Angle Unit Conversion Calculator

How to Convert Angle Units

Converting between different angle units is a fundamental skill in mathematics and many scientific fields. Here's a comprehensive guide on how to convert between various angle units:

Angle Conversion Formulas

The following formulas are used for angle unit conversions:

• Degrees to Radians: $$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$
• Radians to Degrees: $$\text{degrees} = \text{radians} \times \frac{180}{\pi}$$
• Degrees to Gradians: $$\text{gradians} = \text{degrees} \times \frac{10}{9}$$
• Gradians to Degrees: $$\text{degrees} = \text{gradians} \times \frac{9}{10}$$
• Radians to Milliradians: $$\text{milliradians} = \text{radians} \times 1000$$
• Degrees to Minutes of Arc: $$\text{arcminutes} = \text{degrees} \times 60$$
• Degrees to Seconds of Arc: $$\text{arcseconds} = \text{degrees} \times 3600$$
• Degrees to Revolutions: $$\text{revolutions} = \text{degrees} \div 360$$
• Degrees to Mils: $$\text{mils} = \text{degrees} \times \frac{160}{9}$$

Calculation Steps

1. Identify the current unit of the angle.
2. Determine the desired unit for conversion.
3. Select the appropriate formula from the list above.
4. Substitute the given angle value into the formula.
5. Perform the calculation to obtain the converted angle.

Example Calculation

Let's convert 45 degrees to radians:

1. Current unit: degrees
2. Desired unit: radians
3. Formula: $$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$
4. Substitution: $$\text{radians} = 45 \times \frac{\pi}{180}$$
5. Calculation: $$\text{radians} = \frac{\pi}{4} \approx 0.7854 \text{ radians}$$

Visual Representation

This pie chart visually represents 45 degrees, which is equivalent to π/4 radians, 50 gradians, 2700 arcminutes, 162000 arcseconds, 0.125 revolutions, 0.125 circles, or 800 mils.