Enter Circle Data
Example Data Table
| Case | Input Type | Sample Inputs | Center | Radius | Standard Form |
|---|---|---|---|---|---|
| Example 1 | Center and Radius | h = 2, k = -1, r = 5 | (2, -1) | 5 | (x - 2)² + (y + 1)² = 25 |
| Example 2 | General Form | D = -4, E = 2, F = -20 | (2, -1) | 5 | (x - 2)² + (y + 1)² = 25 |
| Example 3 | Diameter Endpoints | (-3, 2) and (5, 2) | (1, 2) | 4 | (x - 1)² + (y - 2)² = 16 |
Formula Used
This calculator handles standard form, general form, three-point reconstruction, and diameter-based reconstruction for a circle.
Standard form: (x - h)² + (y - k)² = r²
General form: x² + y² + Dx + Ey + F = 0
Center from general form: h = -D / 2, k = -E / 2
Radius from general form: r = √(h² + k² - F)
Diameter from radius: d = 2r
Circumference: C = 2πr
Area: A = πr²
Diameter endpoints center: h = (x₁ + x₂)/2, k = (y₁ + y₂)/2
Diameter endpoints radius: r = √((x₂ - x₁)² + (y₂ - y₁)²) / 2
For three points, the circle is found by solving the unique circle passing through all non-collinear coordinates using determinant-based geometry.
How to Use This Calculator
- Select the calculation mode that matches your known data.
- Enter center and radius, general coefficients, three boundary points, or diameter endpoints.
- Press Calculate Circle Equation to generate the equations and geometry values.
- Review the result box shown above the form, directly below the page header.
- Inspect the plot to verify center position, radius shape, and input points.
- Download a CSV or PDF copy for reporting, notes, or coursework.
Frequently Asked Questions
1. What equation forms does this calculator support?
It supports standard form, general form, three-point reconstruction, and diameter-endpoint reconstruction. You can start from whichever representation your problem already gives.
2. Can I find a circle from three points?
Yes. Enter three non-collinear points. The calculator finds the unique circle passing through them, then reports the center, radius, standard form, and general form.
3. What happens if the points are collinear?
A single circle cannot pass through three collinear points uniquely. The calculator checks this condition and shows an error instead of a misleading result.
4. How is the radius found from general form?
The calculator first computes the center using h = -D/2 and k = -E/2. It then uses r = √(h² + k² - F) to find the radius.
5. Does the graph scale equally on both axes?
Yes. The plot uses equal axis scaling so the circle stays visually accurate. Without equal scaling, a circle could appear stretched into an ellipse.
6. Can I use negative coordinates?
Yes. Negative x-values, negative y-values, and mixed-sign coordinates are fully supported. This is useful for analytic geometry, graphing exercises, and coordinate proofs.
7. What do the D, E, and F values mean?
They are the linear and constant coefficients in the general circle equation x² + y² + Dx + Ey + F = 0. They help convert between forms.
8. Can I export the result after calculation?
Yes. Use the CSV button for spreadsheet-friendly output or the PDF button for a formatted summary. Both exports use the current computed result values.