Tetrahedron calculator
Calculation of the volume and surface of an irregular tetrahedron
This function calculates the volume and the surface of an irregular tetrahedron. A tetrahedron is a three-dimensional shape with 4 sides, 6 edges and 4 corners.
To calculate the tetrahedron, enter the length of the 6 edges. Then click on the 'Calculate' button.
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Formulas for irregular tetrahedrons
Volume (\(\small{V}\))
\(\displaystyle fa=b^2+b`^2+c^2+c`^2-a^2-a`^2 \)
\(\displaystyle fb=a^2+a`^2+c^2+c`^2-b^2-b`^2 \)
\(\displaystyle fc=a^2+a`^2+b^2+b`^2-c^2-c`^2 \)
\(\displaystyle δ=a^2· b^2·c^2+a^2·b`^2·c`^2+ a`^2·b^2·c`^2+a`^2·b`^2·c^2\)
\(\displaystyle V=\frac{\sqrt{a^2· a`^2·fa+b^2·b`^2·fb + c^2·c`^2·fc-δ}}{12} \)
Surface (\(\small{S}\))
\(\displaystyle p=a+b+c \)
\(\displaystyle q=a+b`+c` \)
\(\displaystyle r=a`+b+c` \)
\(\displaystyle s=a`+b`+c \)
\(\displaystyle S=\sqrt{\frac{p}{2}·\left(\frac{p}{2}-a\right)·\left(\frac{p}{2}-b\right)·\left(\frac{p}{2}-c\right)}\)
\(\displaystyle \;\;\;\; +\;\sqrt{\frac{q}{2}·\left(\frac{q}{2}-a\right)·\left(\frac{q}{2}-b`\right)·\left(\frac{q}{2}-c`\right)}\)
\(\displaystyle \;\;\;\; +\;\sqrt{\frac{r}{2}·\left(\frac{r}{2}-a`\right)·\left(\frac{r}{2}-b\right)·\left(\frac{r}{2}-c`\right)}\)
\(\displaystyle \;\;\;\; +\;\sqrt{\frac{s}{2}·\left(\frac{s}{2}-a`\right)·\left(\frac{s}{2}-b`\right)·\left(\frac{s}{2}-c\right)}\)
Tetrahedron • Cube • Octahedron • Dodecahedron • Icosahedron
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