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