Cuboid Volume Calculator

Enter a cuboid's length, width, and height to get its volume (V = l×w×h), surface area (SA = 2(lw+lh+wh)), and space diagonal (d = √(l²+w²+h²)), plus an optional fill/material cost estimate.

Quick Facts

Volume formula
V = l × w × h
Multiply length, width, and height together.
Surface area formula
SA = 2(lw + lh + wh)
Sum of the areas of all six rectangular faces.
Space diagonal formula
d = √(l² + w² + h²)
Follows from applying the Pythagorean theorem twice.

Your Results

Calculated
Volume
-
V = l × w × h, in cubic units
Surface Area
-
SA = 2(lw + lh + wh)
Space Diagonal
-
d = √(l² + w² + h²)
Estimated Fill/Material Cost
-
Volume × cost per cubic unit

Ready

Enter length, width, height, and unit, then press Calculate.

Formula and Method for Cuboid Volume

A cuboid (rectangular box or rectangular prism) is a six-sided solid with three pairs of rectangular faces meeting at right angles. Its three dimensions — length, width, and height — can each differ, unlike a cube where all three are equal. Volume, the amount of space enclosed, is simply the product of all three dimensions: V = l × w × h. This calculator also derives the total surface area and the space diagonal from the same three measurements, plus an optional fill or material cost estimate.

How the calculation works

Enter the length, width, and height and choose the unit they are measured in. The calculator multiplies the three values to get the volume (in cubic units, such as ft³ or m³). It finds the surface area by summing the areas of all six rectangular faces — two of each l×w, l×h, and w×h pair — giving SA = 2(lw + lh + wh). It finds the space diagonal, the straight-line distance between opposite corners of the box, using d = √(l² + w² + h²): first the Pythagorean theorem gives the diagonal of the base as √(l² + w²), then applying it again with the height gives the full 3D diagonal. If you enter a cost per cubic unit, the tool multiplies it by the volume to estimate total fill or material cost.

Common mistakes

  • Confusing volume with surface area: a 10 × 6 × 4 in box has a volume of 240 in³ but a surface area of 248 in² — different units, different meanings, and it is easy to mix them up.
  • Mixing units: keep length, width, and height in one consistent unit — convert inches to feet, or centimeters to meters, before entering the values.
  • Diagonal vs. dimensions: the space diagonal is always longer than any single side; do not substitute it for length, width, or height in the volume formula.

Real-world applications

  • Shipping and storage use volume to determine box capacity and how many items fit inside a container.
  • Concrete, soil, mulch, and aquarium water fills use volume to estimate how much material is needed (converted to the supplier's unit, such as cubic yards or gallons).
  • Packaging and box manufacturing use surface area to estimate the amount of cardboard, laminate, or paint required.
  • Furniture and shipping logistics use the space diagonal to check whether an item will fit diagonally through a doorway or opening.

Frequently Asked Questions

What is the formula for the volume of a cuboid?
The volume of a cuboid (rectangular box) equals length times width times height: V = l × w × h. For example, a box that is 10 in long, 6 in wide, and 4 in tall has a volume of 10 × 6 × 4 = 240 in³.
How do I find the surface area of a cuboid?
Add the areas of all six rectangular faces: SA = 2(lw + lh + wh). A 10 × 6 × 4 in box has a surface area of 2(60 + 40 + 24) = 248 in².
How is the space diagonal of a cuboid calculated?
The space diagonal is d = √(l² + w² + h²), which follows from applying the Pythagorean theorem twice — once across the base and once up to the opposite corner. A 10 × 6 × 4 in box has a diagonal of about 12.33 in.
What is the difference between a cuboid and a cube?
A cube is a special cuboid where length, width, and height are all equal, so its volume simplifies to V = s³ and its surface area to SA = 6s². A general cuboid allows the three dimensions to differ.

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