Radians to Degrees Converter

Convert radians to degrees instantly with our interactive calculator, designed for students, engineers, and professionals who need quick and accurate angle conversions.

Result

0.0000°

The Formula Explained

\( \text{degrees} = \text{radians} \times \frac{180}{\pi} \)

This formula converts an angle measured in radians to its equivalent value in degrees.

Data Source and Methodology

All calculations are strictly based on the formulas and data provided by RapidTables. All calculations are rigorously based on these formulas and data.

How It Works: A Step-by-Step Example

For example, to convert π/2 radians (approximately 1.5708) to degrees:

  1. Start with the formula: \( \text{degrees} = \text{radians} \times \frac{180}{\pi} \)
  2. Substitute 1.5708 for radians: \( \text{degrees} = 1.5708 \times \frac{180}{\pi} \)
  3. Simplify: \( \text{degrees} = 1.5708 \times 57.2958 \approx 90 \)

Result: π/2 rad ≈ 1.5708 rad = 90°

Glossary of Variables

  • Radians (rad): The standard unit of angular measure in mathematics. One radian is the angle at the center of a circle whose arc length equals the radius. A full circle is 2π radians.
  • Degrees (°): A measure of angle where 360 degrees form a full circle. Commonly used in everyday applications, navigation, and geometry.
  • Pi (π): A mathematical constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter.

Frequently Asked Questions (FAQ)

What is a radian?

A radian is a unit of angular measure used in mathematics. It is the angle created when the arc length is equal to the radius of the circle. One complete circle equals 2π radians (approximately 6.28318 radians).

Why use radians instead of degrees?

Radians provide a natural way of measuring angles and are often used in calculus and other mathematical contexts for their simplicity and elegance, as they directly relate angles to arc lengths.

How do I convert degrees to radians?

The formula to convert degrees to radians is: \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \)

What is the relationship between π and radians?

π radians is equivalent to 180 degrees, which is why the conversion involves multiplying by 180/π. This relationship comes from the fact that a semicircle has an arc length of πr and subtends an angle of π radians.

Is this calculator accurate?

Our calculator uses precise formulas with JavaScript's built-in Math.PI constant and displays results to four decimal places, ensuring accurate conversions for most mathematical and engineering applications.

Tool developed by Ugo Candido. Content reviewed by the CalcDomain Expert Team. Last reviewed for accuracy on: October 15, 2023.