Angle Converter - Convert Between Degrees, Radians, Gradians Online Free

Understanding the Angle Conversion Algorithm

The Angle Converter tool utilizes a straightforward mathematical formula to convert angles between different units, primarily degrees and radians. This conversion is essential in various fields such as mathematics, physics, and engineering, where angles need to be expressed in a format compatible with the specific requirements of the task at hand.

Mathematical Formula

The conversion between degrees and radians is based on the relationship where 180 degrees is equivalent to π radians. The formulae for conversion are as follows:

• From Degrees to Radians: radians = degrees × (π / 180)
• From Radians to Degrees: degrees = radians × (180 / π)

Variables Explanation

• Degrees: The angle measurement in degrees, a unit of angular measure where a full circle is 360 degrees.
• Radians: The angle measurement in radians, a unit of angular measure used in many areas of mathematics, where a full circle is 2π radians.
• π (Pi): A mathematical constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter.

Step-by-Step Breakdown

1. Identify the initial angle measurement and its unit (degrees or radians).
2. Apply the appropriate formula based on the initial unit.
3. Perform the multiplication to convert the measurement.
4. Output the converted angle in the desired unit.

Practical Example

Consider converting 90 degrees to radians:

1. Start with the formula for degrees to radians: radians = degrees × (π / 180).
2. Substitute 90 for degrees: radians = 90 × (π / 180).
3. Calculate the result: radians = 90 × 0.0174533 ≈ 1.5708 radians.

This calculation shows that 90 degrees is approximately equal to 1.5708 radians. This conversion is crucial when integrating angle measurements into trigonometric functions often used in calculus or physics.