Rectangular Prism Volume: Formula & Calculator

This calculator works out the volume of a rectangular prism (also called a cuboid or a box) when you enter its length, width, and height. You get the volume in cubic units, plus the surface area, so you can use it for anything from packing a moving box to pouring concrete for a slab.

Formula

The volume of a rectangular prism is simply the product of its three dimensions:

V = l × w × h

• V = volume (cubic meters, cubic feet, etc.)
• l = length (meters, feet, etc.)
• w = width (same unit as length)
• h = height (same unit as length)

All three dimensions must be in the same unit before multiplying. If you mix meters and centimeters, the answer will be off by a factor of 100 or more.

Worked Example

Using the default values from the calculator above: 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 the base area by height: 15 × 2 = 30 m³.

The calculator gives the same result: 30.00 m³. The surface area is 2 × (5×3 + 5×2 + 3×2) = 2 × (15 + 10 + 6) = 2 × 31 = 62 m².

When to Use This Calculator

Rectangular prism volume problems show up in everyday tasks and in school math. Common situations include:

• Moving and storage: figuring out how many boxes fit in a truck or a storage unit.
• Construction: estimating concrete for a footing or a patio slab.
• Aquariums and pools: calculating water volume for a tank with a rectangular base.
• Shipping: determining cubic volume for freight charges (often called CBM, cubic meters).
• Homework: solving geometry problems that ask for volume when given three side lengths.

The same formula applies to any shape that has six rectangular faces and right angles – a standard box. If the shape has slanted sides or non-rectangular faces, you need a different formula.

Common Mistakes and How to Avoid Them

The most frequent error in rectangular prism volume problems is mixing units. For example, if a box is 2 m long, 50 cm wide, and 30 cm high, you cannot multiply 2 × 50 × 30 directly. Convert everything to one unit first:

• 50 cm = 0.5 m
• 30 cm = 0.3 m
• Volume = 2 × 0.5 × 0.3 = 0.3 m³

Another common mistake is confusing volume with surface area. Volume is the space inside, measured in cubic units (m³, ft³). Surface area is the total area of all six faces, measured in square units (m², ft²). The calculator above gives both, so you can see the difference.

Rounding too early can also cause errors. If you compute intermediate steps, keep full precision until the end. For example, if a dimension is 0.333 m, do not round it to 0.3 before multiplying.

How to Read the Result

The volume tells you how much space the prism occupies. For a shipping box, that number helps you estimate freight costs or whether it fits in a car. For a concrete slab, the volume tells you how many cubic yards or cubic meters to order.

Remember that volume is always in cubic units. If you enter dimensions in meters, the volume is cubic meters (m³). If you enter feet, the volume is cubic feet (ft³). To convert between common units:

• 1 m³ = 35.3147 ft³
• 1 ft³ = 0.0283168 m³
• 1 liter = 0.001 m³ (so 1 m³ = 1000 liters)
• 1 gallon (US) = 0.00378541 m³

If you need the volume in liters or gallons, multiply the cubic meters by 1000 or by 264.172, respectively.

Limits of the Formula

The formula V = l × w × h works only for right rectangular prisms – boxes where all faces meet at 90° angles. If the shape is a cube, it is a special case where l = w = h, so V = side³. If the shape is a rectangular pyramid, a cylinder, or an irregular solid, this formula does not apply.

Also, the formula assumes the prism is solid and completely filled. If you are calculating the volume of a hollow container, you need the inner dimensions, not the outer ones. For example, a wooden box with 2 cm thick walls has a smaller internal volume than the external dimensions suggest.

Frequently Asked Questions

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

They are the same shape. A cuboid is a convex polyhedron with six rectangular faces. A rectangular prism is the same thing, often used in school math. A cube is a special cuboid where all six faces are squares.

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

You cannot determine the volume from surface area alone because many different rectangular prisms can have the same surface area. For example, a 1×1×10 box has surface area 42 and volume 10, while a 2×3×3 box also has surface area 42 but volume 18. You need at least two dimensions, or one dimension and the surface area, to solve for the third.

What if the box is not a perfect rectangle?

If the faces are not rectangles or the angles are not 90°, the shape is not a rectangular prism. For a triangular prism, use the formula V = (1/2 × base × height of triangle) × length. For a cylinder, use V = πr²h. For irregular shapes, you may need to break them into simpler solids or use water displacement.

Can I use this calculator for a swimming pool?

Yes, if the pool has a rectangular base and vertical walls. Enter the average depth if the bottom slopes. For a pool that is 10 m long, 5 m wide, with an average depth of 1.5 m, the volume is 75 m³, which is 75,000 liters. If the pool has a sloped bottom, use the average depth for a good estimate.

How do I convert volume to weight?

Multiply the volume by the density of the material. For water, density is 1000 kg/m³, so 1 m³ of water weighs 1000 kg (about 2205 lb). For concrete, density is about 2400 kg/m³. For soil or gravel, it varies. Always check the specific density for the material you are using.

Why does the calculator show surface area as well?

Surface area is often needed for tasks like painting a box, wrapping it, or ordering sheet material. The calculator gives both values so you do not have to run a second calculation. The surface area is the sum of the areas of all six faces: 2lw + 2lh + 2wh.

Related

• Minutes to Hours: Quick Conversion & Formula
• Minutes to Hours Calculator in Excel
• Minutes to Hours Calculator: Online Conversion

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
out sa | Surface area | m² | 2 * (l * w + l * h + w * h) | 2