About

A cuboid (rectangular parallelepiped) is defined by three independent edge lengths: l, w, and h. Getting the volume wrong by even 1cm on each dimension of a 2m shipping crate compounds to a cubic error that can exceed 0.12m³ - enough to mis-quote freight costs or under-order concrete fill. This calculator computes volume V, total surface area S, the space diagonal d_s, and all three face diagonals using exact arithmetic. Results are converted across 12 unit systems simultaneously.

The tool assumes a perfect right-angled cuboid. Real-world objects with draft angles, fillets, or thermal expansion require correction factors not included here. For poured concrete or granular fill, multiply the computed volume by a compaction factor (typically 1.05 - 1.10) to account for material settlement.

Formulas

The volume of a cuboid is the product of its three orthogonal edge lengths:

V = l × w × h

The total surface area is the sum of all six rectangular faces:

S = 2(lw + lh + wh)

The space diagonal connects two opposite vertices through the interior:

d_s = √l² + w² + h²

Each face diagonal crosses one rectangular face:

d_lw = √l² + w² , d_lh = √l² + h² , d_wh = √w² + h²

Where l = length, w = width, h = height, V = volume, S = surface area, d_s = space diagonal, and d_lw, d_lh, d_wh = face diagonals of the respective planes.

Reference Data

Object	Length	Width	Height	Approx. Volume
Standard Brick	215 mm	102.5 mm	65 mm	1,432 cm³
Shoebox	35 cm	20 cm	12 cm	8,400 cm³
20 ft Shipping Container	5.9 m	2.35 m	2.39 m	33.1 m³
40 ft Shipping Container	12.03 m	2.35 m	2.39 m	67.6 m³
Standard Pallet (EUR)	1.2 m	0.8 m	0.144 m	0.138 m³
iPhone 15 Box	16.4 cm	8.2 cm	4.5 cm	605 cm³
Swimming Pool (Residential)	10 m	4 m	1.5 m	60 m³
Concrete Foundation Slab	12 m	8 m	0.3 m	28.8 m³
King Size Mattress	203 cm	193 cm	25 cm	979,475 cm³
Rubik's Cube	5.7 cm	5.7 cm	5.7 cm	185.2 cm³
Room (Average)	5 m	4 m	2.7 m	54 m³
Filing Cabinet Drawer	47 cm	62 cm	27 cm	78,678 cm³
Refrigerator (Internal)	55 cm	50 cm	130 cm	357,500 cm³
Water Tank (1000L IBC)	1.2 m	1.0 m	1.16 m	1.392 m³
A4 Paper Ream (500 sheets)	29.7 cm	21 cm	5 cm	3,118.5 cm³

Frequently Asked Questions

Each edge measurement carries its own tolerance. For a cuboid with edges of approximately 1 m, rounding each to the nearest centimeter (±0.005 m) produces a worst-case volume error of about ±0.015 m³ - roughly 15 litres. For concrete pours or liquid tanks, always round dimensions up to the next practical increment and apply a 5-10% overfill factor.

There is no geometric difference. A cuboid, rectangular parallelepiped, and rectangular prism all denote the same solid: six rectangular faces meeting at right angles. A cube is the special case where all three edges are equal (l = w = h).

One cubic metre equals exactly 1,000 litres. One US liquid gallon equals 3.785411784 litres, so 1 m³ ≈ 264.172 US gallons. This calculator displays converted results in multiple unit systems simultaneously.

The space diagonal is the longest straight line that fits inside the cuboid. It determines whether a rigid rod, pipe, or diagonal brace can physically fit inside a box or room. For packaging, the space diagonal of the item must be less than or equal to the space diagonal of the container.

JavaScript uses IEEE 754 double-precision floats, providing approximately 15-17 significant decimal digits. This is sufficient for dimensions ranging from sub-millimetre (e.g., microchip packages) to hundreds of kilometres (theoretical). Beyond 10¹⁵ in any unit, floating-point precision begins to degrade.

Subtract twice the wall thickness from each external dimension before computing volume. For a box with external dimensions 100 × 60 × 40 cm and 2 cm wall thickness, internal volume is (100 − 4) × (60 − 4) × (40 − 4) = 96 × 56 × 36 = 193,536 cm³, versus the external volume of 240,000 cm³ - a 19.4% reduction.