Isosceles, Right Tetrahedron

Calculations for an isosceles, right tetrahedron. Here, this term refers to a tetrahedron in which two faces are isosceles triangles and two faces are identical right triangles. The two right angles are adjacent to each other. The plane containing the edge d (located between the two right angles) and bisecting the opposite edge c is a plane of symmetry. There does not necessarily have to be a right angle between the two legs b. However, if there is, this shape corresponds to the corner of a cuboid.
Enter edge c and two of the three edges of one of the right triangles a, b, and d). Choose the number of decimal places, then click Calculate.

	Edge length a:
	Edge length b:
	Edge length c:
	Edge length d:
	Surface area (A):
	Volume (V):
	Surface-to-volume ratio (A/V):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

Lengths have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^-1.

Such an isosceles, right tetrahedron is a simple variant of the truncated corner of a scutoid based on a regular prism. It is a generalization of the corner of a cuboid with additional regularities, as the regular prism is a generalization of the cuboid.
The third side of a right triangle is, of course, calculated using the Pythagorean theorem. The surface area of ​​the isosceles, right tetrahedron is derived from the individual areas of the four triangles. The two right triangles can be combined into a rectangle with sides b and d. The volume is determined using the general pyramid volume formula, with one of the isosceles triangles bbc serving as the base and the perpendicular edge d as the height.
Calculating a general tetrahedron is quite complicated. If certain regularities are assumed, as is the case here, the calculation becomes vastly simpler, though the possible shapes the tetrahedron can take are of course restricted then. Finally, the formulas for calculating a regular tetrahedron are quite concise, but, size aside, this always retains the same shape.

Calculation of volume and other dimensions: isosceles, right tetrahedron

Last updated on 08/19/2026. Author: Jürgen Kummer

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