Calculator Degrees

Angle Unit Converter

function calculateAngleConversion() { var inputValue = parseFloat(document.getElementById('inputValue').value); var unitDegrees = document.getElementById('unitDegrees').checked; var unitRadians = document.getElementById('unitRadians').checked; var unitGradians = document.getElementById('unitGradians').checked; if (isNaN(inputValue)) { document.getElementById('outputDegrees').innerText = 'Please enter a valid number.'; document.getElementById('outputRadians').innerText = "; document.getElementById('outputGradians').innerText = "; return; } var degrees = 0; var radians = 0; var gradians = 0; if (unitDegrees) { degrees = inputValue; radians = inputValue * (Math.PI / 180); gradians = inputValue * (400 / 360); } else if (unitRadians) { radians = inputValue; degrees = inputValue * (180 / Math.PI); gradians = inputValue * (200 / Math.PI); } else if (unitGradians) { gradians = inputValue; degrees = inputValue * (360 / 400); radians = inputValue * (Math.PI / 200); } document.getElementById('outputDegrees').innerText = degrees.toFixed(6); document.getElementById('outputRadians').innerText = radians.toFixed(6); document.getElementById('outputGradians').innerText = gradians.toFixed(6); } // Run calculation on page load with default values document.addEventListener('DOMContentLoaded', function() { calculateAngleConversion(); });

Understanding Angle Units: Degrees, Radians, and Gradians

Angles are fundamental in mathematics, physics, engineering, and many other fields. However, there isn't just one way to measure them. The three most common units for measuring angles are degrees, radians, and gradians. Each has its specific applications and advantages.

Degrees (°)

The degree is perhaps the most familiar unit of angular measurement. A full circle is divided into 360 degrees. This system originated from ancient Babylonian astronomy, likely due to their base-60 numeral system and the approximate number of days in a year. Degrees are widely used in everyday geometry, navigation, and surveying.

• A right angle is 90°.
• A straight angle is 180°.
• A full circle is 360°.

Radians (rad)

Radians are the standard unit of angular measure in mathematics, particularly in calculus 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. This definition makes radians a 'natural' unit for angles, as it directly relates the angle to the geometry of the circle (arc length and radius).

• A full circle is 2π radians (approximately 6.28318 radians).
• A straight angle is π radians (approximately 3.14159 radians).
• A right angle is π/2 radians (approximately 1.5708 radians).

The use of radians often simplifies formulas in trigonometry and calculus, especially when dealing with derivatives and integrals of trigonometric functions.

Gradians (grad or gon)

Gradians, also known as 'gons' or 'grades', divide a full circle into 400 units. This metric-friendly system was introduced during the French Revolution as part of the broader metrication effort. While less common than degrees or radians, gradians are sometimes used in surveying and some European engineering contexts due to their decimal nature, making calculations easier without fractions.

• A full circle is 400 gradians.
• A straight angle is 200 gradians.
• A right angle is 100 gradians.

Why Convert Between Them?

The need to convert between these units arises because different disciplines and tools (like scientific calculators or software) may default to or require specific units. For instance, while a surveyor might work with gradians, a physicist might need to convert those measurements to radians for use in a formula. Our Angle Unit Converter simplifies this process, allowing you to quickly switch between degrees, radians, and gradians.

Conversion Formulas:

• Degrees to Radians: Radians = Degrees × (π / 180)
• Degrees to Gradians: Gradians = Degrees × (400 / 360)
• Radians to Degrees: Degrees = Radians × (180 / π)
• Radians to Gradians: Gradians = Radians × (200 / π)
• Gradians to Degrees: Degrees = Gradians × (360 / 400)
• Gradians to Radians: Radians = Gradians × (π / 200)

Examples of Angle Conversion:

Let's look at some common angle conversions:

• 90 Degrees:
  • In Radians: 90 * (π / 180) = π/2 ≈ 1.570796 radians
  • In Gradians: 90 * (400 / 360) = 100 gradians
• π Radians (180 Degrees):
  • In Degrees: π * (180 / π) = 180 degrees
  • In Gradians: π * (200 / π) = 200 gradians
• 100 Gradians (90 Degrees):
  • In Degrees: 100 * (360 / 400) = 90 degrees
  • In Radians: 100 * (π / 200) = π/2 ≈ 1.570796 radians

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