Computing Radians to Degrees Calculator

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

Conversion Formula

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

Degrees = Radians × (180/π)

Where π (pi) is approximately 3.141592653589793.

This formula comes from the fact that a full circle is 360 degrees or 2π radians. Therefore, one radian equals 180/π degrees.

When to Use Radians vs Degrees

Both radians and degrees are used to measure angles, but they are used in different contexts:

Degrees are commonly used in everyday life, such as in navigation, geography, and common measurements.
Radians are more commonly used in advanced mathematics, physics, and engineering, particularly in calculus and trigonometry.

In most scientific and technical fields, radians are preferred because they simplify many mathematical formulas and calculations.

Example Conversions

Here are some common angle conversions between radians and degrees:

Radians	Degrees
0	0
π/6	30
π/4	45
π/2	90
π	180
3π/2	270
2π	360

Common Angle Conversions

Here are some common angles and their conversions between radians and degrees:

Angle Name	Radians	Degrees
Right Angle	π/2	90
Straight Angle	π	180
Full Rotation	2π	360
45 Degree Angle	π/4	45
30 Degree Angle	π/6	30

FAQ

Why do we need to convert radians to degrees?

Radians and degrees are used in different contexts. Degrees are more common in everyday life, while radians are more common in advanced mathematics and physics. Converting between the two allows for better understanding and application in different fields.

Is π the same in radians and degrees?

No, π radians is equal to 180 degrees. This is because a full circle is 360 degrees or 2π radians.

Can I convert degrees to radians using this calculator?

Yes, you can use the same formula in reverse: Radians = Degrees × (π/180). Our calculator can handle both conversions.