Angles to Degrees Calculator

Convert angles between degrees and radians with our free online calculator. This tool helps you quickly convert between these two common angular units used in mathematics, physics, and engineering.

How to Use This Calculator

Using our angles to degrees calculator is simple:

Enter the angle value in the input field
Select the unit you're converting from (degrees or radians)
Click the "Calculate" button
View the converted value in the result panel

The calculator will automatically convert between degrees and radians based on your selection. You can also use the "Reset" button to clear all inputs and start over.

Formula Used

The conversion between degrees and radians is based on the relationship between these units:

1 radian = (180/π) degrees ≈ 57.2958 degrees

1 degree = (π/180) radians ≈ 0.0174533 radians

To convert from degrees to radians:

radians = degrees × (π/180)

To convert from radians to degrees:

degrees = radians × (180/π)

Our calculator uses these exact formulas to provide precise conversions.

Worked Examples

Example 1: Convert 90 degrees to radians

Using the formula:

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

So, 90 degrees is approximately 1.5708 radians.

Example 2: Convert π/2 radians to degrees

Using the formula:

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

So, π/2 radians is exactly 90 degrees.

Example 3: Convert 45 degrees to radians

Using the formula:

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

So, 45 degrees is approximately 0.7854 radians.

FAQ

What is the difference between degrees and radians?: Degrees and radians are both units of measurement for angles. A full circle is 360 degrees or 2π radians. Degrees are commonly used in everyday contexts, while radians are more common in advanced mathematics and physics.
When should I use degrees vs radians?: Degrees are typically used in everyday applications like navigation, construction, and basic geometry. Radians are more common in calculus, physics, and engineering where trigonometric functions are involved.
How accurate is this calculator?: This calculator uses precise mathematical formulas and JavaScript's built-in Math.PI value for π. The results are accurate to at least 15 decimal places.
Can I convert between other angle units?: This calculator specifically converts between degrees and radians. For other angle conversions, you would need a different tool.
Is this calculator free to use?: Yes, this calculator is completely free to use with no ads or hidden fees. You can convert as many angles as you need without any restrictions.