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Elliptical Arch Rise and Focal Marking Positions

Elliptical Arch Rise and Focal Marking Positions. Use retained unit controls, geometric inverse relationships and explicit planning assumptions.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Example in initial displayed units: Length of the arch (base) 10, Height of the arch (rise) 3 gives A 5, C 4, Position of focus 1 (F1) -4, Position of focus 2 (F2) 4.

a = span/2; c² = a²−rise²; foci = −c and +c

Worked example

Enter these known values and leave the other values blank.

Length of the arch (base): 10 cm
Height of the arch (rise): 3 cm

Position of focus 1 (F1): -4 cm
Position of focus 2 (F2): 4 cm

Assumptions and limitations

This is the upper half of an ellipse with its base centered at zero. Span exceeds twice the rise, so the major axis is horizontal and the semicircle boundary is excluded. Focal positions are signed distances from the base midpoint.
Use compatible units and enough independent measurements. Clear unknown values before solving backward. Display precision does not quantify uncertainty in site measurements.

Common questions

How do I mark the foci for an elliptical arch?

Mark the base midpoint as zero and place the foci at equal distances to its left and right. The sum of distances from any ellipse point to the two foci equals the full span.

References

Require physical geometric bounds, viable clear spans and whole post counts for the documented planning model. Correct the captured ellipse rise inverse from sqrt(a²+c²) to sqrt(a²−c²), consistent with the horizontal ellipse focal identity.

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