How this instrument works
Density is defined as mass per unit volume, ρ = m ⁄ V. Rearrange that definition for m and you get this instrument's whole job: m = ρ × V, multiplication rather than division. It is the direction most people actually need, because density is the number that comes from a table or a datasheet — steel at roughly 7850 kg/m³, aluminium at 2700 — while volume is the number you can usually see or measure directly, from a container's rated capacity or a drawing's dimensions. What's missing is the weight, and multiplying supplies it.
The arithmetic is one step, but the reasoning behind it matters. Density is intensive — it belongs to the substance, not the sample, so a litre of steel and a tonne of steel share the same 7850 kg/m³. Volume is extensive — it scales with how much material is actually present. Multiply an intensive property by an extensive one and the result becomes extensive too: total mass, which grows in direct proportion to however much of the substance you have. Double the volume at a fixed density and the mass doubles exactly; that proportionality is the entire content of the formula.
Two things have to hold for the answer to be trustworthy: the density figure must apply uniformly through every part of the volume entered, and it must have been measured near the conditions you actually care about. A casting with a hidden air pocket, an aggregate with gaps between grains, or a 3D-printed part with partial infill all contain less solid material than their outer volume suggests, so the formula overstates mass unless you enter the true solid volume rather than the envelope. Liquids and especially gases also drift with temperature and pressure, so a density value pulled from a table at 20°C will be slightly wrong for a tank left in summer sun.
- Enter the material's Density, choosing kg/m³ or g/cm³ from the unit menu to match whatever a datasheet or handbook already gives you.
- Enter the Volume you actually have, in millilitres, litres, or cubic metres — a container's rated capacity or a measured displacement both work.
- Read Mass, switching between grams and kilograms; the instrument converts both inputs to kilograms and cubic metres internally before multiplying.
- If the object has hollow sections or trapped air, subtract that volume first — Density × Volume assumes solid material all the way through.
Worked example — two litres of water
A courier quoting a shipment before it ever reaches a scale needs the weight worked out from what's already known: a two-litre bottle of water, declared volume 2 L, which this instrument reads as 0.002 m³. Water's density is the standard reference value, 1000 kg/m³, so m = ρ × V = 1000 × 0.002 = 2.0 kg exactly — the golden case this instrument is checked against, and the reason 'a litre of water weighs a kilogram' is such a reliable shortcut.
Swap the contents and the same multiplication gives a different answer. Motor oil sits near 900 kg/m³, so an identical two-litre bottle comes out at m = 900 × 0.002 = 1.8 kg, a fifth lighter than water despite occupying the same shape. That is why two boxes of matching size can carry different weight declarations on a shipping label — the volume is equal, but the density inside it is not.
Questions
How do I find a material's density if it isn't listed anywhere?
Weigh a known volume of it once. Pour a measured amount into a graduated container, weigh it on a scale, divide mass by volume, and treat that figure as the material's density from then on — the reciprocal of the calculation this instrument performs. For common substances, engineering handbooks and material datasheets already list a value: steel near 7850 kg/m³, aluminium 2700, oak timber about 700.
Why multiply instead of divide, the way density itself is defined?
Because density's own definition, ρ = m ⁄ V, is already a division — multiplying by volume simply undoes it and returns the mass that division started from. Division stays useful when the unknown is different: divide mass by volume to find density, or divide mass by density to find volume. This instrument covers the case where density and volume are both known and mass is the gap.
Does this work for an irregular or oddly shaped object?
Yes, as long as you know its volume. The formula does not see shape, only a number: cubic metres of material at a given density. Find the volume of an irregular solid by water displacement — submerge it and read how far the level rises — or by measuring it in CAD, and the same multiplication applies whether the object is a brick or a bracket.
What if the object has hollow sections or trapped air?
Subtract that volume before entering it here, or the answer overstates the mass. A 3D-printed part sliced at 20% infill is mostly air behind its shell, so multiplying the filament's density by the part's outer envelope volume would badly overshoot; slicing software reports the actual filament volume for exactly this reason, and that smaller figure belongs in the Volume field.
Why would the same density value give a slightly wrong mass?
Because density tables are pinned to a reference temperature — often 20°C, or 3.98°C for water's peak value — and most materials expand when warmer, thinning their density and shrinking the mass a fixed volume actually contains. The drift is small for solids and cool liquids, under half a percent across an ordinary room-temperature range, but becomes significant for gases, whose density scales directly with pressure and inversely with absolute temperature.