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Volume of prisms

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Volume of a Prism

The volume of a prism is found with base area times height: find the area of the base shape, then multiply by how tall the prism is. This works whether the base is a rectangle, a triangle, or another polygon. Learn the formula and see it worked through with a rectangular prism.

The volume of a prism formula

The volume of a prism is the amount of space inside it, found with a single rule that works for any prism — rectangular, triangular, or any other shape base: volume = base area × height. This asks a simple question: what is the area of one end, and how many "layers" tall is the prism?

Volume of a rectangular prism A rectangular prism with length 5, width 3, and height 4. The base area (length times width) is 15, and the volume (base area times height) is 60 cubic units. length = 5 width = 3 height = 4 V = base area × height base area = 5 × 3 = 15 V = 15 × 4 = 60 units³
A rectangular prism with base 5 × 3 (area 15) and height 4 has volume 60 cubic units.

Why "base area times height" works

Picture the prism sliced into thin horizontal layers, each shaped exactly like the base. Every layer has the same area as the base, and stacking "height" many of those layers fills the prism. Multiplying the base area by the height counts the total space in one step instead of adding up every layer.

Different base shapes

The formula does not change — only the base-area calculation does. For a rectangular prism, base area = length × width. For a triangular prism, base area = ½ × base × height of the triangle. Once you have that one number, multiply it by the prism's height (or length, for a prism lying on its side) the same way every time.

Volume vs. surface area

Volume measures the space inside a prism in cubic units; it is a different measurement from the surface area of a prism, which measures the area of its outside faces in square units. To see how a prism's volume compares to a cylinder's, see volume of cylinders, or work through a mixed example in word problems relating prisms and cylinders.

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