How to Convert From Degrees to Radians on Calculator

Converting degrees to radians is a fundamental skill in trigonometry and physics. This guide explains the conversion process, provides a conversion formula, and includes a built-in calculator for quick conversions.

What is Degrees to Radians Conversion?

Degrees and radians are two different units for measuring angles. Degrees are commonly used in everyday contexts, while radians are more frequently used in advanced mathematics and physics.

The degree is a unit of angular measurement based on the full circle being 360 degrees. The radian is an angle measurement 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.

Key Point: The conversion between degrees and radians is essential for working with trigonometric functions in calculus, physics, and engineering.

How to Convert Degrees to Radians

To convert degrees to radians, you can use the following steps:

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

This conversion is based on the fact that a full circle (360 degrees) is equivalent to 2π radians.

Degrees to Radians Formula

The formula to convert degrees to radians is:

Radians = Degrees × (π / 180)

Where:

Degrees is the angle measurement in degrees.
π (pi) is approximately 3.141592653589793.
180 is the number of degrees in a half-circle.

This formula works because a full circle is 360 degrees, which is equivalent to 2π radians. Therefore, a half-circle (180 degrees) is equivalent to π radians.

Degrees to Radians Examples

Let's look at a few examples to understand how the conversion works.

Example 1: Convert 90 Degrees to Radians

Using the formula:

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

So, 90 degrees is equal to π/2 radians.

Example 2: Convert 180 Degrees to Radians

Using the formula:

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

So, 180 degrees is equal to π radians.

Example 3: Convert 30 Degrees to Radians

Using the formula:

Radians = 30 × (π / 180) = π/6 ≈ 0.5236 radians

So, 30 degrees is equal to π/6 radians.

Degrees to Radians Conversion Table

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

Degrees	Radians	Exact Value
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

FAQ

Why do we need to convert degrees to radians?

Degrees and radians are used in different contexts. Degrees are more intuitive for everyday measurements, while radians are more convenient for advanced mathematics, physics, and engineering calculations.

Is π/180 the same as 180/π?

No, π/180 is not the same as 180/π. The correct conversion factor is π/180, as it relates the number of degrees to the number of radians in a half-circle.

Can I use a calculator to convert degrees to radians?

Yes, you can use a scientific calculator or the built-in calculator on this page to convert degrees to radians quickly and accurately.

What is the difference between degrees and radians?

Degrees are based on the full circle being 360 degrees, 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 that is equal in length to the radius.