Triangular Prism Calculator
Enter the dimensions of a triangular prism to instantly find its volume, total surface area, lateral surface area, and the area of each triangular base. Choose from five ways to describe the triangular face: base and height, right triangle, all three sides (SSS), two sides and an angle (SAS), or two angles and a side (ASA). Switch between metric and imperial units at any time.
Formula
Worked example
A triangular prism with a right-triangle base (legs 3 m and 4 m) and a prism length of 10 m: base area = 0.5 x 3 x 4 = 6 m^2; hypotenuse = 5 m; volume = 6 x 10 = 60 m^3; lateral surface = (3 + 4 + 5) x 10 = 120 m^2; total surface = 120 + 2 x 6 = 132 m^2.
What is a triangular prism?
A triangular prism is a three-dimensional solid with two parallel, congruent triangular faces (called bases) and three rectangular lateral faces connecting them. It has 5 faces, 9 edges, and 6 vertices. The shape appears in architecture, optics (the glass prism that splits light), tent design, Toblerone packaging, and structural engineering. Any triangle, whether equilateral, isosceles, scalene, or right-angled, can form the base of a prism.
Volume and surface area formulas
Volume is always base area times prism length: V = A x L. The base area depends on how the triangle is defined. For a triangle with base b and height h: A = 0.5 x b x h. For a right triangle with legs a and b: A = 0.5 x a x b. For three sides (SSS) use Heron's formula: s = (a + b + c) / 2, then A = sqrt(s(s - a)(s - b)(s - c)). For two sides and an included angle (SAS): A = 0.5 x a x b x sin(C). Lateral surface area is the perimeter of the triangle times the prism length: A_lateral = (a + b + c) x L. Total surface area adds both triangular bases: A_total = A_lateral + 2 x A.
Choosing the right input mode
Select the mode that matches the information you already have. "Base and height" is the most common: you measure the base edge and the perpendicular height of the triangle. "Right triangle" works when the cross-section has a 90-degree corner, and you know both legs. "Three sides (SSS)" requires only the three edge lengths, using Heron's formula internally. "SAS" (two sides + included angle) suits situations where you have two measured edges and the angle between them. "ASA" (two angles + included side) lets you describe the triangle by its angles, which is useful when angles are measured but only one side is accessible. All five modes give the same final outputs.
Real-world applications
Triangular prisms appear in many fields. In construction, a gable roof is essentially a triangular prism sitting on a box; calculating its volume determines how much space it encloses and its surface area sets how much roofing material you need. In optics, glass prisms refract and reflect light, and their geometry determines the angles of dispersion. In packaging and product design, triangular cross-sections are structurally efficient and distinctive. Engineers use triangular cross-sections in trusses because triangles are the only polygon that cannot deform under load without changing side lengths.
Common triangular prism configurations
| Prism length (m) | Volume (m^3) | Total surface area (m^2) |
|---|---|---|
| 1 | 6.00 | 42.00 |
| 2 | 12.00 | 60.00 |
| 5 | 30.00 | 114.00 |
| 10 | 60.00 | 216.00 |
| 20 | 120.00 | 420.00 |
| 50 | 300.00 | 1020.00 |
Approximate volumes for some standard prism lengths with a 3-4-5 right-triangle base (area = 6 m^2).
Frequently asked questions
How do I find the volume of a triangular prism?
Multiply the area of the triangular base by the length (depth) of the prism. V = A x L. The base area depends on the triangle: for a base and height, A = 0.5 x b x h; for three sides, use Heron's formula; for two sides and an angle, A = 0.5 x a x b x sin(C).
What is the surface area of a triangular prism?
Total surface area = lateral surface area + 2 x triangular base area. The lateral surface area is the perimeter of the triangle times the prism length: (a + b + c) x L. The two triangular faces each have area A, so total = (a + b + c) x L + 2A.
How many faces, edges, and vertices does a triangular prism have?
A triangular prism has 5 faces (2 triangular bases + 3 rectangular lateral faces), 9 edges (3 on each triangular face + 3 connecting them), and 6 vertices (3 on each triangular face).
What is Heron's formula and when should I use it?
Heron's formula calculates the area of a triangle when all three side lengths are known, without needing the height. If the sides are a, b, c, compute the semi-perimeter s = (a + b + c) / 2, then the area = sqrt(s x (s - a) x (s - b) x (s - c)). Use it whenever you know three side lengths but not the height.
Is a triangular prism the same as a pyramid?
No. A triangular prism has two identical triangular bases connected by three rectangles; it has a constant cross-section along its length. A triangular pyramid (tetrahedron) has one triangular base and three triangular faces that meet at a single apex point. Volume formulas differ: prism V = A x L, pyramid V = (1/3) x A x h.
Can I calculate the prism length if I know the volume?
Yes. Rearrange the volume formula: L = V / A, where A is the base triangle area. Enter the triangle dimensions first to get the base area, then divide your known volume by that area.