# Volume of a tetrahedron Calculator

## Calculates the volume and surface area of a tetrahedron from six edge lengths.

 edge length a1 a2 a3 a4 a5 a6 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit volume V surface area S
 $\normal Tetrahedron\\\vspace{5}(1)\ volume:\\\hspace{40} V=sqrt{V^2}\\\vspace{5}\hspace{40} V^2=\frac{1}{144}[a_1^2a_5^2(a_2^2+a_3^2+a_4^2+a_6^2-a_1^2-a_5^2)\\\hspace{60}+a_2^2a_6^2(a_1^2+a_3^2+a_4^2+a_5^2-a_2^2-a_6^2)\\\hspace{60}+a_3^2a_4^2(a_1^2+a_2^2+a_5^2+a_6^2-a_3^2-a_4^2)\\\hspace{60}-a_1^2a_2^2a_4^2-a_2^2a_3^2a_5^2-a_1^2a_3^2a_6^2-a_4^2a_5^2a_6^2]\\\vspace{5}(2)\ surface\ area:\\\hspace{40} S=\sqrt{s_1(s_1-a_1)(s_1-a_2)(s_1-a_4)}\\\hspace{60}+\sqrt{s_2(s_2-a_2)(s_2-a_3)(s_2-a_5)}\\\hspace{60}+\sqrt{s_3(s_3-a_3)(s_3-a_6)(s_3-a_1)}\\\hspace{60}+\sqrt{s_4(s_4-a_4)(s_4-a_5)(s_4-a_6)}\\\vspace{5}\hspace{40}s1={\large \frac{a_1+a_2+a_4}{2}},\ s2={\large \frac{a_2+a_3+a_5}{2}}\\\hspace{40}s3={\large \frac{a_3+a_6+a_1}{2}},\ s4={\large \frac{a_4+a_5+a_6}{2}}\\$
Volume of a tetrahedron
 [1-9] /9 Disp-Num5103050100200
[1]  2018/10/02 18:27   Male / 60 years old level or over / A retired person / Very /
Purpose of use
Compute the volume of a tetrahedron as part of a statistical analysis of ancient skulls.
[2]  2018/04/27 10:57   Male / 30 years old level / An engineer / Very /
Purpose of use
Confined space volume calculation.
[3]  2018/01/04 21:38   Male / 30 years old level / Self-employed people / Very /
Purpose of use
To measure the volume of a hipped roof to gable roof extension
Comment/Request
Is it possible to get a copy of the calculations sheet to use as evidence?
from Keisan
Please refer to the following FAQ
[4]  2016/12/28 05:46   Male / 60 years old level or over / A retired people / Useful /
Purpose of use
To transport aliens from a skewed universe into parallel ones and not change their brains.
[5]  2016/01/31 05:36   Male / 60 years old level or over / A retired people / Very /
Purpose of use
Seeking surface to volume ratio for all extremes..
[6]  2015/02/28 02:14   Male / 30 years old level / Others / Very /
Purpose of use
Iam trying to learn myself the principles of multiple variable calculus. I set up and worked out a double integral to find the volume enclosed bij the x, y, z- planes and the plane z=2-y-x. The outcome of my calculation turned out to be 4/3. I needed this tool to check if my answer was right.
[7]  2015/01/15 22:06   Male / 60 years old level or over / A retired people / Useful /
Purpose of use
Tetrahedron volume calculator
To help calculate the volume of an object who's surface is a closed triangular mesh. I am currently using a different formula than you and am interested to see if it is quicker as the number of triangles gets large.
Bug report
While both Tetrahedron volume and surface area calculators produce correct results the formula dislplayed for calculating S2 in the Surface Area formulas is incorrect. It should be:
S2 = (a2 + a3 + a4) / 2 and not S2 = (a3 + a3 + a4) / 2
from Keisan
Thank you for indication. Fixed.
[8]  2014/02/01 17:26   Male / 40 years old level / Others / Very /
Purpose of use
Future need studies
Comment/Request
Nice work Alvin
[9]  2013/04/12 04:33   Male / 60 years old level or over / A teacher / A researcher / Very /
Purpose of use
Area & volume of tetrahedron from edge lengths.

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