1. What Is A Circle?

A circle is a perfectly round shape in a plane, defined as the set of all points that are equidistant from a fixed center point. It is one of the most fundamental geometric shapes with numerous applications in mathematics, engineering, and everyday life.

2. Circle Equation And Properties

The standard equation of a circle is:

Where:

• \( (h, k) \) — Center coordinates of the circle
• \( r \) — Radius of the circle
• \( (x, y) \) — Any point on the circumference

Key Properties:

• Diameter: \( 2r \) (twice the radius)
• Circumference: \( 2\pi r \) (distance around the circle)
• Area: \( \pi r^2 \) (space enclosed by the circle)

3. How The Calculator Works

Calculation Process: The calculator takes the center coordinates (h, k) and radius (r) as inputs, then computes the diameter, circumference, and area using the standard circle formulas.

4. Using The Calculator

Instructions: Enter the x and y coordinates of the circle's center, followed by the radius value. All values must be valid numbers with radius greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What if I only know the diameter?
A: You can calculate the radius by dividing the diameter by 2, then use that value in the calculator.

Q2: Can I use negative values for coordinates?
A: Yes, coordinates can be positive or negative numbers as they represent positions on a coordinate plane.

Q3: What units should I use?
A: Use consistent units (cm, m, inches, etc.) for all measurements. The results will be in the same units squared for area.

Q4: How accurate are the calculations?
A: The calculations are mathematically precise based on the input values, using π with high precision.

Q5: Can this calculator find the equation from points?
A: This calculator requires the center and radius. For finding the equation from points, you would need a different tool that solves for the circle through given points.