Angle to Degree Calculator

Angle Conversion:

\[ \text{Degrees} = \text{radians} \times \frac{180}{\pi} \] \[ \text{Radians} = \text{degrees} \times \frac{\pi}{180} \]

Angle Value:

From Unit:

To Unit:

Converted Angle:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Angle Conversion?

Angle conversion is the process of changing the measurement of an angle from one unit to another. The most common angle units are degrees, radians, and gradians. Different fields of mathematics and engineering use different units, making conversion between them essential.

2. How Does the Calculator Work?

The calculator uses these conversion formulas:

\[ \text{Degrees} = \text{radians} \times \frac{180}{\pi} \] \[ \text{Radians} = \text{degrees} \times \frac{\pi}{180} \] \[ \text{Degrees} = \text{gradians} \times 0.9 \] \[ \text{Gradians} = \text{degrees} \div 0.9 \]

Where:

\( \pi \) — Approximately 3.141592653589793
1 full circle = 360° = 2π radians = 400 gradians

3. Common Angle Units

Degrees: Most common unit, with a full circle being 360 degrees.
Radians: Standard unit in mathematics, with a full circle being 2π radians.
Gradians: Used in some engineering fields, with a full circle being 400 gradians.

4. Using the Calculator

Tips: Enter the angle value, select the unit you're converting from, and select the unit you want to convert to. The calculator will handle all conversions through degrees as an intermediate step.

5. Frequently Asked Questions (FAQ)

Q1: Why are there different angle units?
A: Different units are useful in different contexts. Degrees are intuitive for everyday use, radians simplify calculus and trigonometry, and gradians are used in some surveying applications.

Q2: How do I convert degrees to radians without a calculator?
A: Multiply by π/180 (approximately 0.0174533).

Q3: What's the difference between radians and degrees?
A: Radians measure angles by the length of the arc they subtend in a unit circle, while degrees divide a circle into 360 arbitrary units.

Q4: When should I use radians vs degrees?
A: Use radians for calculus and advanced mathematics, degrees for basic geometry and everyday applications.

Q5: What are gradians used for?
A: Gradians are primarily used in surveying and some engineering applications, particularly in Europe.