Convert Angles to Degrees Calculator

Convert angles between degrees, radians, and gradians with our precise angle conversion calculator. Whether you're working with geometry, navigation, or engineering, this tool provides quick and accurate conversions between different angle measurement systems.

How to Use This Calculator

Using our angle conversion calculator is simple:

Enter the angle value in the input field.
Select the unit you're converting from (degrees, radians, or gradians).
Click the "Calculate" button to see the converted values.
Use the "Reset" button to clear the calculator for new calculations.

The calculator will display the converted values in all three angle units, making it easy to compare and work with different angle measurements.

Angle Conversion Formulas

Angle conversion between different units uses these fundamental formulas:

Degrees to Radians

Radians = Degrees × (π / 180)

Radians to Degrees

Degrees = Radians × (180 / π)

Degrees to Gradians

Gradians = Degrees × (10 / 9)

Gradians to Degrees

Degrees = Gradians × (9 / 10)

Note: π (pi) is approximately 3.141592653589793. For more precise calculations, use the value of π provided by your calculation software.

Common Angle Conversions

Here are some common angle conversions you might encounter:

Degrees	Radians	Gradians
0°	0 rad	0 grad
30°	0.5236 rad	33.3333 grad
45°	0.7854 rad	50 grad
60°	1.0472 rad	66.6667 grad
90°	1.5708 rad	100 grad
180°	3.1416 rad	200 grad
270°	4.7124 rad	300 grad
360°	6.2832 rad	400 grad

This table provides quick reference points for common angle conversions. You can use these values as a guide when working with different angle measurement systems.

Angle Conversion Examples

Let's look at some practical examples of angle conversions:

Example 1: Converting 90 Degrees to Radians

Using the formula: Radians = Degrees × (π / 180)

90° × (3.1416 / 180) ≈ 1.5708 radians

So, 90 degrees is approximately 1.5708 radians.

Example 2: Converting 2 Radians to Degrees

Using the formula: Degrees = Radians × (180 / π)

2 × (180 / 3.1416) ≈ 114.5916 degrees

So, 2 radians is approximately 114.5916 degrees.

Example 3: Converting 100 Gradians to Degrees

Using the formula: Degrees = Gradians × (9 / 10)

100 × (9 / 10) = 90 degrees

So, 100 gradians is exactly 90 degrees.

These examples demonstrate how to convert between different angle units using the appropriate formulas. The calculator can handle these conversions quickly and accurately for any angle value you need to convert.

Frequently Asked Questions

What is the difference between degrees, radians, and gradians?

Degrees, radians, and gradians are all units of measurement for angles. Degrees are the most commonly used unit, with a full circle being 360 degrees. Radians are based on the radius of a circle, with a full circle being 2π radians (approximately 6.2832 radians). Gradians, also known as grads, divide a right angle into 100 parts, making a full circle 400 gradians.

When should I use degrees, radians, or gradians?

Degrees are typically used in everyday applications like navigation and construction. Radians are commonly used in advanced mathematics, physics, and engineering, especially when working with trigonometric functions. Gradians are less common but can be useful in certain technical applications where a different scale is preferred.

How accurate are the conversions in this calculator?

The calculator uses precise mathematical formulas to perform conversions. For most practical purposes, the results are accurate to several decimal places. However, for extremely precise calculations, you might want to use more advanced software or programming tools.

Can I convert angles to other units besides degrees, radians, and gradians?

This calculator specifically converts between degrees, radians, and gradians. If you need to convert to other angle units, you may need to use additional conversion tools or formulas.

Is there a way to save my angle conversion results?

Currently, this calculator does not have a save feature. However, you can manually note down the results or use your browser's print function to save a copy of the conversion.