1. What is Degrees to Radians Conversion?

Degrees and radians are two different units for measuring angles. While degrees are more common in everyday use, radians are the standard unit of angular measure in mathematics and physics.

2. How Does the Calculator Work?

The calculator uses the conversion formula:

Where:

• \( \text{deg} \) — Angle in degrees
• \( \pi \) — Mathematical constant (~3.14159)
• 180 — Conversion factor between degrees and radians

Explanation: A full circle is 360° or 2π radians, so 1° equals π/180 radians.

3. Importance of Angle Conversion

Details: Radians are essential in higher mathematics, physics, and engineering because they simplify many formulas, particularly in trigonometry and calculus.

4. Using the Calculator

Tips: Enter the angle in degrees (positive or negative) and the calculator will automatically compute the equivalent value in radians.

5. Frequently Asked Questions (FAQ)

Q1: Why are radians preferred in mathematics?
A: Radians provide a direct relationship between angle and arc length (1 radian = radius length of arc), making derivatives and integrals of trigonometric functions simpler.

Q2: What's the radian equivalent of common angles?
A: 0°=0 rad, 30°=π/6, 45°=π/4, 60°=π/3, 90°=π/2, 180°=π, 360°=2π.

Q3: Can I convert radians back to degrees?
A: Yes, use the formula: degrees = radians × 180/π.

Q4: Are negative angles valid?
A: Yes, negative angles represent clockwise rotation while positive angles represent counterclockwise rotation.

Q5: How precise is this conversion?
A: The calculator uses PHP's built-in pi() function which provides sufficient precision for most applications.