Triangular Prism Volume Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/10/2026
The volume of a right triangular prism is calculated with V = ½ × triangle base × triangle height × prism length. For a triangle with base 3 cm and height 4 cm, on a prism 10 cm long, the volume is 60 cm³.
Explanation
A right triangular prism is a solid whose two ends are identical triangles, connected by rectangular faces perpendicular to those bases — the shape of a classic camping tent, a gable roof, or a gutter. Its volume is calculated in two steps that combine into a single formula: first the area of the triangular base, exactly the same formula as our standard triangle area calculator (base × height ÷ 2), then that area multiplied by the length of the prism — the general principle for the volume of a right prism, whatever the shape of its base: base area × height (here, the length of the solid). This calculator completes the family of solids already on the site — which notably covers the cylinder and the square pyramid, both built on the same general principle (base area × height, or a third of it for a pyramid) — by adding this triangular-based prismatic shape, very concrete and until now missing from the catalog: a camping tent, a gable roof, or a gutter are familiar examples.
Example: prism with base 3 cm × 4 cm, 10 cm long
Inputs
Triangle base: 3 cm. Triangle height: 4 cm. Prism length: 10 cm.
Calculation
Triangle area = (3 × 4) ÷ 2 = 6 cm². Volume = 6 × 10 = 60 cm³.
Result
The volume of this triangular prism is 60 cm³.
Frequently asked questions
Does this formula work for any base triangle?
Yes, as long as the base and height used correspond to each other (the height measured perpendicular to the chosen base) — exactly the same condition as for calculating the area of a triangle alone. The type of triangle (isosceles, right, scalene) does not change the formula, only the base area matters.
What is the difference from a rectangular-based prism (a cuboid)?
A cuboid is a special case of prism whose base is a rectangle rather than a triangle: its volume is calculated simply by multiplying length × width × height, without the ½ factor needed here. The ½ factor in this calculator comes only from the triangle area formula (base × height ÷ 2), not from a general property of prisms.
How do you calculate the total surface area of this prism, not just its volume?
The total surface area requires summing the area of the two triangles (the two identical bases) and the area of the three lateral rectangular faces, which also requires knowing the three sides of the triangle (not just its base and height) to calculate the widths of those lateral faces — a calculation that this volume-focused calculator does not cover directly.