THE NUMORIX GUIDE
How to use the Rectangular Prism Calculator
Last reviewed September 14, 2026
What this calculator does
For length L, width W, and height H, volume = LWH, surface area = 2(LW+LH+WH), and space diagonal = sqrt(L^2+W^2+H^2).
Formula and method
For length L, width W, and height H, volume = LWH, surface area = 2(LW+LH+WH), and space diagonal = sqrt(L^2+W^2+H^2).
Variables and inputs
Length, width, and height default to 3, 4, and 5. Each is a positive length in a common unit.
Worked example
For 3 by 4 by 5: volume = 3*4*5 = 60 cubic units; surface area = 2(12+15+20) = 94 square units; diagonal = sqrt(9+16+25) = sqrt(50) = 7.0711 units.
How to interpret the result
The volume fills the box, surface area covers all six faces, and the space diagonal connects opposite corners.
Common mistakes to avoid
Do not omit the factor of two in surface area, and do not add dimensions for the diagonal without squaring them.
Assumptions and limitations
The formulas assume a true rectangular box with right angles and uniform dimensions. Real packages may have rounded corners or wall thickness.
Practical use and checks
Use the Rectangular Prism Calculator for boxes, packages, rooms with height, or other right-angled solids. Enter length 3, width 4, and height 5 as a check; volume should be 60 cubic units, surface area 94 square units, and space diagonal about 7.0711 units. Surface area is twice the sum of the three distinct face products: 3 x 4, 3 x 5, and 4 x 5. The diagonal check is the three-dimensional Pythagorean theorem, so dimensions must be squared before they are combined. Use inside dimensions for capacity and outside dimensions for shipping or material coverage, and keep that choice consistent. A box with a missing lid, an open-top tank, or a cutout needs a modified surface-area calculation rather than the full six-face result. The model assumes straight edges, right angles, uniform dimensions, and no wall thickness. It does not calculate packing efficiency, corner radii, seams, doors, or reinforcement. If a package is close to a size limit, do not rely on rounded output; use measured tolerances and the carrier's dimensional rules. An irregular room can be split into rectangular regions for area, but its volume may require a similar decomposition by height.