Rectangular Prism Volume Calculator — Volume & Surface Area
Enter the length, width and height of a rectangular prism (box) to find its volume, surface areas, space diagonal and base perimeter instantly.
units
units
units
V = l × w × h
- 1
Base area
l × w = 10 × 6 = 60 - 2
Volume
base area × h = 60 × 4 = 240
How does this calculator work?
For a rectangular prism with length l, width w and height h: Volume = l × w × h, Total surface area = 2(lw + lh + wh), Space diagonal = √(l² + w² + h²). Enter all three dimensions in the same unit — the result is in that unit cubed.
Formula
How this is calculated
A rectangular prism (also called a cuboid or box) is a three-dimensional solid with six rectangular faces, twelve edges and eight vertices. It is completely described by three mutually perpendicular edge lengths — length l, width w and height h — all in the same unit.
Volume is l × w × h: the number of unit cubes that fit inside. Total surface area sums all six faces — two l×w (top and bottom), two l×h (front and back) and two w×h (left and right) — giving SA = 2(lw + lh + wh). Lateral surface area covers only the four side faces, excluding top and bottom: 2(l + w) × h, useful for estimating paint or wall covering needed when the floor and ceiling are excluded.
The space diagonal is the longest straight line through the interior, joining two opposite corners: d = √(l² + w² + h²). This follows from applying Pythagoras twice in three dimensions — first across the base diagonal √(l² + w²), then treating that as one leg and h as the other. All formulas are exact for a perfect right-angle box and require no approximation.
Frequently asked questions
They are all the same shape — a solid with six rectangular faces and all right angles. "Rectangular prism" is the preferred geometry term, "cuboid" is common in UK school curricula, and "box" is the everyday name. A cube is a special rectangular prism where l = w = h.
Enter all three dimensions in the same unit (feet, metres or centimetres). The volume will automatically be in cubic feet, cubic metres or cubic centimetres respectively. If your measurements are in mixed units, convert them to a common unit first.
The space diagonal d = √(l² + w² + h²) is the longest straight line that fits inside a rectangular prism, running corner-to-corner through the interior. It is useful for checking whether an object will fit inside a box when oriented diagonally — for example, fitting a long rod or a TV screen into a shipping carton.
Also known as
TG we-Calculate Editorial Team. (2026). Rectangular Prism Volume Calculator — Volume & Surface Area [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rectangular-prism-volume-calculator
TG we-Calculate Editorial Team. "Rectangular Prism Volume Calculator — Volume & Surface Area." TG we-Calculate. 2026. https://we-calculate.com/calculator/rectangular-prism-volume-calculator.
TG we-Calculate Editorial Team, "Rectangular Prism Volume Calculator — Volume & Surface Area," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rectangular-prism-volume-calculator
@misc{wecalculate_rectangular_prism_volume_calculator, title = {Rectangular Prism Volume Calculator — Volume & Surface Area}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rectangular-prism-volume-calculator}}, year = {2026}, note = {TG we-Calculate} }
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