Calculate Degrees

Angle Unit Converter

Degrees Radians Gradians

function calculateAngleConversion() { var inputValue = parseFloat(document.getElementById('inputValue').value); var inputUnit = document.getElementById('inputUnit').value; if (isNaN(inputValue)) { document.getElementById('resultDegrees').innerText = 'Invalid Input'; document.getElementById('resultRadians').innerText = 'Invalid Input'; document.getElementById('resultGradians').innerText = 'Invalid Input'; return; } var degrees = 0; var radians = 0; var gradians = 0; if (inputUnit === 'degrees') { degrees = inputValue; radians = inputValue * (Math.PI / 180); gradians = inputValue * (400 / 360); } else if (inputUnit === 'radians') { radians = inputValue; degrees = inputValue * (180 / Math.PI); gradians = inputValue * (200 / Math.PI); } else if (inputUnit === 'gradians') { gradians = inputValue; degrees = inputValue * (360 / 400); radians = inputValue * (Math.PI / 200); } document.getElementById('resultDegrees').innerText = degrees.toFixed(6); document.getElementById('resultRadians').innerText = radians.toFixed(6); document.getElementById('resultGradians').innerText = gradians.toFixed(6); } // Run calculation on page load with default values window.onload = calculateAngleConversion;

Understanding Angle Units: Degrees, Radians, and Gradians

Angles are fundamental in mathematics, physics, engineering, and many other fields. While most people are familiar with degrees, there are other important units for measuring angles, namely radians and gradians. This Angle Unit Converter helps you quickly convert values between these three common systems.

What are Degrees?

The degree (symbol: °) is the most widely recognized unit of angular measurement. A full circle is divided into 360 degrees. This system originated from ancient Babylonian astronomy, likely due to their sexagesimal (base-60) number system and the approximate number of days in a year. Degrees are commonly used in geometry, navigation, and everyday applications.

• A full circle = 360°
• A straight angle = 180°
• A right angle = 90°

What are Radians?

The radian (symbol: rad) is the standard unit of angular measure in the International System of Units (SI) and is particularly prevalent in higher mathematics and physics. A radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.

The circumference of a circle is 2πr, so a full circle corresponds to 2π radians. This makes radians a more natural unit for many mathematical formulas, especially those involving calculus and trigonometry.

• A full circle = 2π radians ≈ 6.283185 radians
• A straight angle = π radians ≈ 3.141593 radians
• A right angle = π/2 radians ≈ 1.570796 radians

What are Gradians?

The gradian (also known as gon or grade, symbol: grad or g) is a unit of plane angle, where a right angle is 100 gradians. Therefore, a full circle is 400 gradians. This unit was developed as part of the metric system to simplify calculations, as it aligns well with decimal arithmetic.

While less common than degrees or radians, gradians are sometimes used in surveying, particularly in some European countries, due to their ease of use with decimal calculations.

• A full circle = 400 gradians
• A straight angle = 200 gradians
• A right angle = 100 gradians

Conversion Formulas:

Here are the basic formulas used for conversion:

• 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)
• Radians to Gradians: gradians = radians × (200 / π)
• Gradians to Radians: radians = gradians × (π / 200)

Examples of Angle Conversion:

Let's look at some practical examples:

Example 1: Converting 90 Degrees

• 90 Degrees = 90 × (π / 180) = π/2 Radians ≈ 1.570796 Radians
• 90 Degrees = 90 × (400 / 360) = 100 Gradians

Example 2: Converting π Radians

• π Radians = π × (180 / π) = 180 Degrees
• π Radians = π × (200 / π) = 200 Gradians

Example 3: Converting 50 Gradians

• 50 Gradians = 50 × (360 / 400) = 45 Degrees
• 50 Gradians = 50 × (π / 200) = π/4 Radians ≈ 0.785398 Radians

Use the calculator above to perform these and other conversions quickly and accurately!