Triangular Prism Calculator

A triangular prism is the solid you get by taking a triangle and extending it straight back to a given length. You see it everywhere: a Toblerone bar, a tent, a roof truss, a wedge door stop, and a glass prism that splits light are all triangular prisms. This calculator takes the three sides of the triangular cross-section and the length of the prism and returns the volume, total surface area, and triangle area in one step. The volume follows the rule that applies to every prism: find the area of the cross-section and multiply by the length. The clever part is the cross-section, because providing three side lengths is the most flexible way to describe a triangle, and the calculator finds its area using Heron's formula, which needs nothing more than those three sides. The surface area adds the two triangular end faces to the three rectangular side faces, which together come to twice the triangle area plus the triangle's perimeter times the prism length. You do not need to measure the height of the triangle separately. Enter the three sides of the base triangle and the prism length in any consistent unit, and the calculator updates instantly. It also checks whether the three sides form a valid triangle and flags the result if they do not. Use this tool for geometry homework, calculating the capacity of a trough or hopper, working out material for a ridge section in construction, or any problem involving a triangular cross-section solid.

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units
units
units
units
60
volume (cubic units)
Surface area132
Triangle area6

The three sides must form a valid triangle (each side less than the sum of the other two).

How it works

The triangle area uses Heron's formula: with semi-perimeter s = (a + b + c) / 2, area = √(s(s-a)(s-b)(s-c)). Volume = triangle area × prism length. Surface area = 2 × triangle area + (a + b + c) × length, which adds the two triangular end faces to the three rectangular side faces.

Worked example

For a 3-4-5 right triangle with prism length 10: semi-perimeter s = (3 + 4 + 5) / 2 = 6. Triangle area = √(6 × 3 × 2 × 1) = √36 = 6 square units. Volume = 6 × 10 = 60 cubic units. Surface area = 2 × 6 + (3 + 4 + 5) × 10 = 12 + 120 = 132 square units. These match the pre-filled defaults above.

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Frequently asked questions

How do you find the volume of a triangular prism?

Find the area of the triangular cross-section, then multiply by the length of the prism. Volume = triangle area x length. For a 3-4-5 right triangle of area 6 and a prism 10 units long, the volume is 60 cubic units.

How do you find the surface area of a triangular prism?

Add the two triangular ends to the three rectangular sides. Surface area = 2 x triangle area + perimeter of triangle x length. For a 3-4-5 triangle with perimeter 12 and length 10: SA = 2 x 6 + 12 x 10 = 132 square units.

What is Heron's formula?

Heron's formula gives the area of any triangle from its three side lengths alone. With semi-perimeter s = (a + b + c) / 2, the area = sqrt(s(s-a)(s-b)(s-c)). It works for any valid triangle without needing the height.