Unlock the Circle Equation

Visualize and derive the equation of a circle effortlessly. Enter the center and radius to get started!

Circle Details

Enter the coordinates of the center (h, k) and the radius (r) of the circle to calculate its equation in standard form.

Center h-coordinate

Center k-coordinate

Radius r

Enter a positive value for the radius.

Equation of the Circle

$$ {(x - h)}^2 + {(y - k)}^2 = r^2 $$ $$ \Rightarrow $$

Interactive Visualization

Explore the circle on the graph. Zoom, pan, and hover for details.

Understanding Circle Equations

The equation of a circle is a fundamental concept in geometry. In its standard form, it is represented as `(x - h)^2 + (y - k)^2 = r^2`, where (h, k) are the coordinates of the center of the circle and r is the radius. This equation helps us define all points (x, y) that lie on the circumference of the circle. By inputting the center and radius into this tool, you can quickly derive and visualize the circle's equation and its graphical representation. This tool is useful for students learning analytic geometry, engineers, and anyone needing to work with circles in mathematical or design contexts.