120
units³
12
units²
160
units²
184
units²
120
units³
12
units²
160
units²
184
units²
A triangular prism is a three-dimensional solid with two congruent, parallel triangular faces (the bases) connected by three rectangular lateral faces. It is one of the most common prismatic shapes, appearing in architecture, structural engineering, optics, and everyday objects like tent structures, Toblerone packaging, and roof gables.
The Triangular Prism Calculator computes the volume, triangular face area, lateral surface area, and total surface area. The primary inputs are the triangle base $$b$$, triangle height $$h_t$$, and the prism length $$l$$ (the distance between the two triangular faces). Advanced inputs allow you to specify the two remaining sides of the triangle for accurate surface area calculations.
The volume of a triangular prism is the product of the triangular cross-sectional area and the length:
$$V = \frac{1}{2} b \cdot h_t \cdot l$$
This is a direct application of Cavalieri's principle: the volume of any prism equals the base area times the height (length). The triangular base area is $$A_{\triangle} = \frac{1}{2} b h_t$$, giving us the simple multiplication $$V = A_{\triangle} \times l$$.
The lateral surface area consists of the three rectangular faces. Each rectangle has a width equal to one side of the triangle and a height equal to the prism length $$l$$. If the triangle sides are $$b$$, $$s_1$$, and $$s_2$$:
$$A_{\text{lateral}} = (b + s_1 + s_2) \times l = P_{\triangle} \times l$$
where $$P_{\triangle}$$ is the perimeter of the triangular base. The total surface area adds both triangular end faces:
$$A_{\text{total}} = A_{\text{lateral}} + 2 A_{\triangle} = (b + s_1 + s_2) l + b h_t$$
Triangular prisms are structurally significant because the triangular cross-section provides excellent resistance to lateral forces. This is why triangular cross-sections appear in bridge trusses, aircraft fuselage frames, and tent poles. In optics, glass triangular prisms decompose white light into its constituent colors through refraction — Newton's famous experiment. In construction, gable roofs are essentially triangular prisms, and calculating their volume is essential for attic insulation estimates and ventilation design. In packaging, triangular prism shapes optimize packing efficiency for certain products. Whether you are a student studying solid geometry or an engineer designing real structures, this calculator delivers the measurements you need from minimal input.
Enter the triangle base $$b$$, triangle height $$h_t$$, and prism length $$l$$. For accurate surface area, expand the advanced section and enter the triangle's other two side lengths $$s_1$$ and $$s_2$$. The calculator multiplies $$\frac{1}{2} b h_t$$ by $$l$$ for volume, sums all three sides times $$l$$ for lateral area, and adds twice the triangular area for total surface area.
The volume is the total enclosed space. The triangular face area is the area of one triangular end. The lateral area covers the three rectangular side faces — useful for painting or wrapping. The total surface area includes all five faces. If the triangle side lengths are left at defaults, the lateral area may not reflect your exact triangle; update $$s_1$$ and $$s_2$$ in the advanced section for precision.
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Results
A prism with an isosceles triangle base (b=6, sides=5, height=4) and length 10. Volume = 120 cubic units.
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Results
A prism with a 3-4-5 right triangle base and length 20. Volume = 120 cubic units, total surface area = 252 square units.
If you know all three sides of the triangle ($$a$$, $$b$$, $$c$$), use Heron's formula to find the area: $$s = (a+b+c)/2$$, then $$A = \sqrt{s(s-a)(s-b)(s-c)}$$. The triangle height relative to base $$b$$ is then $$h_t = 2A/b$$. Enter this value in the calculator.
The volume formula $$V = A_{\triangle} \times l$$ works for both right prisms (lateral faces perpendicular to bases) and oblique prisms (lateral faces at an angle), provided $$l$$ is the perpendicular distance between the two triangular bases. For oblique prisms, the lateral surface area formula assumes rectangular faces, so adjustments may be needed.
A triangular prism has two parallel triangular bases connected by three rectangles — 5 faces total. A triangular pyramid (tetrahedron) has a triangular base connected to a single apex — 4 triangular faces total. The prism has three times the volume of a pyramid with the same base and height.
The volume depends only on the base, height, and length, so those are the primary inputs. The side lengths $$s_1$$ and $$s_2$$ are needed only for the lateral surface area calculation. They are in the advanced section so you can get a quick volume estimate without needing to know every dimension.
Examples include tent structures (A-frame tents), Toblerone chocolate boxes, roof gable sections, optical glass prisms, camping wedge pillows, ramps, and certain bridge cross-sections. In geology, rock formations can form natural prism shapes along fault lines.
Yes. For an equilateral triangle with side $$a$$, enter $$b = a$$, $$h_t = a\sqrt{3}/2$$, and in advanced inputs set $$s_1 = s_2 = a$$. For example, with $$a = 6$$: $$b = 6$$, $$h_t = 5.196$$, $$s_1 = s_2 = 6$$.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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