Triangular Prism
Calculate the volume, surface area, lateral area, and base area of a triangular prism. Free online 3D geometry calculator with formulas V = 1/2bhL and SA formulas.
About This Calculator
Our free triangular prism calculator computes all key properties of a right triangular prism: volume, surface area, lateral surface area, and base area. Whether you are a student studying 3D geometry, a teacher preparing lesson materials, an architect designing triangular structures, or a DIY builder estimating material needs, this tool delivers instant accurate results.
The volume is calculated using the formula V = 1/2 x b x h x L, where b is the triangle base, h is the triangle height, and L is the prism length. The base area is 1/2 x b x h. The lateral area is the perimeter of the triangle times the prism length: L x (b + 2 x s) where s is the equal side length of an isosceles triangle (for a general triangle, it would be L x (a + b + c)). The surface area is the lateral area plus twice the base area: SA = lateral_area + 2 x base_area.
Triangular prisms appear frequently in real life: tent structures, roof trusses, wedge-shaped objects, optical prisms, and packaging. Understanding their geometric properties is essential for construction, manufacturing, packaging design, and education. This calculator works with any consistent unit system -- meters, centimeters, inches, feet, or millimeters.
Frequently Asked Questions
What is the formula for the volume of a triangular prism?
The volume of a triangular prism is V = (1/2) x b x h x L, where b is the base of the triangle, h is the triangle height, and L is the prism length. Calculate the triangular base area (1/2 x b x h) and multiply by the prism length.
What is the formula for the surface area of a triangular prism?
The surface area of a triangular prism is SA = lateral_area + (2 x base_area). The lateral area is the perimeter of the triangle times the prism length L. For an isosceles triangle with base b and height h, the perimeter is b + 2sqrt((b/2)^2 + h^2). The base area is 1/2 x b x h. So SA = L x (b + 2sqrt((b/2)^2 + h^2)) + b x h.
How many faces, edges, and vertices does a triangular prism have?
A triangular prism has 5 faces (2 triangular bases and 3 rectangular lateral faces), 6 vertices (3 on each triangular face), and 9 edges (3 on each triangular face plus 3 connecting the two faces). The cross-section along its length is always a triangle.
What units does this triangular prism calculator use?
This calculator accepts any consistent unit system. Enter all dimensions in the same unit (meters, inches, feet, centimeters, etc.). Volume is in cubic units, and surface areas are in square units matching your input.
What is the difference between lateral area and surface area of a triangular prism?
The lateral area is the sum of the areas of the three rectangular faces only (the sides). The surface area includes both the lateral area and the areas of the two triangular bases. So surface area = lateral area + (2 x base area).
Is this triangular prism calculator free?
Yes, all calculators on Calculy are completely free to use with no registration or downloads required. Use this tool unlimited times for school, work, or personal projects.
What are real-world examples of triangular prisms?
Common real-world examples of triangular prisms include tent structures, triangular roof trusses in buildings, wedge doorstops, certain chocolate bar boxes, glass prisms used in optics, triangular gutters, and some types of packaging containers.