Degrees to Radians Converter

What are Degrees and Radians?

Degrees and radians are two different units used 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 degrees to radians, we use this formula:

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

Where:

• \(\text{Radians}\) is the angle in radians
• \(\text{Degrees}\) is the angle in degrees
• \(\pi\) (pi) is approximately equal to 3.14159

Step-by-Step Conversion

1. Take the degree value.
2. Multiply it by \(\frac{\pi}{180°}\) (approximately 0.01745).
3. The result is the angle in radians.

Example Calculation

Let's convert 90° to radians:

\[ \begin{align*} \text{Radians} &= 90° \times \frac{\pi}{180°} \\ &= 90 \times 0.01745 \\ &= 1.5708 \text{ radians} \\ &= \frac{\pi}{2} \text{ radians} \end{align*} \]

Visual Representation

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