How this calculator works
Treat the opening as the upper half of an ellipse. Half the span is the semi-major axis, and the rise is the semi-minor axis. The two foci sit the same distance to either side of the opening centre. A pencil held against a taut string can trace points whose distances to the two pins add to the full span. Allow for the actual string fastening method when making the jig.
Formula
a = span/2; b = rise; c = sqrt(a² - b²); focus positions = a - c and a + c; distance sum = 2a; half-ellipse area = pi a b / 2.
Worked example
For a 6 m opening rising 2 m, a = 3 m and the centre-to-focus distance is sqrt(5) = 2.236 m. The pins sit 0.764 m and 5.236 m from the left end.
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Frequently asked questions
Can the rise exceed half the span?
This layout assumes a horizontal major axis. A taller ellipse needs vertically placed foci and a different jig.
What happens with a semicircle?
The rise equals half the span and both foci meet at the centre. The profile becomes a semicircle.
Does this design a load-bearing arch?
No. It gives layout geometry only. Masonry thrust, supports and structural capacity need a separate design.