Angle Unit Conversion

What is Angle Unit Conversion?

Angle unit conversion is the process of changing a measurement from one unit of angle to another. This is crucial in mathematics, physics, engineering, and navigation where different systems of measurement are used.

Common Units and Conversion Formulas

Here are some common angle units and their conversion formulas:

• Degrees (°) to Radians (rad): \(rad = ° \times \frac{\pi}{180}\)
• Degrees (°) to Gradians (grad): \(grad = ° \times \frac{10}{9}\)
• Degrees (°) to Turns: \(turns = \frac{°}{360}\)

Calculation Steps

1. Identify the angle value to be converted and its current unit.
2. Determine the desired unit for conversion.
3. Select the appropriate conversion formula.
4. Apply the conversion formula.
5. Calculate the result and round to the desired precision.

Example Calculation

Let's convert 180° to radians:

1. Angle to convert: 180°
2. Desired unit: radians
3. Conversion formula: \(rad = ° \times \frac{\pi}{180}\)
4. Apply the formula: \(rad = 180 \times \frac{\pi}{180} = \pi\)
5. Result: 180° = π radians ≈ 3.14159 radians

Visual Representation

This diagram illustrates the relationship between 180° and π radians, showing their equivalent angle measures.