Formula Volume Rectangular Prism & 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 the three dimensions in any consistent unit, and you get the volume in cubic units, plus the surface area as a bonus. The formula is Volume = length × width × height.

Formula

In words: the volume of a rectangular prism equals its length times its width times its height. In symbols:

V = l × w × h

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

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

Worked Example

Using the calculator defaults: length = 10 cm, width = 5 cm, height = 4 cm.

1. Multiply length × width: 10 × 5 = 50 cm² (this is the area of the base).
2. Multiply by height: 50 × 4 = 200 cm³.

So the volume is 200 cm³, which matches the calculator output. The surface area is 2 × (10×5 + 10×4 + 5×4) = 2 × (50 + 40 + 20) = 2 × 110 = 220 cm².

When to Use This Formula

Use the rectangular prism volume formula any time you need the capacity of a box-shaped object: a shipping carton, a fish tank, a room, a concrete slab, a storage container, or a rectangular pool. It is one of the most common volume calculations in construction, packaging, shipping, and everyday life.

The formula works for any rectangular prism, which is a solid with six rectangular faces. A cube is a special case where l = w = h, so the formula becomes V = s³ (side cubed).

How to Measure Correctly

For a solid object, measure the three external dimensions. For a hollow container (like a tank or a box you fill), measure the inside dimensions to get the actual capacity. If you measure the outside, you get the volume of the material plus the empty space, which overestimates what the container can hold.

When measuring, keep these points in mind:

• Use the same unit for all three dimensions. Convert first if needed (1 m = 100 cm, 1 ft = 12 in).
• Measure to the inside edges for internal capacity.
• For irregular objects, this formula does not apply; use water displacement instead.

Common Mistakes and How to Avoid Them

The most frequent error is mixing units. For example, multiplying 2 m × 50 cm × 30 cm without converting gives 3000, but of what? Convert everything to one unit first: 2 m = 200 cm, so 200 × 50 × 30 = 300,000 cm³, which is 0.3 m³.

Another common mistake is confusing volume with surface area. Volume is the space inside (cubic units); surface area is the total area of all six faces (square units). The calculator provides both, so check which one you need.

Rounding errors also creep in when you round intermediate steps. Keep full precision until the final answer, then round to a sensible number of decimal places.

Unit Conversions and Practical Context

Volume results can be expressed in many units. Here are common conversions:

• 1 cm³ = 1 milliliter (mL)
• 1,000 cm³ = 1 liter (L)
• 1 m³ = 1,000 liters
• 1 in³ = 16.387 cm³
• 1 ft³ = 28.317 liters
• 1 US gallon = 231 in³ = 3.785 L

For example, a rectangular aquarium that is 60 cm long, 30 cm wide, and 40 cm high has a volume of 60 × 30 × 40 = 72,000 cm³, which equals 72 liters. That is the water capacity if filled to the brim; in practice you leave a few centimeters of air space.

Limitations of the Formula

This formula only works for rectangular prisms. For cylinders, spheres, cones, or irregular shapes, you need different formulas. Also, if the object is not perfectly rectangular (e.g., tapered or curved sides), the volume will be approximate at best.

Another limit: the formula gives the geometric volume, not the amount of material the object can hold if it has walls. For a container, subtract the wall thickness if you need the interior volume precisely. For most everyday purposes, inside measurements are enough.

Frequently Asked Questions

How do you find the volume of a rectangular prism?

Multiply the length by the width by the height: V = l × w × h. Make sure all three dimensions are in the same unit, and the result will be in cubic units (like cm³ or ft³).

What is the difference between volume and surface area?

Volume measures the space inside the prism, in cubic units. Surface area measures the total area of all six faces, in square units. For a box 10×5×4 cm, volume is 200 cm³, surface area is 220 cm².

Can I use this formula for a cube?

Yes. A cube is a rectangular prism where all sides are equal. So V = s × s × s = s³. For a cube with side 3 cm, volume = 27 cm³.

What if my measurements are in different units?

Convert all dimensions to the same unit before multiplying. For example, if length is 2 m and width is 50 cm, convert 2 m to 200 cm, then multiply 200 × 50 × height (in cm).

How do I convert cubic centimeters to liters?

Divide by 1,000. So 200 cm³ = 0.2 liters. Conversely, multiply liters by 1,000 to get cm³.

Does the order of multiplication matter?

No. Multiplication is commutative, so l × w × h gives the same result regardless of order. However, it is often convenient to multiply the base area (l × w) first, then multiply by height.

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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 area | Surface area | cm² | 2 * (l * w + l * h + w * h) | 2