Angle Converter: Radians to Degrees & Degrees to Radians

What is an Angle?

An angle is like a slice of pizza! It's the space between two lines that meet at a point. We can measure this space in two ways: degrees or radians. Degrees are like slicing your pizza into 360 pieces, while radians are based on the size of the pizza itself!

How to Convert Between Degrees and Radians

Converting between degrees and radians is like translating between two languages. We use simple multiplication or division to switch between them. It's as easy as following a recipe!

Formulas

Here are the magic formulas we use:

Degrees to Radians: \[ \text{radians} = \frac{\text{degrees} \times \pi}{180} \]

Radians to Degrees: \[ \text{degrees} = \frac{\text{radians} \times 180}{\pi} \]

Where:

• \(\text{degrees}\) is the angle measured in degrees
• \(\text{radians}\) is the angle measured in radians
• \(\pi\) (pi) is approximately 3.14159

Calculation Steps

1. Decide if you're converting from degrees to radians or radians to degrees
2. If converting degrees to radians:
   • Multiply your angle in degrees by π
   • Divide the result by 180
3. If converting radians to degrees:
   • Multiply your angle in radians by 180
   • Divide the result by π
4. Round your answer if needed

Example and Visual Representation

Let's convert 90 degrees to radians:

\[ \frac{90 \times \pi}{180} = \frac{\pi}{2} \approx 1.5708 \text{ radians} \]

Now, let's see this visually:

In this circle, the red line shows a 90-degree angle (or π/2 radians). The blue arc measures the angle. You can see it's exactly one-quarter of the full circle!