Size to Weight Calculator (Rectangular Box)

Background.

Before anything gets lifted, shipped or stacked on a floor, somebody has to know what it weighs. For an object shaped like a brick, a slab, a plate or a beam, that comes down to two facts: how much space the piece fills, and how heavy its material is per cubic metre. Two plates cut to identical sizes can still be very different loads — steel is close to three times as heavy as aluminium for the same volume.

The geometry is the easy half. A rectangular solid's volume is its length times its width times its height, and that is exact. Density is where judgement comes in. Handbook figures for metals are tight: carbon steel is usually taken as about 7,850 kg/m³ and aluminium about 2,700. Timber is looser, shifting with species and with how much water the wood still holds, and concrete depends on its aggregate and reinforcement. For loose material heaped into a box shape — sand, gravel, soil — the right figure is bulk density, which counts the air between the grains.

Size has a stronger effect than intuition suggests. Double every dimension of a block and it weighs eight times as much, which is why a part one person carries easily can need a hoist once it is scaled up.

The answer assumes a solid piece of uniform material. A box-section tube, a hollow-core door or a crate with air inside will come out heavier on paper than in reality, and no margin is added for lifting gear or structural loading; those belong to whoever plans the lift or the design.

What is size to weight calculator (rectangular box)?

Mass is the amount of matter in an object, measured in kilograms, and it is what an ordinary scale reports as weight. A rectangular cuboid is a solid with six rectangular faces meeting at right angles, so its volume is simply the product of its three edge lengths. Multiply that volume by the material's density, the mass contained in each cubic metre, and you have the mass. Water is a handy benchmark: at room temperature it is close to 1,000 kg/m³, so a cubic metre of it weighs about a tonne.

How to use this calculator.

1. 01Measure the three edges and enter them in metres. Divide millimetres by 1,000 (a 10 mm plate is 0.01 m) and multiply inches by 0.0254; it does not matter which edge you call the length.
2. 02Enter the density in kg/m³. Prefer the supplier's figure for the exact grade or species; for sand, gravel, soil or stacked goods use a bulk density, which includes the gaps.
3. 03Read the mass in kilograms and the volume in cubic metres. Multiply the kilograms by 2.20462 if you need pounds.
4. 04For something hollow, run the outer block and the empty inner space as two separate blocks and subtract the smaller mass from the larger.

The formula.

Mass = length × width × height × density, or m = L × W × H × ρ. The first three terms are the edge lengths in metres; their product is the volume in cubic metres. ρ (rho) is density in kilograms per cubic metre, and multiplying it by the volume cancels the cubic metres and leaves kilograms. No conversion constant is needed because SI units are coherent — that is the point of the BIPM's system. Every input appears to the first power, so a 10% error in any one dimension, or in density, becomes a 10% error in mass. Density usually carries the most uncertainty, because a wet beam or an unusual alloy can sit well away from the handbook value, whereas a careful measurement keeps the dimensional error small. All four values must be greater than zero; a zero or negative dimension is refused rather than producing a meaningless mass.

A worked example.

Frequently asked questions.

References& sources.

1. [1]BIPM, The International System of Units (SI Brochure), 9th ed.
2. [2]NIST Special Publication 811, SI units and conversion guidance.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.