Pi 90 Radians to Degrees Calculator

Convert π radians to degrees with our precise calculator. Learn the conversion formula, see worked examples, and understand 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, 1 radian equals 180/π degrees.

How to Convert Radians to Degrees

Multiply the radian value by 180.
Divide the result by π (approximately 3.141592653589793).
The result is the equivalent angle in degrees.

For example, to convert π radians to degrees:

π radians × (180/π) = 180 degrees

π Radians Example

Let's convert π radians to degrees using the formula:

π radians × (180/π) = 180 degrees

This shows that π radians is exactly 180 degrees, which is half of a full circle (360 degrees).

Radians vs Degrees

Radians and degrees are two different units for measuring angles. Here's how they compare:

Unit	Full Circle	Common Use
Degrees	360°	Everyday measurements, navigation
Radians	2π ≈ 6.283 radians	Calculus, physics, engineering

Degrees are more intuitive for everyday use, while radians are more mathematically convenient for advanced calculations.

Common Angle Conversions

Here are some common angle conversions between radians and degrees:

Radians	Degrees
0	0°
π/6	30°
π/4	45°
π/3	60°
π/2	90°
π	180°
3π/2	270°
2π	360°

FAQ

Why do we need both radians and degrees?

Degrees are more intuitive for everyday measurements, while radians are more mathematically convenient for advanced calculations, especially in calculus and physics.

Is π radians equal to 180 degrees?

Yes, π radians is exactly equal to 180 degrees because a full circle is 360 degrees or 2π radians.

How do I convert degrees to radians?

To convert degrees to radians, multiply by π/180. For example, 90° × (π/180) = π/2 radians.