1. What Are Circle Calculations?

Circle calculations involve determining the circumference (perimeter) and area of a circle using its radius. These fundamental geometric formulas are widely used in mathematics, engineering, and physics.

2. How Do the Formulas Work?

The calculator uses these circle formulas:

Where:

• \( C \) — Circumference (length units)
• \( A \) — Area (square length units)
• \( r \) — Radius (length units)
• \( \pi \) — Mathematical constant (≈3.14159)

Explanation: The circumference formula shows the linear relationship between radius and circumference, while the area formula shows the quadratic relationship between radius and area.

3. Importance of Circle Calculations

Details: Circle calculations are essential in many real-world applications including construction, manufacturing, astronomy, and any field involving circular objects or motion.

4. Using the Calculator

Tips: Simply enter the radius of your circle in any length unit. The calculator will output both circumference and area in corresponding units.

5. Frequently Asked Questions (FAQ)

Q1: What if I know the diameter instead of radius?
A: The diameter is twice the radius (d = 2r). Divide your diameter by 2 before entering.

Q2: How precise is the value of π used?
A: The calculator uses PHP's built-in pi() function which provides about 14 decimal digits of precision.

Q3: Can I use negative radius values?
A: No, radius must be a positive number as physical distances can't be negative.

Q4: What units should I use?
A: Any consistent length unit can be used (meters, inches, etc.), just be sure to interpret results in the same units.

Q5: Why are my results rounded to 2 decimal places?
A: For practical purposes, we display results with 2 decimal places, though calculations use full precision.