Triangular Prism Volume Calculator

Enter the base, triangle height and length of a triangular prism to get its volume and surface area, drawn to scale. Click any dimension on the drawing to change it.

Dimensions

Triangular Prism
Blueprint · Isometric Click an amber dimension to edit it · isometric, not to printed scale

Result

Volume of a triangular prism

A prism is its cross-section swept along a length. For a triangular prism the cross-section is a triangle of area ½·b·t, so the volume is ½·b·t·L. The surface is the two triangular ends plus three rectangles wrapping the sides.

Editing on the drawing

The base, triangle height and length are each editable on the figure — click a value, type a new one and press Enter to redraw the prism to scale.

How to find the volume of a triangular prism

A prism is a flat shape swept along a straight length, keeping the same cross-section the whole way. For a triangular prism that cross-section is a triangle, so three measurements set it: the triangle's base, the triangle's height and the prism's length.

The formulas

Volume is the area of the triangular end times the length. The surface is the two triangular ends plus the three rectangles that wrap the sides.

V = ½·b·t·L
A = b·t + L(b + 2√((b⁄2)² + t²))

Worked example

Take a prism with base 60, triangle height 52 and length 96 (an isosceles cross-section).

Step 1 — cross-section area

Area of the triangular end.

½ × 60 × 52 = 1,560
Step 2 — volume

Cross-section times length.

V = 1,560 × 96 = 149,760
Step 3 — surface area

Two ends plus three side rectangles.

A = 60·52 + 96(60 + 2√(30² + 52²)) ≈ 3,120 + 17,286 ≈ 20,406

What else the calculator returns

You also get the cross-section area, the lateral area and the slant side of the triangle. The tool assumes an isosceles cross-section, with the apex centred over the base.

Where it comes up

Triangular-prism volumes describe roof trusses and ridge beams, ramps and wedges, optical prisms — and, famously, a bar of Toblerone.

Frequently asked questions

How do you find the volume of a triangular prism?

Find the area of the triangular cross-section (½ × base × height) and multiply by the prism's length.

Is the triangle height the same as the prism length?

No. The triangle height is measured across the end face; the length is how far the prism extends. They are independent measurements.

What if the triangle is not isosceles?

The volume is still cross-section area times length. Only the sloping sides — and therefore the surface area — change. This tool assumes an isosceles cross-section.

How do I find the length from the volume?

Rearrange the formula: L = V / (½ · b · t) = 2V / (b · t).

How is a prism different from a pyramid?

A prism keeps the same cross-section along its length, while a pyramid tapers to a point. A pyramid with the same base and height holds a third as much as the matching prism.