Right Rectangular Prism Volume Formula & Calculator

This calculator works out the volume of a right rectangular prism (a box) from its length, width, and height. You enter the three dimensions in any order of length, width, and height, and it returns the volume in cubic units. The formula is simply Volume = length × width × height, and the calculator below applies it instantly.

Formula

The volume V of a right rectangular prism is given by:

V = l × w × h

• V = volume (cubic units, e.g., m³, cm³, ft³)
• l = length (linear unit, e.g., m, cm, ft)
• w = width (same linear unit as length)
• h = height (same linear unit as length)

All three dimensions must be in the same unit before multiplying. If you mix meters and centimeters, the result will be meaningless.

Worked Example

Using the calculator defaults: length = 5 m, width = 3 m, height = 2 m.

1. Multiply length by width: 5 × 3 = 15 m² (this is the area of the base).
2. Multiply the base area by height: 15 × 2 = 30 m³.

The volume is 30 cubic meters. The calculator shows the same result: 30.00 m³.

What Is a Right Rectangular Prism?

A right rectangular prism is a three-dimensional shape with six rectangular faces, where all adjacent faces meet at 90° angles (right angles). It is also called a rectangular box, a cuboid, or a rectangular parallelepiped. Everyday objects like a shoebox, a brick, a fish tank, or a shipping container are right rectangular prisms. The key feature is that every corner is a right angle, and opposite faces are identical and parallel.

If the length, width, and height are all equal, the prism is a cube, and the formula reduces to V = side³.

How to Use the Volume Formula

To apply the formula correctly:

1. Measure the length, width, and height of the prism. Use the same unit for all three measurements.
2. Multiply the three numbers together. The order does not matter; multiplication is commutative.
3. The result is the volume in cubic units. For example, if you measured in inches, the volume is in cubic inches (in³). If you measured in centimeters, it is in cubic centimeters (cm³).

For real-world objects, measure the internal dimensions if you need the capacity (e.g., how much water a tank holds) and external dimensions if you need the space the object occupies.

Common Mistakes and Misconceptions

• Mixing units: Multiplying 2 m × 30 cm × 5 m gives a wrong number. Convert all to the same unit first: 30 cm = 0.3 m, then 2 × 0.3 × 5 = 3 m³.
• Confusing volume with surface area: Volume is the space inside (cubic units), while surface area is the total area of all faces (square units). For a 5×3×2 m prism, volume is 30 m³, but surface area is 2(5×3 + 5×2 + 3×2) = 62 m².
• Using the diagonal instead of height: The formula uses the perpendicular height, not the diagonal of the prism. If you only know the space diagonal, you cannot find the volume without additional information.
• Forgetting to cube the unit: When you multiply three linear measurements, the unit becomes cubed. Write the unit correctly (e.g., m³, not m).

When to Use This Formula

Use the right rectangular prism volume formula whenever you need to find the capacity or space inside a box-shaped object. Common applications include:

• Calculating the volume of a shipping box to estimate shipping costs (though carriers often use dimensional weight).
• Determining how much water a rectangular aquarium or pool holds.
• Finding the amount of concrete needed for a rectangular slab or footing.
• Calculating the volume of a room for heating/cooling or air circulation.
• Estimating the capacity of a storage container or a truck bed.

The formula is exact for any right rectangular prism, regardless of size. It does not apply to cylinders, spheres, or irregular shapes.

Units and Conversions

Volume is always expressed in cubic units. If you measure in the metric system, common units are cubic meters (m³), cubic centimeters (cm³), and liters (1 L = 1000 cm³). In the US customary system, common units are cubic feet (ft³), cubic inches (in³), and gallons (1 US gallon = 231 in³).

To convert between units, convert each linear dimension to the target unit before multiplying, or convert the final volume using a conversion factor. For example, to convert cubic feet to cubic yards, divide by 27 (since 1 yard = 3 feet, so 1 yd³ = 27 ft³).

Frequently Asked Questions

What is the difference between a right rectangular prism and a rectangular prism?

All rectangular prisms have six rectangular faces. “Right” means all lateral edges are perpendicular to the base, so all faces meet at 90° angles. A non-right (oblique) rectangular prism would have slanted sides, but in practice, the term “rectangular prism” almost always refers to the right version. The volume formula for an oblique prism is still base area × height, where height is the perpendicular distance between bases.

Can I use the formula if the prism is not a cube?

Yes, the formula V = l × w × h works for any right rectangular prism, including cubes (where l = w = h). For a cube, you can also use V = side³, which is just a special case.

How do I find the volume if I only know the surface area?

You cannot determine the volume from surface area alone. Different prisms with the same surface area can have different volumes. For example, a 1×1×10 prism has surface area 42 and volume 10, while a 2×2×4 prism has surface area 40 and volume 16. You need at least two independent dimensions (or one dimension plus a relationship) to find the volume.

What if the prism is tilted or slanted?

If the prism is oblique (slanted), the formula V = base area × height still works, but the height is the perpendicular distance between the two bases, not the length of a slanted edge. For a right prism, the height equals the length of the vertical edge, so it is simpler.

How do I convert volume to liters or gallons?

Use these conversions: 1 m³ = 1000 liters; 1 cm³ = 0.001 liters; 1 ft³ = 7.48052 US gallons; 1 in³ = 0.004329 US gallons. For example, a 30 m³ tank holds 30,000 liters. For a 5×3×2 ft tank, volume is 30 ft³, which is about 224.4 US gallons.

Why is the volume in cubic units?

Volume measures three-dimensional space. When you multiply three lengths, each with a unit, the unit is multiplied three times, giving a cubed unit (e.g., m × m × m = m³). This reflects that you are counting how many unit cubes fit inside the shape.

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in l | Length | m | 5 | 0
in w | Width | m | 3 | 0
in h | Height | m | 2 | 0
out V | Volume | m³ | l * w * h | 2