Convert Degrees Radians Calculator

Convert between degrees and radians with our precise online calculator. Degrees and radians are two common units for measuring angles, with degrees being more familiar in everyday contexts and radians being more common in advanced mathematics and physics. This calculator provides an easy way to switch between these units.

What is Degrees vs Radians?

Degrees and radians are both units of measurement for angles, but they represent different concepts in geometry and trigonometry.

Degrees

Degrees are a unit of measurement for angles based on the full circle being divided into 360 equal parts. This system is commonly used in everyday contexts, such as navigation, construction, and basic geometry.

Radians

Radians are a unit of measurement for angles based on the radius of a circle. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius. A full circle is 2π radians (approximately 6.283 radians).

The relationship between degrees and radians is fundamental in trigonometry and calculus. Many mathematical formulas and equations are expressed more naturally in radians than in degrees.

Conversion Formula

The conversion between degrees and radians is straightforward using the relationship between these units:

radians = degrees × (π / 180) degrees = radians × (180 / π)

Where π (pi) is approximately 3.141592653589793.

This formula allows you to convert any angle measurement from degrees to radians or vice versa. The calculator implements this formula to provide accurate conversions.

How to Use the Calculator

Using the degrees to radians calculator is simple:

Enter the angle value you want to convert in the input field.
Select whether you want to convert from degrees to radians or radians to degrees.
Click the "Calculate" button to perform the conversion.
The result will be displayed in the result panel below the calculator.

The calculator also provides a visual representation of the conversion using a chart, showing the relationship between degrees and radians.

Common Conversions

Here are some common angle conversions between degrees and radians:

Degrees	Radians
0°	0 rad
30°	0.5236 rad
45°	0.7854 rad
60°	1.0472 rad
90°	1.5708 rad
180°	3.1416 rad
270°	4.7124 rad
360°	6.2832 rad

These common conversions can be useful for quick reference when working with angles in different units.

Frequently Asked Questions

What is the difference between degrees and radians?: Degrees are based on dividing 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.
When should I use degrees and when should I use radians?: Degrees are more commonly used in everyday contexts, such as navigation and construction, while radians are more common in advanced mathematics and physics, particularly in calculus and trigonometry.
How do I convert degrees to radians?: To convert degrees to radians, multiply the degree value by π/180. For example, 90 degrees is 90 × (π/180) = π/2 radians.
How do I convert radians to degrees?: To convert radians to degrees, multiply the radian value by 180/π. For example, π/2 radians is (π/2) × (180/π) = 90 degrees.
What is the relationship between degrees and radians?: The relationship between degrees and radians is defined by the formula: radians = degrees × (π/180). This formula allows you to convert any angle measurement from degrees to radians or vice versa.