To find the center of the circle, add the **x**-coordinates of the two endpoints of the diameter and divide by 2 to get the **h** coordinate. Similarly, add the **y**-coordinates and divide by 2 to get the **k** coordinate. The result will be the center point **(h, k)**.

The Center of Circle Calculator is a useful tool for determining the coordinates of the center of a circle using the coordinates of any two points lying on its circumference. Understanding the center of a circle is essential in various mathematical and practical applications.

**Formula:**

$(h, k) = \left( \frac{x₁ + x₂}{2}, \frac{y₁ + y₂}{2} \right)$

Variable | Meaning |
---|---|

(h, k) |
Coordinates of the center of the circle |

(x₁, y₁) |
Coordinates of one endpoint of the diameter |

(x₂, y₂) |
Coordinates of the other endpoint of the diameter |

**Solved Calculations :**

**Example 1:**

**Given Values**:

**(x₁, y₁)**= (2, 4)**(x₂, y₂)**= (6, 8)

Calculation | Instructions |
---|---|

h = $\frac{2 + 6}{2}$ | Add the x-coordinates and divide by 2. |

h = $\frac{8}{2} = 4$ | Simplify the result to find the x-coordinate of the center. |

k = $\frac{4 + 8}{2}$ | Add the y-coordinates and divide by 2. |

k = $\frac{12}{2} = 6$ | Simplify the result to find the y-coordinate of the center. |

**Answer**: The center of the circle is at (4, 6).

**Example 2:**

**Given Values**:

**(x₁, y₁)**= (-3, 7)**(x₂, y₂)**= (5, 3)

Calculation | Instructions |
---|---|

h = $\frac{-3 + 5}{2}$ | Add the x-coordinates and divide by 2. |

h = $\frac{2}{2} = 1$ | Simplify the result to find the x-coordinate of the center. |

k = $\frac{7 + 3}{2}$ | Add the y-coordinates and divide by 2. |

k = $\frac{10}{2} = 5$ | Simplify the result to find the y-coordinate of the center. |

**Answer**: The center of the circle is at (1, 5).

**What is Center of Circle Calculator ?**

Finding the **center of a circle** is a fundamental task in geometry, whether you’re calculating it from known points or using the equation of a circle. The **Center of Circle Calculator** provides several methods to find the center. For example, when given the general equation of a circle **(x – h)² + (y – k)² = r²**, the center can be identified as the point **(h, k)**.

This calculator can also handle cases where you have two or three points on the circle, using mathematical methods to find the exact center. The calculator offers easy solutions for complex problems like finding the center using the midpoint formula between two points on the diameter.

In more advanced applications, such as finding the **center of a circle with three points**, this tool becomes indispensable. Using techniques like **circumcenter calculations**, the calculator provides the exact coordinates of the center by analyzing the intersection of perpendicular bisectors.

You can also use it to derive the **circle equation** from given points or identify the center and radius for graphing purposes. Whether you’re solving for academic purposes or working on design projects, the **Center of Circle Calculator** ensures accuracy and saves time by automating complex geometric calculations.

### Final Words:

The Center of Circle Calculator is a valuable tool for finding the coordinates of the center of a circle based on the coordinates of two points on its circumference. Its simplicity, accuracy, and versatility make it indispensable for professionals and students working with circles in geometry, engineering, design, and other fields.