Angles and Degrees Calculator

This angles and degrees calculator provides precise conversion between degrees, radians, and gradians. Whether you're working with geometric problems, navigation, or scientific calculations, this tool helps you quickly and accurately convert between different angle measurement systems.

How to Use This Calculator

Using the angles and degrees calculator is simple:

Enter the angle 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 converted value.
Use the "Reset" button to clear all fields and start over.

The calculator will display the converted value along with a visual representation of the angle conversion when available.

Angle Conversion Basics

Angles can be measured in different units, each with its own scale and applications:

Degrees (°): The most common unit for measuring angles, with a full circle being 360 degrees.
Radians (rad): A unit based on the radius of a circle, with π radians equal to 180 degrees.
Gradians (grad): Also known as gon, with 400 gradians equal to 360 degrees.

Understanding these different units is essential for various fields, including geometry, trigonometry, navigation, and engineering.

Formula Used

The conversion between degrees, radians, and gradians uses the following formulas:

Degrees to Radians: radians = degrees × (π/180)
Radians to Degrees: degrees = radians × (180/π)
Degrees to Gradians: gradians = degrees × (400/360)
Gradians to Degrees: degrees = gradians × (360/400)

These formulas are used by the calculator to provide accurate conversions between the different angle measurement systems.

Worked Examples

Example 1: Converting 90 Degrees to Radians

Using the formula for degrees to radians:

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

So, 90 degrees is approximately 1.5708 radians.

Example 2: Converting π/2 Radians to Degrees

Using the formula for radians to degrees:

degrees = (π/2) × (180/π) = 90°

So, π/2 radians is exactly 90 degrees.

Example 3: Converting 100 Degrees to Gradians

Using the formula for degrees to gradians:

gradians = 100° × (400/360) ≈ 111.111 gradians

So, 100 degrees is approximately 111.111 gradians.

Frequently Asked Questions

What is the difference between degrees and radians?

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 360 degrees or 2π radians.

How do I convert gradians to degrees?

To convert gradians to degrees, multiply the gradians value by 0.9 (since 1 gradian = 0.9 degrees). Alternatively, use the formula: degrees = gradians × (360/400).

When would I use radians instead of degrees?

Radians are commonly used in advanced mathematics, physics, and engineering, particularly in calculus and trigonometry, where they simplify many formulas and equations.

Is there a difference between gradians and degrees?

Yes, gradians (or gon) are an alternative angle measurement system where a full circle is divided into 400 equal parts, making each gradian equal to 0.9 degrees.