1. What is Radian Measure?

A radian is the standard unit of angular measure used in many areas of mathematics. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.

2. How Does the Conversion Work?

The calculator uses the conversion formula:

Where:

• \( \theta_{rad} \) — Angle in radians
• \( \theta_{deg} \) — Angle in degrees
• \( \pi \) — Mathematical constant (~3.14159)

Explanation: Since 180 degrees equals π radians, this conversion factor scales degrees to radians.

3. Importance of Radian Measure

Details: Radians are essential in higher mathematics because they simplify many formulas, particularly in calculus and trigonometry. Most mathematical functions use radians by default.

4. Using the Calculator

Tips: Enter the angle in degrees (any real number). The calculator will convert it to radians. Negative values represent angles measured clockwise.

5. Frequently Asked Questions (FAQ)

Q1: Why convert degrees to radians?
A: Many mathematical operations (especially trigonometric functions) require angle measurements in radians for accurate results.

Q2: What's the exact value of π in the calculation?
A: The calculator uses PHP's built-in M_PI constant which has about 14 decimal digits of precision (3.1415926535898).

Q3: How many radians are in a full circle?
A: A full 360° circle equals 2π radians (approximately 6.28319 radians).

Q4: When should I use radians vs degrees?
A: Use degrees for simple angle measurements and navigation. Use radians for calculus, physics, and advanced mathematics.

Q5: Can I convert radians back to degrees?
A: Yes, using the formula: degrees = radians × (180/π).