Size to Weight Calculator (Rectangular Box)

Two things decide how much a rectangular box weighs: the space inside its outline and what the material is made of. Enter the length, the width and the height, add the density of the material, and the page returns the volume the box encloses together with the mass of a solid block that size.

Nothing in the six boxes is fixed. Clear any one of them and it is solved from the rest, which covers the three jobs this page is used for most:

• How heavy is this crate, slab or block? Enter its size and the density of the material and read the weight.
• What is this block made of? Weigh it, enter its size, and read the density; that number narrows the material down quickly.
• How big does it have to be? Enter the weight you need, let the volume be solved, then give two of the three dimensions and the third one follows.

The three dimensions can be read on different scales at the same time — a length in feet, a width in centimeters and a height in inches all enter the same multiplication — and the answer can be shown in cubic millimeters, liters, cubic yards or in micrograms up to imperial tons.

A one-liter block of concrete

A 20 cm × 10 cm × 5 cm block of a 2,400 kg/m³ material is 1,000 cm³, which is exactly 0.001 m³:

Two point four kilos for a box you can hold in one hand is a useful calibration: a full cubic meter of the same material would be 2,400 kg, and every factor of ten you shave off a dimension cuts the volume by a thousand.

The page runs two multiplications, one after the other.

where $\mathrm{V}$ is the enclosed volume, $\mathrm{L},\ \mathrm{W},\ \mathrm{H}$ are the three dimensions, $\rho$ is the density and $m$ is the mass. The volume is shared by both statements, and that is what makes the reverse directions work:

• A missing side comes from the volume and the other two: $\mathrm{L} = \mathrm{V} / (\mathrm{W} \times \mathrm{H})$, and the same for the width or the height.
• A missing volume comes from the weight and the density: $\mathrm{V} = m / \rho$.
• A missing density comes from the weight and the volume: $\rho = m / \mathrm{V}$.

Every entry is converted before it multiplies

The multiplication needs one scale, so each number is converted to a base unit first: meters for the sides, cubic meters for the volume, kilograms per cubic meter for the density and kilograms for the mass.

For example, 92 mm is multiplied as 0.092 m, and 1 cu ft is 0.028316846592 m³. The imperial factors are exact definitions rather than rounded table entries: the international foot is exactly 0.3048 m and the yard exactly 0.9144 m, which is where the cubic factors come from (NIST Guide to the SI, Appendix B). If your density is printed on a scale that is not in the menu, convert it first with the density conversion calculator.

Work in cubic feet or gallons instead of liters? The cubic feet calculator takes the same three dimensions and reads the volume out in those units.

• Measure the piece in front of you. Lumber is sold under a nominal size, and the dressed board is noticeably smaller; a sheet of material is rarely its stated thickness. The number that belongs in the boxes comes from the tape, not from the label.
• Never write 5 ft 7 in as 5.7 ft. The decimal part of a feet-and-inches measurement is inches, not tenths of a foot: $7\ \mathrm{in} = 0.583\ \mathrm{ft}$, so 5 ft 7 in is 5.583 ft and 5.7 ft is about 5 ft 8.4 in. Use the feet / inches entry and the conversion is done for you.
• Keep the density on the scale you actually have. A number copied from a table in g/cm³ and entered as kg/m³ is a thousand times too small, and the same trap sits between lb/cu in and lb/cu ft, which differ by 1,728. Check the unit menu before blaming the answer.
• Bulk materials bring their air with them. A box of loose pellets, grain or sand holds voids, so it is lighter than a solid block of the same material. Use the bulk density — the value that already includes the air — and the result matches what a scale would tell you.
• A small measurement error costs three times as much volume. Because all three sides multiply, a one percent error on each side becomes about three percent in the volume, and the weight moves with it: $1.01^3 \approx 1.030$. On a small block, measure to the nearest millimeter.
• Read a red density as a units warning. A density far above anything a real solid reaches usually means the number came from another scale. The box stays red so the digits stay visible — it is a prompt to check the number, not a hidden result.