Square Cupola Calculation
Calculators and formulas for a square cupola (Johnson solid J4)
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.
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Square Cupola Formulas
Volume (\(\small{V}\))
\(\displaystyle V=\left(1+\frac{2·\sqrt{2}}{3}\right)·a^3 \;\;\;\;≈ 1.9428 ·a^3\)
Surface area (\(\small{S}\))
\(\displaystyle S= (7+2 · \sqrt{2} +\sqrt{3})· a^2\;\;\;\;≈ 11.56 ·a^2\)
Height (\(\small{h}\))
\(\displaystyle h=\frac{\sqrt{2}}{2} · a\;\;\;\;≈0.7071 ·a \)
Circumradius (\(\small{r}\))
\(\displaystyle r=\left(\frac{1}{2}·\sqrt{5+2·\sqrt{2}}\right)·a\;\;\;\;≈1.399 ·a \)
Square Pyramid • Pentagonal Pyramid • Triangular Cupola • Square Cupola • Pentagonal Cupola • Rotunda • Elongated Triangular Pyramid • Elongated Square Pyramid • Elongated Pentagonal Pyramid • Triangular Bipyramid • Pentagonal Bipyramid • Elongated Square Bipyramid • Gyrobifastigium • Gyroelongated Square Dipyramid • Snub Disphenoid
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