The volume of any pyramid is V = 1/3 × base area × vertical height. For a triangular pyramid the base is a triangle, so V = 1/3 × A_base × h. Example: a pyramid with an equilateral base of edge a = 6 units and height h = 7 units has base area A = √3/4 × 6² = 15.5885 square units, so V = 1/3 × 15.5885 × 7 = 36.3731 cubic units.

First compute the base triangle's area as A = 1/2 × b × h_b, where b is one side of the triangle and h_b is the altitude to that side. Then V = 1/3 × A × h_pyramid. Example: b = 8, h_b = 5, pyramid height = 9 gives A = 1/2 × 8 × 5 = 20, and V = 1/3 × 20 × 9 = 60 cubic units.

Use Heron's formula. With sides a, b, c, the semi-perimeter is s = (a + b + c)/2 and the base area is A = √(s(s − a)(s − b)(s − c)). Example: sides 5, 6, 7 give s = 9 and A = √(9 × (9 − 5) × (9 − 6) × (9 − 7)) = 14.6969. With pyramid height 8, V = 1/3 × 14.6969 × 8 = 39.1918 cubic units. The three sides must satisfy the triangle inequality (each side shorter than the sum of the other two).

For a regular triangular pyramid — equilateral base of edge a, apex directly above the centroid, vertical height h — the slant height (apex to the midpoint of a base edge) is s = √(h² + a²/12), because the centroid sits at distance a/(2√3) from each base edge. Example: a = 6, h = 7 gives s = √(49 + 36/12) = √52 = 7.2111 units.

For a regular triangular pyramid (equilateral base, apex above the centroid), the lateral area is 3 identical triangular faces: lateral = 3 × (1/2 × a × slant) = 1.5 × a × slant, and the total surface area adds the base: total = lateral + √3/4 × a². Example: a = 6, h = 7 gives lateral = 64.8999 and total = 80.4884 square units. For a general (non-equilateral) triangle base, the three side faces are not fixed by the base area and height alone, so surface area needs extra measurements — this calculator shows volume and base area in that case.

A regular tetrahedron is the special case where all six edges are equal (a) and the height is h = a√(2/3). Its volume simplifies to V = a³/(6√2). Example: edge 6 gives h = 6√(2/3) ≈ 4.899 and V = 25.4558 cubic units.

Only the base shape. A triangular pyramid has a triangle for its base (4 faces total); a rectangular pyramid has a rectangle for its base (5 faces total). Both use V = 1/3 × base area × height, but the base area and surface area formulas differ. If your base is a rectangle or square, use our rectangular pyramid volume calculator; if your pyramid's top is cut off (two bases), that is a frustum — see our pyramid frustum calculator.

No. A triangular pyramid tapers to a single apex point; a triangular prism has two congruent triangular faces joined by rectangles. Their volumes differ by the factor of 1/3: pyramid V = 1/3 × A_base × h, prism V = A_base × h. A common mistake is forgetting the 1/3 for the pyramid.

h is the perpendicular distance from the base plane to the apex — the shortest, vertical distance, not the length of a slanted lateral edge. If you measured along a slant, the true h is always shorter. The volume formula V = 1/3 × A × h uses this perpendicular height regardless of where the apex sits above the base plane.

Any consistent length unit works: enter all inputs in the same unit (cm, m, in, ft…), and the volume comes out in cubic units while areas come out in square units. Mixing units — for example a base edge in inches with the height in feet — will give a wrong answer, so convert everything to one unit first.