Calculation: An Angle Conversion Calculator is a tool designed to help users convert angles between different units of measurement. This is particularly useful for applications in geometry, trigonometry, and engineering where precise angle conversions are often necessary.
What Does an Angle Conversion Calculator Do?
This calculator allows users to convert angles between various units, such as degrees, radians, and gradians. By inputting the angle in one unit, the tool provides an instant conversion to the desired unit, saving time and ensuring accuracy.
Angle Conversion Formula
To convert between common angle units, the following formulas are used:
Degrees = Radians × (180 / π)
Radians = Degrees × (π / 180)
Gradians = Degrees × (10 / 9)
Where:
- Degrees, Radians, and Gradians represent the respective angle values.
- π (pi) is approximately 3.14159, which is the constant used to relate radians and degrees.
Angle Conversion Examples
Example 1: Converting 90 Degrees to Radians
Let’s convert 90 degrees into radians.
- Start with the formula: Radians = Degrees × (π / 180).
- Plug in the values: Radians = 90 × (π / 180).
- Simplify the calculation: Radians = 90 × (3.14159 / 180) = π / 2 ≈ 1.5708 radians.
So, 90 degrees is approximately equal to 1.5708 radians.
Example 2: Converting 3 Radians to Degrees
Now let’s convert 3 radians into degrees.
- Start with the formula: Degrees = Radians × (180 / π).
- Plug in the values: Degrees = 3 × (180 / 3.14159).
- Simplify the calculation: Degrees = 3 × 57.2958 = 171.89 degrees.
So, 3 radians is equal to approximately 171.89 degrees.
The Angle Conversion Calculator is an essential tool for anyone needing to perform accurate and quick angle conversions between degrees, radians, and gradians in various fields such as mathematics, physics, and engineering.