Radians to Degrees Online Calculator

Convert radians to degrees with our free online calculator. Learn the conversion formula, see examples, and understand when to use radians vs degrees.

How to Convert Radians to Degrees

Radians and degrees are two common units for measuring angles. While degrees are more familiar in everyday contexts, radians are widely used in advanced mathematics, physics, and engineering because they simplify many calculations involving circles and trigonometry.

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

Conversion Formula

Degrees = Radians × (180/π)

This formula works because a full circle is 360 degrees or 2π radians. Therefore, one radian equals 180/π degrees.

For example, π radians is equal to 180 degrees because π × (180/π) = 180. Similarly, π/2 radians equals 90 degrees.

Conversion Formula

The exact formula for converting radians to degrees is:

Radians to Degrees Formula

Degrees = Radians × (180/π)

Where π (pi) is approximately 3.141592653589793.

This formula is derived from the fact that a full circle (360 degrees) is equivalent to 2π radians. Therefore, to convert radians to degrees, you multiply the radian value by 180/π.

For precise calculations, it's best to use the mathematical constant π rather than its approximation. Most programming languages and scientific calculators provide π as a built-in constant.

Worked Examples

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

Example 1: Convert 1 radian to degrees

Using the formula:

Degrees = 1 × (180/π) ≈ 1 × 57.2958 ≈ 57.2958 degrees

So, 1 radian is approximately 57.2958 degrees.

Example 2: Convert π/4 radians to degrees

Using the formula:

Degrees = (π/4) × (180/π) = (π × 180)/(4 × π) = 180/4 = 45 degrees

So, π/4 radians equals exactly 45 degrees.

Example 3: Convert 3 radians to degrees

Using the formula:

Degrees = 3 × (180/π) ≈ 3 × 57.2958 ≈ 171.8874 degrees

So, 3 radians is approximately 171.8874 degrees.

Note

When working with radians, it's often helpful to remember that π radians equals 180 degrees. This relationship makes many trigonometric calculations simpler.

Radians vs Degrees

Both radians and degrees are units for measuring angles, but they have different properties and uses.

Feature	Radians	Degrees
Full circle	2π radians	360 degrees
Common in	Advanced math, physics, engineering	Everyday measurements, navigation
Trigonometric functions	Simpler formulas (e.g., sin(π/2) = 1)	More familiar for basic angles
Range of angles	0 to 2π radians	0 to 360 degrees

In most scientific and engineering applications, radians are preferred because they simplify many calculations, especially those involving calculus and differential equations. However, degrees are more intuitive for everyday measurements and navigation.

FAQ

How do I convert radians to degrees?: Multiply the radian value by 180/π to get the equivalent in degrees. For example, π radians equals 180 degrees.
Why do we use radians instead of degrees?: Radians are often used in advanced mathematics and physics because they simplify many calculations, especially those involving calculus and trigonometric functions.
What is the difference between radians and degrees?: A full circle is 360 degrees or 2π radians. This means that 1 radian is equal to 180/π degrees, approximately 57.2958 degrees.
When should I use radians vs degrees?: Use radians for advanced mathematical and scientific calculations. Use degrees for everyday measurements and navigation.
Can I convert degrees to radians with the same formula?: Yes, to convert degrees to radians, multiply by π/180. For example, 180 degrees equals π radians.