How this calculator works
A triangular pyramid has a triangular floor and three triangular side faces. First find the floor area using the selected triangle method. Multiplying that area by the perpendicular height and dividing by three gives the volume. The base triangle altitude lies inside the floor, while the pyramid height rises out of that plane: they are different measurements. The same volume equation works for an oblique apex. Reverse modes recover base area or pyramid height without assuming a particular triangle shape.
Formula
V = KH/3; H = 3V/K; K = 3V/H. Base methods: K = bh/2; Heron K² = s(s-a)(s-b)(s-c); SAS K = ab sin C/2; ASA K = a² sin B sin C/[2sin(B+C)].
Worked example
A base triangle with sides 3 m, 4 m and 5 m has area 6 m². With perpendicular pyramid height 9 m, its volume is 6 × 9 / 3 = 18 m³. Keeping the same area and volume in reverse mode recovers the 9 m height.
Advertisement
Frequently asked questions
Is every triangular pyramid regular?
No. A regular tetrahedron has four equal equilateral faces. This calculator also accepts irregular triangular bases and oblique apex positions.
Can I use a slanted corner edge as pyramid height?
Only if that edge is perpendicular to the base plane. Otherwise it is longer than the needed perpendicular height.
Does base area determine the three base sides?
No. Many triangles share the same area. Reverse base-area mode reports only area and does not invent side lengths.