Example Data Table
| Center (h,k) | Radius r | Point (x,y) | Tolerance | Expected |
|---|---|---|---|---|
| (0, 0) | 5 | (3, 4) | 0 | On circle |
| (0, 0) | 5 | (1, 1) | 0 | Inside |
| (2, -1) | 2 | (5, -1) | 0.01 | Outside |
| (-3, 4) | 0 | (-3, 4) | 0 | On circle |
Formula Used
A point (x, y) is compared to a circle with center (h, k) and radius r. Compute the Euclidean distance:
- d = √((x − h)² + (y − k)²)
- margin = r − d
If |margin| ≤ tolerance, the point is on the boundary. If margin > tolerance, it is inside. Otherwise, it is outside.
How to Use This Calculator
- Enter the circle center coordinates (h, k) and the radius r.
- Enter a single point (x, y), or paste many points in the batch box.
- Set a tolerance if your values are rounded or measured.
- Choose whether boundary points count as inside.
- Press Calculate. Export the report using CSV or PDF buttons.
FAQs
1) What does “tolerance” change?
Tolerance creates a small band around the circle boundary. If the distance differs from the radius by less than this value, the point is treated as on the boundary.
2) How do I check many points at once?
Paste one point per line in the batch box. Use formats like “x,y”, “x y”, or “x; y”. Batch input overrides the single point fields.
3) Why might a point be “on circle” when it seems inside?
Rounding can make distances appear equal to the radius. A nonzero tolerance may classify points very close to the boundary as on the circle for stability.
4) What is the margin value used for?
Margin equals r minus distance. Positive margin means inside. Negative margin means outside. Near-zero margin indicates the boundary, depending on tolerance.
5) Can radius be zero?
Yes. A zero-radius circle is a single point at the center. A test point matches “on circle” only when it equals the center within tolerance.
6) Does “Treat boundary as inside” affect calculations?
No. It only changes how boundary results are reported. Distances and margins remain the same, so you can still see the exact geometry values.
7) What coordinate units should I use?
Any consistent unit works. If your coordinates are meters, then radius and tolerance must also be in meters. The calculator does not assume a specific unit.
8) Why is my batch limited?
Large batches can slow down browsers and exports. The 300-point limit keeps the output readable and the PDF size manageable for quick reporting.