Equation of a Circle with Diameter Endpoints Calculator

Created by Vishnuvardhan Shakthibala
Reviewed by Krishna Nelaturu
Last updated: Feb 02, 2023

Do you have endpoints of a diameter? And are you looking for an easy way to find the equation of a circle? If you are saying YES, then our equation of a circle with diameter endpoints calculator is a perfect fit for you. Go on and insert the diameter endpoints in the indicated fields. You will obtain circle equations in standard, general, and parametric form.

Please read the following article to learn more about:

  • How to find the equation of a circle with diameter endpoints?; and
  • How to use our equation of a circle with diameter endpoints calculator?

What is a circle?

A circle is a 2-D closed geometrical shape whose boundary points are at an equal distance from the center of the geometry.

Equation of a circle with diameter endpoints

To find the equation of a circle with diameter endpoints, you can use the following steps:

  1. Find the distance between the endpoints (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2) by using distance formula:
d=(x2x1)2+(y2y1)2\qquad \scriptsize d=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}
  1. Divide dd by 2 to get the radius rr of the circle.
  2. Next, you can use the midpoint formula to find the x coordinates hh and y coordinates kk for the circle's center. The equation is given as:
h=(x2+x1)2k=(y2+y1)2\qquad\qquad \scriptsize \begin{align*} h=\frac{(x_2+x_1)}{2} \\ k=\frac{(y_2+y_1)}{2} \end{align*}

By knowing the center coordinates: hh,kk, and radius rr we can get the circle equation in standard form. It is given as:

(xh)2+(yk)2=r2\qquad \scriptsize (x-h)^2 +(y-k)^2=r^2

More calculators to assist you!


What is the equation of the circle whose diameter endpoints are (6,4) and (2,8)?

The equation of a circle is (x-4)² + (y-6)² = 8. You can find this equation by using the following steps:

  1. Find the x-coordinate (h) & y-coordinate (k) of the center of the circle by taking the summation of x-coordinates & y-coordinates of the endpoints of the diameter respectively and dividing by 2.
  2. Calculate the distance between (6,4) and (2,8) using the distance formula and divide by 2 to get the circle's radius.
  3. Substitute the center coordinates and radius into a standard form to get the equation of the circle.

What is the midpoint between the points (3,-6) and (4,7)?

The midpoint is (1.5,0.5). To calculate the midpoint coordinates: sum the corresponding coordinates, and divide by 2.

Vishnuvardhan Shakthibala
Endpoints of a diameter
(x - A)² + (y - B)² = C
x = A + r cos(α), y = B + r sin(α)
x² + y² + Dx + Ey + F = 0
Center coordinates
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