Radians to Degrees in Terms of Pi Calculator
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Reviewed by Calculator Editorial Team
Convert radians to degrees in terms of π with this precise calculator. Learn the conversion formula, see examples, and visualize the relationship between radians and degrees.
Conversion Formula
The relationship between radians and degrees is defined by the constant π (pi), which is approximately 3.141592653589793. The conversion formula is:
This formula allows you to express the degree measure in terms of π. For example, π radians is equal to 180 degrees, and π/2 radians is equal to 90 degrees.
Note: The calculator automatically simplifies the result to show the degree measure in terms of π when possible.
How to Use the Calculator
- Enter the radian value you want to convert in the input field.
- Select whether you want the result in decimal degrees or in terms of π.
- Click the "Calculate" button to see the result.
- Use the "Reset" button to clear the form and start over.
Examples
Example 1: Converting π/4 radians to degrees
Using the formula:
So, π/4 radians is equal to 45 degrees.
Example 2: Converting 2π radians to degrees
Using the formula:
So, 2π radians is equal to 360 degrees, which is a full circle.
Visualization
The chart below shows the relationship between radians and degrees for common angle measures.
FAQ
Why is π involved in the radian to degree conversion?
π is involved because a full circle (360 degrees) is equivalent to 2π radians. This relationship defines the conversion factor between radians and degrees.
Can I convert degrees to radians using this calculator?
No, this calculator specifically converts radians to degrees. For the reverse conversion, you can use our Degrees to Radians Calculator.
What is the difference between radians and degrees?
Degrees are based on the division of a circle into 360 equal parts, while radians are based on the radius of a circle. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius.