Convert Degrees to Radians Calculator Online

Convert degrees to radians quickly and accurately with this online calculator. Learn the conversion formula, understand when radians are used, and see practical examples.

How to Convert Degrees to Radians

The conversion between degrees and radians is fundamental in trigonometry and physics. Degrees are commonly used in everyday measurements, while radians are the standard unit in calculus and advanced mathematics.

Conversion Formula

To convert degrees to radians, multiply the degree value by π/180.

Radians = Degrees × (π / 180)

The formula works because a full circle is 360 degrees or 2π radians. Therefore, π radians equals 180 degrees, leading to the conversion factor of π/180.

Step-by-Step Conversion

Identify the degree value you want to convert.
Multiply the degree value by π (pi).
Divide the result by 180.
The result is the equivalent value in radians.

Precision Note

For most practical purposes, π can be approximated as 3.14159265359. However, calculators and programming languages often use more precise values.

When to Use Radians

Radians are the preferred unit in advanced mathematics and physics because they simplify many calculations. Here are common scenarios where radians are used:

Calculus: Derivatives and integrals are defined using radians.
Physics: Angular velocity and acceleration are measured in radians per second.
Engineering: Rotational motion problems often use radians.
Computer Graphics: Trigonometric functions in programming typically use radians.

While degrees are more intuitive for everyday measurements, radians provide a more natural mathematical framework for higher-level applications.

Conversion Examples

Here are some common degree-to-radian conversions:

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

These values are rounded to four decimal places. The exact values would use π in the calculation.

FAQ

Why do we convert degrees to radians?: Radians provide a more natural mathematical framework for calculus and advanced physics. They simplify many trigonometric calculations.
Is π always the same value?: π (pi) is a mathematical constant approximately equal to 3.14159265359. It's an irrational number that cannot be expressed as a simple fraction.
Can I convert radians back to degrees?: Yes, to convert radians to degrees, multiply the radian value by 180/π.
When would I use degrees instead of radians?: Degrees are more intuitive for everyday measurements like temperature, angles in construction, and navigation.
Is there a difference between grads and radians?: Yes, grads (also called gradians or gon) are another unit of angle measurement where a full circle is 400 grads. They're used in some European countries.