If you need to convert radians to degrees, this guide will help you understand the conversion formula, provide a reference table, and offer practical examples to make the process easier.

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Conversion Formula

To convert radians (rad) to degrees (°), use the following formula:

Degrees (°) = Radians (rad) × (180 / π)

Explanation:

• π (Pi) is approximately 3.14159.
• 1 radian is equal to 180/π degrees.

Thus, to convert radians to degrees, multiply the number of radians by 180/π, or approximately 57.2958.

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Conversion Table: Radians to Degrees

Here’s a quick reference table for converting radians to degrees:

Radians (rad)	Degrees (°)
0	0°
0.1	5.7296°
0.5	28.6479°
1	57.2958°
2	114.5916°
π/2	90°
π	180°
2π	360°
5	286.478°
10	572.957°

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Quick Conversion Example

Let’s say you have 2 radians and want to convert it to degrees.

Degrees (°) = 2 × (180 / π) = 2 × 57.2958 = 114.5916°

So, 2 radians is equal to approximately 114.59 degrees.

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Frequently Asked Questions (FAQs)

1. How do I convert degrees to radians?

To convert degrees (°) to radians (rad), use the inverse formula:

Radians (rad) = Degrees (°) × (π / 180)

For example, to convert 90 degrees to radians:

Radians (rad) = 90 × (π / 180) = π / 2 ≈ 1.5708 rad

2. Why do we multiply by (180 / π) in this conversion?

We multiply by (180 / π) because 1 radian is defined as the angle subtended by an arc whose length is equal to the radius of the circle. π radians is equivalent to 180 degrees, which is why the conversion factor is 180/π.

3. Can I use an online converter for this?

Yes! Online converters are quick and convenient for converting radians to degrees. Simply input the value in radians, and the result will be displayed in degrees.

4. Where is this conversion used?

This conversion is commonly used in trigonometry, geometry, physics, engineering, and computer graphics, where angles are often measured in radians for more accurate mathematical modeling.

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Conclusion

Now that you have the formula, conversion table, and example, converting radians to degrees is simple. Whether you’re working in mathematics, physics, or engineering, understanding this conversion will help you perform calculations with angular measurements more effectively. Online tools can make this process faster, but knowing the formula will help you when you need to convert manually.