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Circle Equation from Diameter Endpoints Calculator — result sheet
Build a circle’s center, radius, and Cartesian equation from the two endpoints of a diameter.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Center=((x₁+x₂)/2,(y₁+y₂)/2); radius=½√((x₂−x₁)²+(y₂−y₁)²); equation=(x−h)²+(y−k)²=r².
The center of a circle is the midpoint of its diameter, and its radius is half the endpoint distance. Those two derived values determine the standard Cartesian equation.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Endpoint 1 x — minimum -1000000000; maximum 1000000000
- Endpoint 1 y — minimum -1000000000; maximum 1000000000
- Endpoint 2 x — minimum -1000000000; maximum 1000000000
- Endpoint 2 y — minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Endpoint 1 x | -2 |
| Endpoint 1 y | 1 |
| Endpoint 2 x | 4 |
| Endpoint 2 y | 5 |
Center=(1,3); radius=√13; equation=(x−1)²+(y−3)²=13.
Assumptions and limits
- The two endpoints are distinct finite points in one Cartesian plane.
- The circle is the unique circle whose diameter is the entered segment.
- The result is a geometric equation, not a geographic or projected-distance model.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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