Calculator for Degrees

This calculator helps you convert between different degree units: degrees, radians, and gradians. Whether you're working with angles in geometry, trigonometry, or navigation, this tool provides quick and accurate conversions.

How to Use This Calculator

Using the degree calculator is simple:

Enter the value you want to convert in the input field.
Select the unit you're converting from in the "From" dropdown.
Select the unit you want to convert to in the "To" dropdown.
Click the "Calculate" button to see the result.
Use the "Reset" button to clear all fields and start over.

The calculator will display the converted value and show a visual representation of the conversion when possible.

Conversion Formulas

The calculator uses these standard formulas for degree conversions:

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)

Important Notes

The calculator uses π (pi) with a precision of 15 decimal places for accurate conversions. The formulas above are the standard mathematical conversions between these units.

Common Degree Units

Here's a quick reference for the three main degree units:

Unit	Symbol	Full Name	Range
Degree	°	Degree of arc	0° to 360°
Radian	rad	Radian	0 to 2π (≈6.283)
Gradian	grad	Gradian	0 to 400

Degrees are the most commonly used unit for measuring angles, while radians are more common in advanced mathematics and physics. Gradians are used in some European countries and are sometimes preferred for their simplicity in certain calculations.

Practical Examples

Here are some practical examples of degree conversions:

Example 1: Converting 90° to Radians

Using the formula: Radians = 90 × (π / 180) ≈ 1.5708 radians

Example 2: Converting 1 Radian to Degrees

Using the formula: Degrees = 1 × (180 / π) ≈ 57.2958°

Example 3: Converting 100 Gradians to Degrees

Using the formula: Degrees = 100 × (9 / 10) = 90°

These examples show how the calculator can be used in real-world scenarios, from basic geometry to advanced physics calculations.

Frequently Asked Questions

What is the difference between degrees and radians?

Degrees and radians are both units for measuring angles, but they have different scales. A full circle is 360 degrees or 2π radians. Degrees are more intuitive for everyday use, while radians are more common in advanced mathematics and physics.

How accurate is this degree calculator?

The calculator uses precise mathematical formulas and π with 15 decimal places, ensuring accurate conversions. However, for extremely precise applications, you may want to verify with a scientific calculator.

Can I convert between gradians and radians directly?

No, you need to convert through degrees first. For example, to convert gradians to radians, first convert gradians to degrees, then degrees to radians.

What are some common uses for degree conversions?

Degree conversions are used in geometry, trigonometry, navigation, engineering, and physics. They're essential for calculating angles in triangles, understanding circular motion, and working with waves.

Is this calculator free to use?

Yes, this calculator is completely free to use. There are no hidden fees or premium features.