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Cuboid Volume Calculator

Find the volume of a cuboid.

How it is calculated

You enter the three edges of a rectangular box, l (length), w (width) and h (height), all in the same unit. The tool returns the volume V = l × w × h, the total surface area SA = 2(lw + lh + wh) and the space diagonal d = √(l² + w² + h²). Each value is rounded to two decimals.

All three edges must be greater than zero. Results are labelled only as units, units² and units³: if you typed centimetres, the volume is in cubic centimetres, the area in square centimetres and the diagonal in centimetres. The order of length, width and height does not change any result. The surface area counts all six faces and ignores wall thickness, so it is the outer area of the box.

Worked example

A box measures 4 by 3 by 12. Volume: 4 × 3 × 12 = 144.00 units³. Surface area: the three face pairs are 4×3 = 12, 4×12 = 48 and 3×12 = 36, so 2 × (12 + 48 + 36) = 192.00 units². Space diagonal: √(16 + 9 + 144) = √169 = 13.00 units.

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Common mistakes

  • Mixing units, for example length in metres and height in centimetres; the volume is then off by a factor of 100 or more.
  • Reading the volume as a capacity of the inside when you measured outer edges; wall thickness makes the usable inner volume smaller.
  • Adding the three edges or multiplying only two; volume needs all three, and the surface area is a different quantity measured in square units.
  • Confusing the space diagonal with the diagonal of one face: the face diagonal ignores the third edge and is always shorter.
  • Converting units after the calculation by the linear factor; cubic units scale with the cube (1 m³ = 1,000,000 cm³, not 100).

About this calculator

For a cuboid (rectangular box) with length l, width w, and height h, the volume is V = l·w·h, the total surface area is SA = 2(lw + lh + wh) — the sum of the areas of all six rectangular faces — and the space diagonal (the longest straight line that fits inside the box, corner to opposite corner) is d = √(l² + w² + h²), an extension of the Pythagorean theorem into three dimensions.

Geometry students use these formulas as a foundational 3D-measurement exercise, while shipping and logistics companies use volume calculations to determine how many boxes fit in a container or truck and to compute dimensional (volumetric) weight for freight pricing. Packaging designers use surface area to estimate material needed for a box, and carpenters, cabinet makers, and DIY furniture builders use the space diagonal to check whether a piece will fit through a doorway or stairwell during a move.

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Comments (1)

  • Editorial team

    The result comes in cubic units of whatever you typed, so pick units that match your next step. With edges in centimetres, divide the volume by 1,000 to get litres. For freight, the carrier's volumetric weight rule divides the volume by its own divisor, which varies by carrier, so check theirs rather than assuming. What are you measuring, a shipping box, a tank or a room?

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