Convert Radians to Degrees in Calculator

Converting radians to degrees is a fundamental skill in trigonometry and physics. This calculator provides an easy way to perform the conversion, along with explanations of when and why you might need to convert between these two units of angular measurement.

Conversion Formula

The relationship between radians and degrees is defined by the following formula:

degrees = radians × (180/π)

Conversely, to convert degrees to radians:

radians = degrees × (π/180)

Where π (pi) is approximately 3.141592653589793.

This conversion is based on the fact that a full circle is 360 degrees or 2π radians. Therefore, the conversion factor is 180/π.

How to Use the Calculator

Enter the value you want to convert in the "Radians" field.
Click the "Calculate" button to perform the conversion.
The result in degrees will appear in the result box below.
To convert degrees to radians, use the "Convert Degrees to Radians" link below the calculator.

The calculator will automatically handle the conversion using the formula shown above. You can also see a visual representation of the conversion on the chart.

Examples

Example 1: Converting π/2 radians to degrees

Using the formula:

degrees = (π/2) × (180/π) = 90 degrees

So, π/2 radians is equal to 90 degrees.

Example 2: Converting 1.5708 radians to degrees

Using the formula:

degrees = 1.5708 × (180/π) ≈ 90 degrees

So, 1.5708 radians is approximately equal to 90 degrees.

Example 3: Converting 3 radians to degrees

Using the formula:

degrees = 3 × (180/π) ≈ 171.887 degrees

So, 3 radians is approximately equal to 171.887 degrees.

Radians vs Degrees

Both radians and degrees are units of angular measurement, but they are used in different contexts:

Degrees are commonly used in everyday contexts, such as measuring angles in geometry and navigation. A full circle is 360 degrees.
Radians are more commonly used in advanced mathematics, physics, and engineering. A full circle is 2π radians.

When working with trigonometric functions, it's important to know whether the angle is in radians or degrees. Most programming languages and calculators assume angles are in radians, while many scientific calculators have a "Deg" or "Rad" button to switch between the two.

FAQ

Why do I need to convert radians to degrees?

You might need to convert radians to degrees when working with measurements that are more commonly expressed in degrees, such as angles in geometry or navigation. Many people find degrees easier to visualize and work with in everyday contexts.

Is there a difference between radians and degrees?

Yes, radians and degrees are different units of angular measurement. A full circle is 360 degrees or 2π radians. The conversion factor between them is 180/π.

Can I convert degrees to radians with this calculator?

Yes, you can convert degrees to radians by entering the value in the "Degrees" field and clicking the "Calculate" button. The calculator will show the equivalent value in radians.

What is the difference between π radians and 180 degrees?

π radians is exactly equal to 180 degrees. This is because the conversion factor between radians and degrees is 180/π, so π × (180/π) = 180 degrees.