Circular and Elliptic
Arch
and Axis Calculator
Given: Two Arch Dimensions
(x/a) ² + (y/b) ² = 1
Scope: Width > 0 , Height < b
Arch Width 2 > Arch Width 1
Arch Height 2 > Arch Height 1
2x1 ... Arch Width 1 =
Arch Height 1 =

2x2 ... Arch Width 2 =
Arch Height 2 =
y1 =
y2 =
Ratio of Axes ... a/b =
on x-axis ... 2a =
on y-axis ... 2b =
± on Major Axis ... Foci =
Arch Length 1 =
Arch Length 2 =
Elliptic Arch given two Dimensions
Solution of Ellipse Axes given two Arch Dimensions
a = semi-axis on x-axis         b = semi-axis on y-axis
Elliptic Arch Formulas
Setting the equations equal to one another and solving for b and a:
Ellipse Semi-Axes
Or, since b is known, one arch height and value of x is sufficient to solve for a:
Ellipse Semi-Axis on X-Axis

Joe Bartok