Prism calculator
To calculate a prism, choose the base shape and enter its dimensions and the height; you get volume, lateral area and surface area with the formulas.
Example: Base of the prism: Any triangle (three sides) · Side / leg a 3 · Side / leg b 4 · Side c 5 · Height h of the prism 10 → Result: Volume 60, surface area 132. Source: Wikipedia – Prisma (Geometrie): V = G·h, M = U·h, O = 2G + M. Updated: .
How it is calculated
The volume of a right prism is base area times height: V = B · h. A prism with a 3-4-5 right-triangle base (B = 6) and 10 cm height has a volume of 60 cm³ and a surface area of 132 cm².
How it is calculated
The base area depends on the shape: any triangle by Heron (A = √(s·(s−a)(s−b)(s−c)) with s = P/2), right triangle a·b/2, equilateral triangle √3/4·a², regular n-gon n·a²/(4·tan(π/n)). The lateral area is L = P · h, the surface area S = 2·B + L.
Good to know
- The prism must be right, so the lateral edges stand perpendicular to the base. For oblique prisms V = B · h still holds with the perpendicular height, but the lateral area does not.
- A prism with a hexagonal base is roughly a nut or the cross-section of a pencil; a cuboid is a prism with a rectangular base.
- Rectangles and cuboids have their own calculators; cylinders are prisms with a circular base.
Frequently asked questions
How do you calculate the volume of a prism?
Base area times height: V = B · h. For a triangular prism with B = 6 cm² and h = 10 cm that is 60 cm³.
How do you calculate the surface area of a prism?
S = 2 · B + P · h: twice the base area plus the lateral area from perimeter times height.
How do you find the area of a triangle from three sides?
With Heron's formula: A = √(s·(s−a)·(s−b)·(s−c)), where s is half the perimeter. For 3, 4, 5 it gives 6.
What is the difference between a prism and a pyramid?
A prism has two equal, parallel bases; a pyramid has one base and an apex. The pyramid volume is B·h/3.
Sources and legal basis
- Wikipedia – Prisma (Geometrie): V = G·h, M = U·h, O = 2G + M
- Wikipedia – Satz des Heron: area of a triangle from its three sides
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