Weight from shape and density, hollow sections done properly, plus a density finder
Mass is volume times density, and the errors live in both halves. This calculator handles the volume half with real shapes (plate and box, solid round bar, hollow tube computed as outer minus inner, never as a solid, and sphere), a quantity multiplier, and the density half with a material table whose value you can override when your alloy, timber moisture or concrete mix differs from the book figure, which it often does. A second mode runs the equation backwards: weigh a sample, measure its volume, and read its density with the closest listed material named as a rough identification only.
Disclaimer: This calculator gives estimates for general information only. It is not financial, medical or other professional advice. Lifting, shipping and structural decisions need verified weights; weigh safety-critical items on a scale.
What this calculator does
Weight mode computes the piece’s volume from the chosen shape, multiplies by the working density (the material preset, or your override), and reports volume, per-piece mass and the total for the quantity, in kilograms and pounds. The tube shape subtracts the bore before multiplying, which is the whole point of the brief’s instruction to compute hollow sections correctly: a tube weighed as a solid bar of its outer diameter is overweight on paper by exactly the missing core, easily 30 to 50 percent on thin walls. Density mode inverts the same identity and adds a cautious material hint from the built-in table, labelled as the closest listed neighbour rather than an identification, because density alone cannot tell alloys apart.
How to use it
- Density is an assumption with a name. The results print the density used. Steels cluster tightly; timbers swing with moisture (the table is dry timber; green oak can run 30 percent heavier), and concrete varies with aggregate and reinforcement, so override whenever a mill certificate, supplier sheet or sample weighing gives you a real figure.
- Nominal versus actual dimensions. Plate is sold by nominal thickness and delivered within tolerance; bar diameters likewise. For shipping estimates the nominal figures serve; for a lift plan, measure.
- The displacement method for the density mode. Submerge the sample in a measuring jug and read the rise: that volume, with a scale weight, identifies a mystery metal far better than colour or magnetism alone.
- Quantity is a multiplier, not a packing model. Totals exclude packaging, pallets, weld metal and coatings; add them explicitly when the total drives a freight or lifting decision.
The formulas
- Mass = volume × density. Plate volume = L × W × T. Bar volume = π/4 × d² × L. Tube volume = π/4 × (OD² – ID²) × L. Sphere volume = π/6 × d³.
- Density (finder) = mass / volume, reported in kg/m³ and g/cm³.
Worked examples
The steel plate. 1,000 × 500 × 10 mm in mild steel: volume 0.005 m³, mass 39.25 kg (86.53 lb). The plate most people guess at “about twenty kilos” is a two-person lift, which is the practical value of doing this arithmetic before the van is loaded.
The tube, honestly hollow. 50 mm outside, 42 mm inside, 2 m long, steel: metal volume 0.00116 m³, mass 9.08 kg. Computed as a solid 50 mm bar it would claim 30.83 kg, an overstatement of 21.75 kg or about 240 percent, printed here as the standing warning about why the hollow formula exists.
The mystery sample. A metal piece weighing 250 g displacing 32 cm³ has density 7.81 g/cm³, nearest in the table to the steels: a plausible identification, offered as a starting point for a spark test or a certificate, not as proof of grade.
Reading your results
Read the volume as carefully as the mass: it is the figure that exposes input errors (a misplaced decimal shows up as a swimming pool or a thimble). Read totals against the decision they feed: courier pricing bands, axle limits, rigging capacities, each with thresholds a small overrun crosses expensively. And read the stated density as part of the result: a weight quoted without its density assumption cannot be checked, scaled or defended.
Limitations
- Table densities are typical, not certified. Alloy grades, timber moisture, concrete mixes and composites all move real density; the override field and a sample weighing beat any table, including this one.
- Simple shapes only. Castings, forgings and assemblies need decomposition into simple volumes (or CAD mass properties); adding the pieces’ results here is the manual version of that method.
- Identification by density is indicative. Steels, cast iron and some brasses crowd together; density narrows the field, it does not close the case.
- Weight is not load capacity. Knowing a beam’s mass says nothing about what it can carry; the Beam and Spring and Stress tools address stress, and structural adequacy needs proper design.
Frequently asked questions
Why is my real piece heavier than the calculation?
Work the suspects in order: dimensions at the top of tolerance (plate thickness especially), density higher than the table value (a different alloy, wetter timber, reinforced concrete), additions the geometry omitted (welds, fasteners, coatings, attached hardware), and, for tubes, a wall thicker than specified. A persistent few percent is normal tolerance; a persistent thirty percent is a wrong input, and weighing a known sample backwards through the density mode finds which one.
How do I weigh an awkward shape?
Decompose it: every complex solid is a sum and difference of the simple shapes here (a flanged pipe is a tube plus two discs; a bracket is plates minus holes). Compute each piece, let the quantity and totals do the adding, and sanity-check the volume at the end against a bounding box: the true volume must be smaller than the box that contains it, a check that catches most geometry mistakes.
Does temperature change the answer?
Slightly, and usually negligibly: materials expand as they warm, so density falls a fraction of a percent over ordinary temperature ranges, far inside dimension and density tolerances for workshop purposes. Moisture in timber and porous materials is the environmental variable that actually matters, which is why the timber entries are labelled dry and the override field exists.
Kilograms or pounds: which mass does the page report?
Both, kilograms first with pounds alongside, because drawings, suppliers and freight documents arrive in both systems, sometimes on the same page. The conversion is the standard 2.20462 lb per kg, applied to the same mass, so the two figures can never disagree about the object, only about the unit.
Related calculators
Method: mass equals volume times density with shape formulas including the hollow-section subtraction; densities from the printed table with user override. Last reviewed: 14 October 2026.