Box Volume Calculator
A rectangular box (also called a rectangular prism or cuboid) is a three-dimensional shape with six rectangular faces. This calculator computes the volume, surface area, and space diagonal from the length, width, and height. The volume is simply the product of the three dimensions. The surface area is calculated by finding the area of each of the six faces and summing them. The space diagonal is the longest line inside the box, connecting one corner to the opposite corner through the interior. All calculations use the Pythagorean theorem for three dimensions.
Box formulas
Volume = length * width * height
Surface area = 2 * (lw + lh + wh)
Space diagonal = sqrt(l^2 + w^2 + h^2)
Example calculation
For a box with length 10, width 8, and height 6:
- Volume = 10 * 8 * 6 = 480.00 cubic units
- Surface area = 2 * (10*8 + 10*6 + 8*6) = 2 * (80 + 60 + 48) = 376.00 square units
- Space diagonal = sqrt(10^2 + 8^2 + 6^2) = sqrt(200) = 14.14 units
Box volume calculator: frequently asked questions
What is a rectangular box?
A rectangular box (also called a rectangular prism or cuboid) is a three-dimensional shape with six rectangular faces, where opposite faces are equal. All angles are right angles (90 degrees).
What is the formula for the volume of a box?
The volume of a rectangular box is the product of its length, width, and height: Volume = length * width * height, where all three dimensions must be in the same units.
What is the surface area of a box?
The surface area of a rectangular box is the sum of the areas of all six faces: Surface area = 2 * (lw + lh + wh), where l is length, w is width, and h is height.
What is the space diagonal of a box?
The space diagonal (body diagonal) is the longest line inside the box, connecting opposite corners: Diagonal = sqrt(l^2 + w^2 + h^2), where l, w, and h are the three dimensions.
What are practical applications of box volume calculations?
Box volume calculations are used for storage containers, shipping boxes, refrigerators, shipping cost estimation, and material requirements. Surface area is used for packaging, painting, and material costs.
Official sources
- Wolfram MathWorld: Rectangular Box.
- ISO 80000-2: Mathematical signs and symbols.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.