Triangular Prism Calculator

Background.

A triangular prism is a triangle pushed straight along a line: a wedge of cheese, a ridge tent, the roof space above a gable-ended house, a doorstop, the glass prism that splits light. Because the cross-section never changes, two multiplications describe it. The triangle's area times the length gives the volume; the triangle's perimeter times the length gives the area of the three rectangular faces that wrap around it.

Those two results need different measurements of the triangle, which is why the page asks for three. Area needs a base and the height measured at right angles to it, then half their product. The wrapping faces need all three sides, entered together as the perimeter. For the isosceles 5-5-6 triangle in the default example, the base is 6, the height from the apex down to that base is 4, and the perimeter is 5 + 5 + 6 = 16.

Nothing checks that the three triangle figures belong to the same triangle. With base 6 and height 4, no triangle has a perimeter below 16: the isosceles shape is the shortest way round, and sliding the apex sideways only lengthens the slanted sides. A smaller perimeter, or one copied from a different triangle, yields a lateral area for a shape that cannot exist, while the volume stays correct because it never uses the perimeter.

The prism is assumed to be right, its ends square to its length, and the lateral area leaves out the two triangular ends. Add base × height once, which covers both end triangles together, when you need the full surface for painting or wrapping. Units follow your measurements: centimetres in gives cubic and square centimetres out.

What is triangular prism calculator?

A right triangular prism is a solid with two identical, parallel triangular ends joined by three rectangular faces that meet the ends at right angles. Its volume is the area of one triangular end multiplied by the distance between the ends, the prism's length. Its lateral area is the combined area of the three rectangles, equal to the triangle's perimeter times that length; the two triangular ends are not included in it.

How to use this calculator.

1. 01Pick one side of the triangle as the base and measure it. For a roof or tent this is usually the floor width; for a right-angled wedge, either leg will do.
2. 02Measure the triangle's height at right angles to that base, from the base line to the opposite corner, not along a sloping side.
3. 03Add all three side lengths and enter the total as the perimeter. If a right triangle's third side is unknown, find it with Pythagoras first.
4. 04Enter the prism length, the distance between the two triangular ends, in the same unit, then read the volume and lateral area. For the full surface, add base × height to the lateral area.

The formula.

V = (b × h ÷ 2) × L, and lateral area = P × L. Here b is the triangle's base, h its height perpendicular to that base, P the sum of its three sides and L the length of the prism.

The volume formula is the general prism rule, cross-sectional area times length, with the triangle's area b × h ÷ 2 as the cross-section. The lateral formula comes from unrolling the three side faces into one long strip: its width is the distance around the triangle and its other dimension is the prism length.

Both results grow in direct proportion to L, so doubling the length doubles each. Volume also scales with b and with h separately, whereas the lateral area depends only on the perimeter, so two triangles with the same perimeter but very different areas give the same lateral area. The total surface is P × L + b × h, since the two triangular ends together add one full b × h.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.