Density: identifying a material from mass and volume

Density is mass divided by volume — how much stuff is packed into a given space. It's the fastest way to check whether something is what it claims to be, whether it will float, or whether a mix is at the concentration you think it is, and it needs nothing but a scale and something to measure volume.

The method

Weigh the object to get its mass. Find its volume — for a regular shape (a block, a bar) multiply length × width × height; for an irregular shape, drop it into water and read how much the level rises, since the water displaced equals the object's volume (the trick Archimedes is said to have used in the bath). Then divide: density = mass ÷ volume.

A real example: identifying a metal bar

A rectangular bar measures 4 cm × 5 cm × 3 cm, so its volume is 4 × 5 × 3 = 60 cm³. On a scale it reads 534 g.

534 ÷ 60 = 8.9 g/cm³

Commonly published reference tables put copper at about 8.96 g/cm³ and brass in the 8.4–8.7 range, so 8.9 g/cm³ points to copper, not brass. It won't confirm the exact alloy — a lab would do that a different way — but as a five-minute check it rules out most of the other likely metals: aluminum (about 2.7), steel (about 7.85) and lead (about 11.3) are all far enough away that a scale and a ruler already answer the question.

A real example: water displacement on an irregular piece

An oddly shaped piece of metal won't give you a clean length × width × height. Instead, fill a container to 150 mL, drop the piece in, and read the new level: 200 mL. The volume of the piece is the difference, 200 − 150 = 50 cm³ (1 mL of water occupies exactly 1 cm³). Weighed on a scale, it comes to 135 g.

135 ÷ 50 = 2.7 g/cm³

That's aluminum, almost exactly — and a piece of steel or copper the same size would have come in three to four times heavier, so the scale alone would have told most of the story before you even divided.

A real example: checking a syrup

Density isn't just for metal. Bartenders and candy-makers check simple syrup the same way: 355 mL of syrup weighs 462 g on a kitchen scale (with the container's own weight already subtracted).

462 ÷ 355 ≈ 1.30 g/mL

Plain water is 1.00 g/mL, so this syrup is noticeably denser — consistent with the standard 1:1 sugar-to-water simple syrup recipe, which runs close to 1.3 g/mL. A syrup that came out at 1.05 would mean far less sugar dissolved than the recipe called for.

Floating and sinking

Water is the usual yardstick because it's 1.00 g/mL (1,000 kg/m³) at room temperature. Anything denser than the liquid it's placed in sinks; anything less dense floats. Ice, at about 0.92 g/cm³, floats on water for exactly this reason — and most woods, roughly 0.4 to 0.9 g/cm³ depending on species, float too.

Switching units

The same figure changes its label depending on the units you measured in, not its meaning. To go from g/cm³ to kg/m³, multiply by 1,000, because a cubic meter holds a million cubic centimeters but a kilogram is only a thousand grams: 2.7 g/cm³ = 2,700 kg/m³. Always check which units a reference table uses before comparing your own result to it.

Run your own numbers

The free Density calculator divides mass by volume in any consistent unit pair, entirely on your device.