You are using the new UI (Beta).Return to the original UI

This page has been automatically translated by machine translation. Please note that translations may not be entirely accurate.

keisanHigh-precision calculations for everyday life and work
Login|Register

Volume of a tetrahedron formed by four points

TOP/Collection of Mathematical Formulas/Spatial Geometry
Manage Bookmarks
Calculate the volumes of the parallelepiped and tetrahedron formed by four points.
Points A (,
,
)
Points B (,
,
)
Points C (,
,
)
Points D (,
,
)
Volume of the parallelepiped Vp 
Volume of the tetrahedron Vt 
The dot product of vector AD with the cross product of vectors AB and AC gives the volume of the parallelepiped spanned by vectors AB, AC, and AD.
The volume of tetrahedron ABCD is 1/6 of the volume of the parallelepiped.

\(\normalsize Parallelepiped\ and\ Tetrahedron\\ (1)\ V_p=\vec{AD}\cdot(\vec{AB}\times\vec{AC})\\ {\small \hspace{18px}= (x_4-x_1)[(y_2-y_1)(z_3-z_1)-(z_2-z_1)(y_3-y_1)] \\ \hspace{18px}+(y_4-y_1)[(z_2-z_1)(x_3-x_1)-(x_2-x_1)(z_3-z_1)] \\ \hspace{18px}+(z_4-z_1)[(x_2-x_1)(y_3-y_1)-(y_2-y_1)(x_3-x_1)]} \\ (2)\ V_t={\large\frac{V_p}{6}}\\\)

No customer feedback for this calculation yet.