Graphing Calculator Radians to Degrees

Radians and degrees are two common units for measuring angles. This graphing calculator converts between radians and degrees, provides the conversion formula, and visualizes the relationship between the two units.

Conversion Formula

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

Degrees = Radians × (180/π)

Radians = Degrees × (π/180)

Where π (pi) is approximately 3.141592653589793.

This formula comes from the fact that a full circle is 360 degrees or 2π radians. Therefore, the conversion factor between degrees and radians is 180/π.

How to Use the Calculator

Enter the angle value in either radians or degrees in the input field.
Select the unit of your input value (radians or degrees).
Click the "Calculate" button to perform the conversion.
The result will appear in the result panel below the calculator.
Use the "Reset" button to clear all inputs and results.

Note: The calculator will automatically convert between radians and degrees based on your input selection.

Examples

Example 1: Convert 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: Convert 45 degrees to radians

Using the formula:

Radians = 45 × (π/180) ≈ 0.7854 radians

So, 45 degrees is approximately 0.7854 radians.

Visualization

The graph below shows the relationship between radians and degrees. The blue line represents the conversion from radians to degrees, and the red line represents the conversion from degrees to radians.

FAQ

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. A full circle is 2π radians or 360 degrees.
Why do we need to convert between radians and degrees?: Different fields use different units. For example, trigonometry often uses radians, while everyday measurements typically use degrees. Converting between the two allows for easier communication and calculation.
Is the conversion between radians and degrees exact?: Yes, the conversion is exact because it's based on mathematical definitions. The only approximation comes from using a finite number of decimal places for π.
Can I use this calculator for negative angles?: Yes, the calculator works with both positive and negative angles. The conversion formulas apply the same way to negative values.
What if I enter an angle larger than 360 degrees or 2π radians?: The calculator will still perform the conversion, but the result will be an angle that's coterminal with your input. For example, 400 degrees is equivalent to 40 degrees.