Volume of a Prism: Formula & Calculator

This calculator works out the volume of any right prism when you enter the area of its base and its height. You get the volume in cubic units, plus the base area if you only knew the base dimensions. The formula is simply base area times height, and the worked example below shows the exact steps.

Formula

For any prism, the volume V is:

V = B × h

• V = volume (cubic units, e.g., cm³, m³, in³)
• B = area of one base (square units, e.g., cm², m², in²)
• h = height of the prism (linear units, e.g., cm, m, in) — the perpendicular distance between the two bases

This works for every prism: rectangular, triangular, pentagonal, hexagonal, or any other polygon base. The only requirement is that the two bases are identical, parallel, and the sides are parallelograms (for a right prism, the sides are rectangles).

Worked Example

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

1. Write the formula: V = B × h
2. Plug in the numbers: V = 50 cm² × 10 cm
3. Multiply: V = 500 cm³

The calculator shows 500.00 cm³, matching the manual calculation.

How to Find the Base Area

Often you don’t know the base area directly — you know the base shape’s dimensions. Here are common cases:

• Rectangular base: B = length × width
• Triangular base: B = ½ × base of triangle × height of triangle
• Regular polygon base: B = (perimeter × apothem) / 2, where the apothem is the distance from the center to the midpoint of a side
• Trapezoidal base: B = ½ × (sum of parallel sides) × height of trapezoid

For a cube (a special rectangular prism), all edges are equal, so V = side³.

Common Mistakes and Unit Mix-Ups

The most frequent error is mixing units. If the base area is in square meters and the height is in centimeters, you must convert one before multiplying. For example, convert height to meters (10 cm = 0.1 m) or base area to cm² (1 m² = 10,000 cm²).

Another mistake: confusing the height of the prism with the height of the base triangle. In a triangular prism, the triangle has its own height (used to find the base area), and the prism has a separate height (the distance between the two triangles). Both are needed, but they are different measurements.

Rounding too early can also throw off results, especially in multi-step problems. Keep full precision until the final answer, then round.

When to Use This Formula

Use the prism volume formula whenever you need the space inside a shape with two identical, parallel polygon faces. Real-world examples include:

• Concrete for a driveway slab (rectangular prism)
• Water in a fish tank (rectangular prism)
• Volume of a tent (triangular prism)
• Air in a room (rectangular prism)
• Soil in a planter box (often a trapezoidal prism)

If the shape is not a prism (e.g., a cylinder, sphere, or cone), this formula does not apply — those have their own volume formulas.

Limits of the Formula

The formula V = B × h assumes the prism is right (sides perpendicular to the bases) or at least that you use the perpendicular height, not the slant height. For an oblique prism, the height is the perpendicular distance between the bases, not the length of a slanted side. If you only know the slant height, you’ll need trigonometry to find the true height.

Also, the base must be a flat polygon. If the base is curved (like a circle), you have a cylinder, not a prism, though the volume formula is the same (V = πr²h).

Frequently Asked Questions

What is the difference between a prism and a pyramid?

A prism has two identical, parallel bases and parallelogram sides. A pyramid has one base and triangular sides that meet at a single point (apex). The volume of a pyramid is one-third of the prism volume with the same base and height: V = (1/3) × B × h.

How do I find the volume of a triangular prism?

First find the area of the triangular base: B = ½ × base of triangle × height of triangle. Then multiply by the prism’s height (the length between the two triangles). 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.

Can I use this formula for a cylinder?

Yes, the same logic applies. A cylinder is like a prism with a circular base. The base area is πr², so V = πr²h. Many textbooks treat cylinders separately, but the concept is identical.

What if my prism is tilted (oblique)?

Use the perpendicular height, not the slant height. The perpendicular height is the shortest distance between the two bases. If you only have the slant height and the angle, use trigonometry (h = slant × sin(angle)) to find it.

How do I convert volume to liters?

1 liter = 1,000 cm³ = 0.001 m³. So divide the volume in cm³ by 1,000 to get liters, or multiply the volume in m³ by 1,000. For example, 500 cm³ is 0.5 liters.

Why is the volume in cubic units?

Because you are multiplying three linear dimensions (or an area by a length). Each dimension carries a unit, so the product carries the unit cubed. If you multiply cm × cm × cm, you get cm³, which measures three-dimensional space.

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