Volume of Prism: Formula & Examples

Updated 11 November 2026 · Standard formula, shown below

Volume 240.00 cm³

Base area: 24 cm²; You entered
Height: 10 cm; You entered

The volume of a prism is the amount of space it occupies, calculated by multiplying the area of its base by its height. To use this calculator, enter the base area and the prism height (or the dimensions needed to compute the base area), and you will get the volume in cubic units. The calculator also shows the step‑by‑step working so you can check your own sums.

Formula

The volume of any prism — triangular, rectangular, trapezoidal, or any other shape with two identical parallel faces — is given by:

V = A_base × h

V = volume (cubic units, e.g. cm³, m³, in³)
A_base = area of one of the two identical bases (square units)
h = perpendicular height between the two bases (linear units)

The formula works for every prism because the cross‑section is constant along the height. You multiply the area of that cross‑section (the base) by the length (the height). It is the same idea as stacking identical slices of a shape.

Worked Example

Using the default values from the calculator: base area = 24 cm² and height = 10 cm.

Write down the formula: V = A_base × h
Substitute the numbers: V = 24 × 10
Multiply: V = 240

The volume is 240 cm³. The calculator gives the same result (240.00 cm³).

When to Use This Formula

You use the prism volume formula whenever you have a solid with two identical, parallel faces (the bases) and straight sides connecting them. Common examples include:

Rectangular boxes (cuboids) – base area = length × width
Triangular prisms – base area = ½ × base of triangle × height of triangle
Trapezoidal prisms – base area = ½ × (sum of parallel sides) × height of trapezoid
Cylinders – although often treated separately, a cylinder is a prism with a circular base; volume = πr² × h

If you know the base area and the height, you do not need to know the exact shape of the base — the formula is the same.

How to Read the Result

The result is always in cubic units. If you measure the base area in square centimetres and the height in centimetres, the volume is in cubic centimetres (cm³). For metres, it is m³; for inches, in³; and so on. One cubic metre equals 1,000 litres, which is useful when converting to liquid capacity. For example, a prism with a volume of 0.5 m³ holds 500 litres.

Common Mistakes and Misconceptions

Using the slant height instead of the perpendicular height. For a prism that is not vertical (oblique), the height is the perpendicular distance between the two bases, not the length of a slanted edge.
Mixing units. If the base area is in m² and the height is in cm, convert one first. The volume will be wrong if you mix units without converting.
Forgetting to halve for triangular bases. The area of a triangle is ½ × base × height of the triangle. A common error is to use the full base × height.
Confusing the base area with the perimeter. The formula needs area, not perimeter. For a rectangular base, area = length × width, not 2(length + width).
Thinking the formula only works for right prisms. It works for oblique prisms too, as long as you use the perpendicular height.

Limitations of the Formula

The formula V = A_base × h applies only to prisms — solids with constant cross‑section. It does not apply to pyramids, cones, or spheres, which have different volume formulas (e.g. V = ⅓ × base area × height for a pyramid). Also, if the shape is not a prism (e.g. a frustum or a composite solid), you need to break it into prism‑like parts or use a different method. The formula assumes the bases are parallel and identical; if they are not, it is not a prism.

Frequently Asked Questions

What is the difference between a prism and a pyramid?

A prism has two identical parallel bases and rectangular (or parallelogram) sides, so the cross‑section is constant. A pyramid has one base and triangular sides that meet at a point (apex). The volume of a pyramid is one‑third of the prism volume with the same base and height.

How do I find the volume of a triangular prism?

First find the area of the triangular base: ½ × base of triangle × height of triangle. Then multiply by the length (the distance between the two triangular faces). For example, a triangle with base 6 cm and height 4 cm has area 12 cm²; if the prism is 10 cm long, the volume is 120 cm³.

Does the formula work for a cylinder?

Yes. A cylinder is essentially a prism with a circular base. The base area is πr², so the volume is πr² × h. Many textbooks treat cylinders separately, but the underlying principle is identical.

What if the prism is tilted (oblique)?

For an oblique prism, the bases are still parallel, but the sides are not perpendicular to them. The volume formula still holds, but you must use the perpendicular height — the shortest distance between the two bases — not the length of a slanted edge.

Can I use this formula for a trapezoidal prism?

Yes. Calculate the area of the trapezoidal base: ½ × (sum of parallel sides) × height of trapezoid. Then multiply by the length of the prism. For example, a trapezoid with parallel sides 4 cm and 6 cm and height 5 cm has area 25 cm²; with a prism length of 8 cm, the volume is 200 cm³.

Why do I get different answers when I use different units?

Because the volume depends on the units. If you measure in centimetres, you get cm³; in metres, m³. Always ensure the base area and height are in compatible units. Convert everything to the same unit system before multiplying.

Formula used

in a | Base area | cm² | 24 | 0
in h | Height | cm | 10 | 0
out v | Volume | cm³ | a * h | 2

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.