Volume of Rectangular Prism: 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 (like cm³, m³, or in³) instantly, along with the surface area. The formula is simple: multiply the three dimensions together.

Formula

The volume of a rectangular prism is found by multiplying its length, width, and height.

V = l × w × h

• V = volume (cubic units: cm³, m³, in³, ft³, etc.)
• l = length (units: cm, m, in, ft, etc.)
• w = width (same unit as length)
• h = height (same unit as length)

The order of multiplication doesn’t matter; you get the same result no matter which dimension you call length, width, or height. The unit of volume is always the cube of the unit you measure with. If you measure in meters, volume is in cubic meters (m³).

Worked Example

Using the default values from the calculator above (length = 10 cm, width = 5 cm, height = 4 cm):

1. Write down the formula: V = l × w × h
2. Plug in the numbers: V = 10 × 5 × 4
3. Multiply length × width first: 10 × 5 = 50
4. Multiply the result by height: 50 × 4 = 200

The volume is 200 cm³. The calculator also shows the surface area: 2 × (10×5 + 10×4 + 5×4) = 2 × (50 + 40 + 20) = 2 × 110 = 220 cm². The cube of the unit (cm³) tells you it’s a volume, not an area.

When to Use This Calculator

You need the volume of a rectangular prism whenever you’re dealing with a box-shaped object and you need to know how much it can hold or how much space it takes up. Common real-world situations include:

• Finding the capacity of a fish tank, shipping box, or storage container.
• Calculating how much concrete, soil, or water fills a rectangular space.
• Estimating the volume of a room for heating, cooling, or sound calculations.
• Checking the size of a package against shipping limits.

If the object isn’t a perfect rectangular prism (e.g., a cylinder or an irregular shape), this formula doesn’t apply directly. For a cylinder, you’d use πr²h; for an irregular shape, you might use water displacement.

How to Read the Result

The result is in cubic units, which represent three-dimensional space. For example:

• If you entered centimeters, the volume is in cubic centimeters (cm³). 1 cm³ is the volume of a small cube that is 1 cm on each side.
• If you entered meters, the volume is in cubic meters (m³). 1 m³ is roughly the volume of a standard washing machine.
• If you entered inches, the volume is in cubic inches (in³). 1 in³ is about the volume of a large dice.

To convert to liters (a common need for aquariums), remember that 1 liter = 1,000 cm³. So a 200 cm³ box holds 0.2 liters. For larger volumes, 1 m³ = 1,000 liters.

If you need the volume in a different unit than the one you measured, convert the measurements to the target unit first, then multiply. For instance, to get cubic feet from inches, convert inches to feet (divide by 12) before multiplying.

Common Mistakes and How to Avoid Them

The most frequent error is mixing units. If you measure length in meters but width in centimeters, the result is meaningless. Always convert all three dimensions to the same unit before multiplying.

Another common mistake is confusing volume with surface area. Volume is the space inside (cubic units), while surface area is the total area of all six faces (square units). This calculator gives both, so make sure you read the correct one.

Rounding too early can also cause errors. If you round each dimension to the nearest whole number before multiplying, your result may be off by more than you expect. It’s better to keep full precision until the final step.

Forgetting that the order of dimensions doesn’t matter is not a mistake, but some people worry they’ve entered the wrong numbers. If you swap length and width, the volume stays the same.

Limits of the Formula

The formula V = l × w × h only works for perfect rectangular prisms – objects with six rectangular faces and all right angles. If the shape has slanted sides (like a pyramid or a wedge), or curved surfaces, this formula will overestimate or underestimate the true volume.

Also, the formula assumes the object is solid, not hollow. If you’re calculating the volume of material needed to make a hollow box (like a glass aquarium), you need to subtract the inner volume from the outer volume, which requires knowing the wall thickness.

For very large or very small objects, the same formula works, but you need to be careful with units. For example, the volume of a room in cubic meters is straightforward, but the volume of a grain of sand in cubic millimeters is tiny – you might want to use scientific notation or a smaller unit.

Frequently Asked Questions

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

You can’t determine the volume from surface area alone. Many different rectangular prisms can have the same surface area but different volumes. For example, a cube with side 2 has surface area 24 and volume 8, while a box with dimensions 1×2×3.33 also has surface area about 24 but a different volume. You need at least one more piece of information, such as the ratio of the sides or one dimension.

What’s the difference between a rectangular prism and a cuboid?

They are the same thing. A cuboid is a special type of rectangular prism where all faces are rectangles. In some countries, “cuboid” is the standard term, while in others “rectangular prism” is more common. Both refer to a 3D shape with six rectangular faces.

Can I use this calculator for a cube?

Yes. A cube is a rectangular prism where all three dimensions are equal. If you enter the same number for length, width, and height, the calculator will give you the volume (side³) and surface area (6 × side²).

How do I convert cubic centimeters to liters?

Divide the volume in cubic centimeters by 1,000. For example, 200 cm³ ÷ 1,000 = 0.2 liters. This is useful for aquariums or any liquid container. Conversely, multiply liters by 1,000 to get cubic centimeters.

What if my box has different units for each side?

Convert all measurements to the same unit first. For instance, if length is in meters and width is in centimeters, convert the width to meters (divide by 100) or the length to centimeters (multiply by 100) before multiplying. The calculator assumes all inputs are in the same unit, so you must do the conversion yourself.

Why is the volume in cubic units, not square units?

Because volume measures three-dimensional space. When you multiply three lengths (each with one dimension), you get a unit with three dimensions – hence cubic. Square units (like cm²) measure area, which is two-dimensional. If you accidentally use square units for volume, you’re measuring the wrong thing.

Related

• Varas to Acres: Land Conversion Explained
• Window Sill Slope Angle: Why 5 Degrees?
• Buffer Density Calculator: Formula & How to Use

in l | Length | cm | 10 | 0
in w | Width | cm | 5 | 0
in h | Height | cm | 4 | 0
out volume | Volume | cm³ | l * w * h | 2
out surface | Surface area | cm² | 2 * (l * w + l * h + w * h) | 2