees and Radians

The following table shows common angles in both degrees and radians:

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

This table provides quick reference for common angle conversions.

FAQ

What is the difference between degrees and radians?: Degrees and radians are two different units for measuring angles. A full circle is 360 degrees or 2π radians. Radians are the standard unit in most scientific and mathematical contexts.
Why is π used in degree to radian conversion?: π (pi) is used because it represents the ratio of a circle's circumference to its diameter. This relationship is fundamental in trigonometry and makes π the natural unit for measuring angles in radians.
Can I convert radians back to degrees?: Yes, you can convert radians back to degrees using the formula: degrees = radians × (180/π). This is the inverse of the degree to radian conversion formula.
What are some practical uses of radians?: Radians are commonly used in physics, engineering, and higher mathematics. They are particularly useful in calculus, where derivatives and integrals of trigonometric functions are expressed in radians.
Is there a difference between π and pi?: Both π and pi refer to the same mathematical constant, which is approximately 3.14159265359. The choice between the two symbols depends on the context and the conventions of the field.