VolLab

Triangular Prism Volume Calculator

Cross-section area, extruded along the prism's length.

Triangle base

Triangle height

Prism length

Volume

120

Triangle cross-section area: 12
Surface area (isosceles cross-section): 184

What you entered

Base: 6Triangle height: 4Prism length: 10

1
Triangular cross-section area
0.5 × 6 × 4= 12
2
Volume = cross-section area × length
12 × 10= 120
3
Surface area (assumes isosceles cross-section)
2 × 12 + 10 × (b + 2×slant)= 184

Result

Volume: 120

A triangular prism with a 6 × 4 triangular cross-section, extruded 10 deep, has a volume of 120.

Triangular prism volume and surface area

Volume is the triangular base area times the length. The base area is half the base times its height.

Base	Triangle height	Prism length	Base area	Volume	Surface area
3	4	20	6.00	120.00	242.88
4	3	10	6.00	60.00	124.11
5	5	12	12.50	150.00	219.16
6	4	8	12.00	96.00	152.00
8	6	15	24.00	360.00	384.33

Rows one and two have identical base areas of 6.00 but very different volumes, because the prism length differs by a factor of two - volume is simply base area times length, exactly as for any prism. The same principle means a cylinder is a prism with a circular base. Surface area is less tidy: it needs the two triangular ends plus three rectangular faces, and computing the sloping sides requires the triangle's actual side lengths rather than just its base and height.

Volume is just cross-section × length

Any prism's volume is its constant cross-sectional area multiplied by how far that cross-section is extruded — for a triangular prism, that means ½ × base × height × length.

Classic optics example

The triangular glass prism that splits white light into a rainbow is exactly this shape — its volume follows the same formula as any other triangular prism.

Frequently asked questions

How do I calculate the volume of a triangular prism?

Volume = (½ × base × height of triangle) × length of prism. A triangular prism with triangle base 6, triangle height 4, and prism length 10: V = (½ × 6 × 4) × 10 = 120 cubic units.

What is a triangular prism?

A 3D shape with two identical triangular faces (the ends) connected by three rectangular faces. Think of a Toblerone box. Volume = cross-sectional area × length. The cross-section is always the triangle.

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

SA = 2 × (triangle area) + (perimeter of triangle × length). Find the triangle's area (½bh), add the three rectangular sides. A prism with 3-4-5 triangle and length 10: SA = 2×6 + (12×10) = 132 square units.