Dodecahedron calculator
Online calculator and formulas for calculating the properties of a dodecahedron
This function calculates the volume, the surface and the diagonal of a dodecahedron. A dodecahedron is a three-dimensional shape with 12 sides, 30 edges and 20 corners.
To calculate it, select the property you know and enter its value. Then click on the 'Calculate' button.
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Dodecahedron Formulas
Volume (\(\small{V}\))
\(\displaystyle V=\frac{ a^3}{4}·(15+7·\sqrt{5})\)
Surface (\(\small{S}\))
\(\displaystyle S= 3 · a^2 · \sqrt{25+10·\sqrt{5}}\)
Circumradius (\(\small{R_c}\))
\(\displaystyle R_c=\frac{a}{4} · \sqrt{3} ·(1+\sqrt{5}) \)
Midradius (\(\small{R_m}\))
\(\displaystyle R_m=\frac{a}{4} · 3 +\sqrt{5} \)
Inradius (\(\small{R_i}\))
\(\displaystyle R_i=\frac{a}{2} · \sqrt{\frac{25+11·\sqrt{5}}{10}} \)
Diagonal (\(\small{d}\))
\(\displaystyle d=2 · R_c \)
Height (\(\small{h}\))
\(\displaystyle h=2 · R_i \)
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