Rectangular Prism Volume: Formula & Calculator

This calculator works out the volume of a rectangular prism (also called a cuboid or a box) from its length, width, and height. Enter those three dimensions in any consistent unit, and you get the volume in cubic units, plus the surface area. The volume is simply length × width × height.

Formula

The volume of a rectangular prism is given by:

V = l × w × h

Where:

• V = volume (cubic units: m³, cm³, ft³, in³, etc.)
• l = length of the base (same linear unit as w and h)
• w = width of the base (same unit)
• h = height (perpendicular distance between the two bases, same unit)

All three dimensions must be in the same unit before multiplying. If you mix meters and centimeters, the result is meaningless. The surface area formula, shown as a second output, is A = 2(lw + lh + wh).

Worked Example

Using the default values: length = 5 m, width = 3 m, height = 2 m.

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

So the volume is 30 cubic meters. The surface area is 2 × (5×3 + 5×2 + 3×2) = 2 × (15 + 10 + 6) = 2 × 31 = 62 m².

What Is a Rectangular Prism?

A rectangular prism is a three-dimensional shape with six faces, all of which are rectangles. Opposite faces are parallel and identical. It has 12 edges and 8 vertices. When all six faces are squares, it is a cube, a special case where l = w = h. Everyday objects shaped like this include bricks, shoeboxes, rooms, shipping containers, and fish tanks. The term “cuboid” is often used in British English, and “rectangular parallelepiped” is the formal geometric name.

When to Use This Calculation

You need the volume of a rectangular prism whenever you want to know how much space it occupies or how much it can hold. Common situations:

• Filling a rectangular aquarium or pool – volume tells you how much water it holds.
• Ordering concrete or soil for a rectangular garden bed or foundation.
• Calculating the capacity of a box or shipping crate.
• Estimating the volume of a room for heating, cooling, or ventilation.
• Converting between volume and weight when density is known (e.g., water = 1000 kg/m³).

How to Measure the Dimensions

Measure the three internal dimensions if you are calculating capacity, or the external dimensions if you are calculating the volume of the object itself. For a box with walls, the internal volume (what it holds) is slightly smaller than the external volume. Use a tape measure or ruler, and ensure the object has straight, perpendicular edges – if the shape is tilted or warped, the formula still works as long as you measure the perpendicular height, not the slanted edge.

Common Mistakes and How to Avoid Them

• Mixing units: Always convert all dimensions to the same unit. For example, 1 m × 50 cm × 20 cm must be either 1 × 0.5 × 0.2 = 0.1 m³ or 100 × 50 × 20 = 100,000 cm³.
• Forgetting that volume is cubic: A result like 30 m³ is not the same as 30 m². Volume is three-dimensional; area is two-dimensional.
• Using the wrong height: The height must be the perpendicular distance between the two bases, not the length of a slanted edge.
• Confusing volume with capacity: The volume of the material of a hollow box is external volume minus internal volume. For a simple box, the capacity is the internal volume.

Unit Conversions and Practical Context

Volume results come in cubic units. Common conversions:

• 1 m³ = 1,000 liters = 1,000,000 cm³
• 1 ft³ = 1,728 in³ ≈ 28.317 liters
• 1 gallon (US) = 231 in³ ≈ 3.785 liters
• 1 gallon (UK) ≈ 4.546 liters

For example, a fish tank 60 cm long, 30 cm wide, and 40 cm high has a volume of 60 × 30 × 40 = 72,000 cm³ = 72 liters. If you are filling it, you need about 72 liters of water, but the actual water volume will be slightly less because of gravel, decorations, and the glass thickness.

Limitations of the Formula

The formula V = l × w × h applies only to perfect rectangular prisms. If the shape has rounded corners, tapered sides, or irregular surfaces, the formula overestimates the volume. For a cylinder, use πr²h; for a sphere, use (4/3)πr³. For a pyramid, use (1/3) × base area × height. The rectangular prism formula is the simplest volume calculation, but it is precise only for true right-angled boxes.

Frequently Asked Questions

How do I find the volume of a rectangular prism if I only know the surface area?

You cannot determine the volume from surface area alone. Many different length, width, and height combinations can produce the same surface area but different volumes. You need at least two dimensions and the surface area, or all three dimensions.

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

A rectangular prism has two rectangular bases and rectangular side faces, so it looks like a box. A rectangular pyramid has one rectangular base and four triangular faces that meet at a single point (apex). The volume of a pyramid is one-third of the base area times the height.

Can I use this formula for a cube?

Yes. A cube is a rectangular prism where length = width = height. So the formula becomes V = s³, where s is the side length. For example, a cube with side 4 cm has volume 64 cm³.

How do I convert cubic meters to liters?

Multiply by 1,000. One cubic meter equals 1,000 liters. So a volume of 0.5 m³ is 500 liters. This is handy for aquarium or pool volumes.

What if my dimensions are in inches and I want gallons?

First calculate the volume in cubic inches (l × w × h), then divide by 231 (the number of cubic inches in a US gallon). For example, a box 12 in × 10 in × 8 in = 960 in³ ÷ 231 ≈ 4.16 gallons.

Does the order of multiplication matter?

No. Multiplication is commutative, so l × w × h gives the same result as w × h × l. Just make sure all three dimensions are in the same unit.

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in l | Length | m | 5 | 0
in w | Width | m | 3 | 0
in h | Height | m | 2 | 0
out volume | Volume | m³ | l * w * h | 2
out area | Surface area | m² | 2 * (l * w + l * h + w * h) | 2