Center of a Circle Calculator
Find the center coordinates of a circle from various equation forms
Calculate Circle Center
Standard Form: (x - A)² + (y - B)² = C
Quick Examples
Circle Center Results
Circle Equation Forms
Standard Form
(x - A)² + (y - B)² = C
Center: (A, B), Radius: √C
General Form
x² + y² + Dx + Ey + F = 0
Center: (-D/2, -E/2)
Parametric Form
x = A + r⋅cos(α)
y = B + r⋅sin(α)
Center: (A, B), Radius: r
Circle Tips
In standard form, watch the signs carefully
General form needs D² + E² - 4F > 0 for a valid circle
Parametric form directly shows center and radius
All forms represent the same circle with different notation
Understanding Circle Equations and Centers
What is the Center of a Circle?
The center of a circle is the point equidistant from all points on the circle's circumference. It's the reference point from which the radius is measured and forms the basis for all circle equations.
Why Different Equation Forms?
- •Standard Form: Most intuitive, shows center and radius directly
- •General Form: Result of expanding standard form
- •Parametric Form: Useful for calculations involving angles
Conversion Formulas
Standard to General
Expand (x - A)² + (y - B)² = C to get:
x² + y² - 2Ax - 2By + (A² + B² - C) = 0
General to Standard
Complete the square on x² + y² + Dx + Ey + F = 0
Center: (-D/2, -E/2), Radius: √((D² + E² - 4F)/4)
Real-World Applications
Engineering
Designing circular components, wheels, gears, and determining optimal positioning
Computer Graphics
Rendering circles, collision detection, and geometric transformations
Architecture
Designing circular structures, arches, and determining spatial relationships