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Circle Center from Three Points Calculator — result sheet
Find the circumcenter and radius of the unique circle through three non-collinear points.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Solve the perpendicular-bisector equations for (h,k), then r=√[(x₁−h)²+(y₁−k)²].
The center is equidistant from all three points; the determinant check prevents a false answer when the points lie on one line.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Point 1 x — minimum -1000000; maximum 1000000
- Point 1 y — minimum -1000000; maximum 1000000
- Point 2 x — minimum -1000000; maximum 1000000
- Point 2 y — minimum -1000000; maximum 1000000
- Point 3 x — minimum -1000000; maximum 1000000
- Point 3 y — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Point 1 x | 0 |
| Point 1 y | 0 |
| Point 2 x | 4 |
| Point 2 y | 0 |
| Point 3 x | 0 |
| Point 3 y | 3 |
Center = (2, 1.5); radius = 2.5.
Assumptions and limits
- All coordinates are finite and the three points are not collinear.
- The points define one Euclidean circle in a common coordinate system.
- Rounding in the entered coordinates can change the resulting center.
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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