Radians to Degrees Converter

What are Radians and Degrees?

Radians and degrees are two different ways to measure angles. While degrees are more commonly used in everyday life, radians are often preferred in advanced mathematics and physics due to their natural relationship with the radius of a circle.

• Degrees: In the degree system, a full circle is divided into 360 equal parts, with each part being one degree (°).
• Radians: In the radian system, one radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.

The Conversion Formula

To convert radians to degrees, we use this formula:

\[ \text{Degrees} = \text{Radians} \times \frac{180°}{\pi} \]

Where \(\pi\) (pi) is approximately equal to 3.14159.

Step-by-Step Conversion

1. Take the radian value.
2. Multiply it by \(\frac{180°}{\pi}\) (approximately 57.2958).
3. The result is the angle in degrees.

Example Calculation

Let's convert π/2 radians to degrees:

\[ \begin{align*} \text{Degrees} &= \frac{\pi}{2} \times \frac{180°}{\pi} \\ &= \frac{180°}{2} \\ &= 90° \end{align*} \]

Visual Representation

This diagram shows the angle π/2 radians represented as 90° on a circle.