Square Cupola Calculation

The square cupola has an regular octagon as its base and a square as its top. The sides of the cupola are bounded by four squares and four equilateral triangles. All edges have the same length. The square cupola is one of the Johnson solids (J₄).

To perform the calculation select the property you know from the menu and enter its value. Then click on the 'Calculate' button.

Square Cupola Calculator  Input Delete Entry Edge length Volume Surface area Height Decimal places 0 1 2 3 4 6   Results Edge length a Volume V Surface area S Height h Circumradius r

Formulas for Square Cupolas

Volume

\(\displaystyle V=\left(1+\frac{2·\sqrt{2}}{3}\right)·a^3 \;\;\;\;≈ 1.9428 ·a^3\)

Surface area

\(\displaystyle S= (7+2 · \sqrt{2} +\sqrt{3})· a^2\;\;\;\;≈ 11.56 ·a^2\)

Height

\(\displaystyle h=\frac{\sqrt{2}}{2} · a\;\;\;\;≈0.7071 ·a \)

Circumradius

\(\displaystyle r=\left(\frac{1}{2}·\sqrt{5+2·\sqrt{2}}\right)·a\;\;\;\;≈1.399 ·a \)