Prism Volume (Any Base) Calculator
Find the volume of any prism from its base area and length using V = base area × length — works for any cross-section.
How it works
V = A · L · where A = area of the constant cross-section, L = length
A prism is any solid with the same cross-section all along its length, so its volume is just that cross-sectional area multiplied by the length — no matter whether the base is a triangle, rectangle, hexagon or any irregular shape. This is Cavalieri’s principle in action: stack identical slices and the total is the slice area times the stack height. Because it works for any base, you can first find the base area with a separate area calculator, then multiply here.
Worked example
For a prism whose base area is 20 square units and whose length is 15 units, V = 20 · 15 = 300 cubic units.
Sources: Prism (geometry) — Wikipedia
Frequently asked questions
Does the shape of the base matter?
Only its area matters. Any prism with the same base area and length has the same volume, whether its cross-section is a triangle, a circle or an irregular polygon.
Does this work for an oblique (slanted) prism?
Yes, as long as the length you enter is the perpendicular distance between the two parallel bases. By Cavalieri’s principle a slanted prism has the same volume as an upright one with the same base and perpendicular height.
How do I get the base area first?
Use a matching area calculator for the cross-section — for example the triangle, trapezoid or regular-polygon area tools — then enter that area here as the base area.
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This calculator is for educational purposes. Double-check important results before acting on them.