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Circle Equation from Diameter Endpoints Calculator.

Find the center, radius, and standard equation of a circle from its diameter endpoints.

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01

Set your values

Results update as you type.

centerX: 1

centerX

0.000000
centerY: 3

centerY

0.000000
radius: 3.605551

radius

0.000000
equation: (x − 1)² + (y − 3)² = 13.000000000000002

equation

(x − 1)² + (y − 3)² = 13.000000000000002

Results update automatically as you type.

Use Cases

Geometry homework and exam prep

Quickly verify your manual calculations for circle equations from diameter endpoints, ensuring accuracy in assignments or study sessions.

Example: Check that endpoints (0,0) and (4,6) give center (2,3) and radius sqrt(13).

Engineering and design drafting

Determine the circle that fits between two points on a component or layout, useful for CAD or mechanical design.

Example: Find the circle for a hole centered between two mounting points.

Frequently Asked Questions

How do I find the center of the circle from the diameter endpoints?
The center is the midpoint of the two endpoints. Use the midpoint formula: ((x1+x2)/2, (y1+y2)/2). For example, if endpoints are (1,2) and (3,4), the center is (2,3).
How is the radius calculated from the endpoints?
The radius is half the distance between the two endpoints. First find the distance using the distance formula, then divide by 2. For endpoints (1,2) and (3,4), distance is sqrt((3-1)^2+(4-2)^2)=sqrt(8)=2.828, so radius is 1.414.
What is the equation of a circle given the center and radius?
The standard form is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center and r is the radius. For center (2,3) and radius 1.414, the equation is (x-2)^2 + (y-3)^2 = 2.

Tips & Common Mistakes

Tips

  • Ensure you enter the coordinates in the correct order: Endpoint 1 x, Endpoint 1 y, Endpoint 2 x, Endpoint 2 y.
  • Double-check that the two points are indeed the endpoints of a diameter; any two points define a circle, but the diameter endpoints must be opposite ends of a line through the center.
  • Use the calculator to verify your manual midpoint and distance calculations, especially when dealing with negative coordinates.
  • Remember that the radius is half the distance between the endpoints, so if you need the diameter, just multiply the radius by 2.

Common Mistakes to Avoid

  • Swapping the x and y coordinates when entering the endpoints, leading to an incorrect center and equation.
  • Forgetting to divide the distance by 2 to get the radius, instead using the full distance as the radius.
  • Misinterpreting the equation format: the calculator outputs the standard form (x - h)^2 + (y - k)^2 = r^2, not the expanded form.

Last updated: August 13, 2026