Circle Equation Calculator (General Form)
Easily convert the equation of a circle from center-radius form to general form with our online calculator. Visualize the circle and copy the equation.
Enter Circle Details
Specify the center coordinates (x, y) and the radius of the circle to calculate its general equation.
General Form of Circle Equation:
Circle Visualization
Understanding the Circle Equation
The equation of a circle is a fundamental concept in geometry. A circle is defined as the set of all points in a plane that are equidistant from a given point called the center. This fixed distance is the radius of the circle.
Center-Radius Form vs. General Form
The center-radius form of a circle's equation is given by: $$ (x-h)^2 + (y-k)^2 = r^2 $$ where (h, k) are the coordinates of the center and r is the radius.
The general form of a circle's equation is: $$ x^2 + y^2 + Cx + Dy + E = 0 $$ This calculator converts from center-radius form to general form, making it easy to see the expanded polynomial representation of the circle's equation. You can use this tool to quickly get the general form equation for any circle given its center and radius.
How to Use This Calculator
- Enter the x and y coordinates of the center of the circle in the respective input boxes.
- Enter the radius of the circle.
- Click the "Calculate Equation" button to convert to general form.
- The general form equation will be displayed, and a visualization of the circle will appear below.
- Use the "Copy Equation" button to copy the equation for use elsewhere.