Volume of Prism: Formula, Examples & Calculator

This calculator works out the volume of any right prism (a solid with two identical, parallel bases and rectangular sides) when you enter the base area and the height. You get the volume in cubic units, and the tool also shows the formula and a worked example so you can check your own working. The volume of a prism is always the base area multiplied by the height, no matter the shape of the base.

Formula

The volume V of a right prism is given by:

V = A_b × h

• V = volume (cubic units, e.g., cm³, m³, in³)
• A_b = area of one base (square units, e.g., cm², m², in²)
• h = height of the prism, measured perpendicular to the base (linear units, e.g., cm, m, in)

This formula works for any prism whose bases are congruent, parallel polygons, and whose lateral faces are parallelograms (or rectangles for a right prism). The base can be a triangle, rectangle, pentagon, hexagon, or any other polygon.

Worked Example

Using the default values from the calculator: base area = 50 cm², height = 10 cm.

1. Write down the formula: V = A_b × h
2. Substitute the values: V = 50 cm² × 10 cm
3. Multiply: V = 500 cm³

The calculator shows 500.00 cm³, matching the manual calculation.

When to Use This Calculator

Use this tool when you already know the base area and the height of a prism. For example, you might have a triangular prism with a base area of 20 cm² and a height of 8 cm; enter those numbers and the volume appears instantly. This is especially handy for geometry homework, packing problems, or estimating material quantities (like concrete in a prism-shaped mold).

If you don’t know the base area, you first need to compute it from the base shape. For instance:

• Rectangular base: area = length × width
• Triangular base: area = ½ × base × height of the triangle
• Regular polygon base: area = (perimeter × apothem) / 2

How to Read the Result

The volume is always in cubic units. If your base area is in square centimeters and height in centimeters, the volume is in cubic centimeters (cm³). Similarly, if you use square meters and meters, you get cubic meters (m³). For US customary units, if the base area is in square inches and height in inches, the volume is in cubic inches (in³). Remember that 1 m³ = 1,000,000 cm³, and 1 ft³ = 1,728 in³.

Common Mistakes

• Mixing units: Ensure the base area and height are in matching units. If the base is in cm² and height in m, convert one first.
• Forgetting the height is perpendicular: For oblique prisms, the height is the perpendicular distance between the bases, not the slant length.
• Using the wrong base area: The base is the shape that is repeated, not necessarily the side the prism sits on. For a triangular prism, the base is the triangle, not the rectangle.
• Rounding too early: Keep more decimal places during intermediate steps, then round at the end.

Limits of the Formula

The formula V = A_b × h applies only to prisms, where the bases are congruent polygons and the lateral faces are parallelograms. It does not apply to cylinders (which use a circular base and a different formula, though similar in spirit), pyramids (which use ⅓ of the base area times height), or spheres. For irregular solids, you would need integration or water displacement.

Frequently Asked Questions

How do I find the base area if I don’t know it?

You need to calculate it from the base shape. For a rectangle, multiply length by width. For a triangle, use ½ × base × height of the triangle. For a regular hexagon, use the formula (3√3/2) × side². Once you have the base area, plug it into the prism volume formula.

What is the difference between a prism and a pyramid?

A prism has two identical bases and rectangular (or parallelogram) sides, so its volume is base area × height. A pyramid has one base and triangular sides that meet at a point, so its volume is ⅓ × base area × height. The ⅓ factor is a key difference.

Does the formula work for a cube?

Yes. A cube is a special prism where all faces are squares. If the side length is s, the base area is s² and the height is s, so the volume is s² × s = s³, which matches the cube volume formula.

What if the prism is oblique (slanted)?

The volume formula still works, but the height must be the perpendicular distance between the bases, not the slant length. For a right prism, the height equals the lateral edge length. For an oblique prism, you need the perpendicular height, which is shorter than the slant edge.

Can I use this calculator for a cylinder?

No, because a cylinder has a circular base, not a polygon. The volume of a cylinder is π × r² × h, where r is the radius. You can think of it as base area (πr²) times height, but the calculator here expects a base area you provide, so if you enter the circular base area, it would give the correct volume for a cylinder too, but the base area must be computed separately.

Why is the volume in cubic units?

Volume measures how much 3D space an object occupies. When you multiply three lengths (or an area by a length), you get cubic units, just as multiplying two lengths gives square units. For example, cm × cm × cm = cm³.

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in a | Base area | cm² | 50 | 0
in h | Height | cm | 10 | 0
out v | Volume | cm³ | a * h | 2