Calculate volume, surface area (total and lateral), base area, perimeter, and edge lengths of a triangular prism. Supports any triangle base with unit conversion and presets.
A triangular prism is a three-dimensional solid with two congruent triangular bases and three rectangular lateral faces. It is one of the most common prisms in geometry, appearing in everything from Toblerone chocolate boxes to architectural roof trusses, camping tents, and structural wedges.
The volume of a triangular prism equals the area of the triangular base multiplied by the prism's height, which in this calculator is the prism length between the two triangular ends. If the base triangle has sides a, b, and c, you can find the base area using Heron's formula: A = √[s(s−a)(s−b)(s−c)], where s = (a + b + c)/2 is the semi-perimeter.
The total surface area combines the two triangular bases with the three rectangular lateral faces: SA = 2 × A_base + (a + b + c) × h. The lateral surface area alone is the perimeter of the base triangle multiplied by the prism height: LSA = (a + b + c) × h.
Triangular prisms are essential in engineering for calculating material usage in structural beams, packaging design, and fluid volumes. This calculator accepts the three sides of the base triangle and the prism height, then computes volume, base area, total and lateral surface area, base perimeter, and a breakdown of each rectangular face. Presets for common real-world objects and a reference table make exploration easy.
Triangular prisms show up whenever a fixed triangular cross-section is extended through space, so volume alone is rarely the only quantity you need. This calculator also reports the base area, lateral wrap area, total surface area, inscribed-circle radius of the base, and total edge length, which makes it more useful for packaging, materials estimation, and geometry practice than a single-formula tool. It is a good fit for comparing prism designs built from different base triangles but the same overall length.
Semi-perimeter: s = (a + b + c) / 2
Base Area (Heron): A = √[s(s−a)(s−b)(s−c)]
Volume: V = A × h
Lateral Surface Area: LSA = (a + b + c) × h
Total Surface Area: TSA = 2A + LSA
Base Perimeter: P = a + b + cResult: Volume = 60, Base Area = 6, TSA = 132, LSA = 120
A 3-4-5 right triangle base has area = ½ × 3 × 4 = 6. With prism height 10: Volume = 6 × 10 = 60. Lateral SA = (3 + 4 + 5) × 10 = 120. Total SA = 2 × 6 + 120 = 132.
Every triangular prism calculation starts with the cross-section. If the three base sides do not make a valid triangle, the rest of the solid does not exist. Once the base is valid, Heron's formula gives its area, and that single result drives the volume, the inradius of the base, and the contribution of the two triangular ends to the total surface area.
In many real jobs, the side wrap and the end caps matter differently. A label wrapped around a prism depends on lateral surface area, while paint, sheet material, or insulation may depend on total surface area. Reporting both values is useful because a long narrow prism can have a moderate volume but still require a large amount of covering material along its rectangular faces.
This shape appears in tents, wedges, optical prisms, roof ridge components, and product packaging. Comparing presets helps build intuition for how changing only the prism height affects volume linearly, while changing the side lengths of the triangular base affects both footprint and surface area in more complicated ways. That makes the calculator a practical tool for both classroom geometry and dimension planning.
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Volume = Base Area × Height. You find the base area using Heron's formula from the three sides of the triangle, then multiply by the prism height.
Total surface area includes both triangular bases plus all three rectangular faces. Lateral surface area counts only the three rectangular faces (the "wrap-around" part).
Each side must be less than the sum of the other two (triangle inequality). For example, sides 3, 4, 5 work because 3 < 4 + 5, 4 < 3 + 5, and 5 < 3 + 4.
Yes — equilateral, isosceles, scalene, right-angled, obtuse, or acute. Heron's formula works for any valid triangle.
Toblerone boxes, camping tents, roof ridges, optical prisms, door wedges, and structural I-beam flanges are all triangular prisms or close approximations.
Rearrange the formula: Height = Volume / Base Area. First compute the base area from the three triangle sides, then divide the volume by it.
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