Cuboid Calculator
Compute volume, surface area, aspect ratio, space and face diagonals of any rectangular box, or scale to a target volume.
Dimensions
Updates as you typePresets (real boxes)
Mode
How do you want to work? ?
Target volume
—
cm³
Measurements
Length (l) ?
cm
—
Width (w) ?
cm
—
Height (h) ?
cm
—
Shape
Fit check · what goes inside
volumetric upper bound| Item | Item volume | Max count | Used | Utilisation |
|---|---|---|---|---|
| Enter l, w, h to see the fit check. | ||||
Volumetric upper bound — a perfect-packing ceiling. Real packing loses 5–25% to gaps and orientation constraints, so treat the counts as "definitely fewer than this."
Formula
V
=
l · w · h
SA
=
2(lw + lh + wh)
d
=
√(l² + w² + h²)
E
=
4(l + w + h)
- V
- Volume — space enclosed by the cuboid
- SA
- Surface area — sum of the six rectangular faces (three pairs)
- l, w, h
- Length, width, height — the three independent edge lengths
- d
- Space diagonal — corner to opposite corner through the interior
- flw, flh, fwh
- Face diagonals — three different values, one per face pair
- E
- Total edge length — 4 edges of each of the three sizes
Worked example — your numbers
- l = —, w = —, h = —
- Volume = l · w · h = —
- Surface area = 2(lw + lh + wh) = —
- Space diagonal = √(l² + w² + h²) = —
- Face diagonals = —
- Total edge length = 4(l + w + h) = —
A cuboid is a cube's more general cousin — when l = w = h it collapses into a cube with all three face diagonals equal. Real boxes are almost never cubes because packing, carrying, and stacking all reward one dominant axis; "flat" shapes have high SA relative to V, which is great for heat exchange and bad for insulation.