KEVOS® MAKEOS · Geometry
Circle Through Three Points
What centre and radius pass through these three measured points?
Centre coordinates, radius and diameter of the circle through three points, for checking arcs, bores and bolt circles from coordinate measurements.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Point 1 X | mm | X coordinate of the first point. |
| Point 1 Y | mm | Y coordinate of the first point. |
| Point 2 X | mm | X of the second point. |
| Point 2 Y | mm | Y of the second point. |
| Point 3 X | mm | X of the third point. |
| Point 3 Y | mm | Y of the third point. Spread the points well around the arc for accuracy. |
Method and formulas
- Solve the perpendicular bisectors: D = 2[x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)].
- Centre X = [(x₁² + y₁²)(y₂ − y₃) + (x₂² + y₂²)(y₃ − y₁) + (x₃² + y₃²)(y₁ − y₂)] ÷ D, and similarly for Y.
- Radius = distance from the centre to any point.
- Example: the default points give a centre at (0, 0) and a radius of 50 mm.
Limitations
- Exactly three points define a circle but give no estimate of form error; use more points and a best fit for inspection.
- Points close together make the result very sensitive to measurement error.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find a bore or boss centre from three probe points
- Check an arc radius from coordinates
- Lay out a radius through known points
Who it is for
- Quality inspectors
- Toolmakers
- Metrology technicians
What you get
- Centre X and Y
- Radius and diameter
- Arc spread of the points
Interpreting the result
- Points spread over 120° or more give a reliable centre.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 40–48. Topic reference; no source tables or recommended settings are reproduced.
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