Density Calculator

The density formula, and what the number actually tells you

Density is mass divided by volume — how much matter is packed into the space an object occupies. Written out it is d = m / V, and the whole of this calculator is that one line rearranged: m = d x V when you want mass, and V = m / d when you want volume. What makes it useful is that density is an intensive property. A gram of aluminium and a ten-kilogram aluminium block have the same density, so the number identifies the material rather than the sample, which is why it shows up in metal testing, shipping, chemistry labs and recipes alike.

Worked example: 250 g in 100 mL

Say a lab sample weighs 250 grams and displaces 100 millilitres of water. One millilitre is exactly one cubic centimetre, so the volume is 100 cm³. Divide: 250 / 100 = 2.5 g/cm³. Multiply by 1,000 and you get 2,500 kg/m³; multiply the g/cm³ figure by 62.428 and you get about 156.1 lb/ft³. Because 2.5 is well above water's 1.00, the sample sinks. Glass sits near 2.5 and common granite near 2.65, so those are the first candidates — aluminium at 2.70 is close enough that you would want a second measurement before deciding.

Unit walkthrough: g/cm³, kg/m³ and lb/ft³

The three units in this tool are the same quantity in different clothes. One g/cm³ equals exactly 1,000 kg/m³, because a cubic metre holds a million cubic centimetres and a kilogram holds a thousand grams. One g/cm³ also equals about 62.428 lb/ft³, which is where the familiar figure of 62.4 pounds per cubic foot for fresh water comes from — the number US civil engineers and plumbers carry around in their heads. Seawater runs a little denser, around 64 lb/ft³, thanks to dissolved salt.

A handy shortcut for the metric side: g/cm³ and kg/L are numerically identical. Water is 1 g/cm³ and 1 kg/L. So a litre of water weighs a kilogram, a litre of milk about 1.03 kg, and a litre of petrol only about 0.75 kg. That last one is why fuel is sold by volume but airlines plan by mass.

Solving backwards for mass or volume

Switch the "solve for" selector and the same relationship runs in reverse. Need the mass of a 0.5 m³ block of concrete at 2,400 kg/m³? Enter the density and the volume and you get 1,200 kg. Need the volume of 500 g of mercury at 13.53 g/cm³? That is 36.9 cm³ — a shot glass would hold it, and it would weigh half a kilo. Reverse calculations are the common case in shipping and materials estimating, where you know what the material is and need to know whether it fits or whether the floor will hold it.

Archimedes and the awkward crown

The classic story has Hiero II of Syracuse suspecting his goldsmith had swapped in silver. Archimedes noticed the water rising as he got into a bath and realised submerged volume could be measured directly. Whether or not he ran through the streets shouting, the method survives: weigh an object in air, weigh it again suspended in water, and the apparent weight lost in grams equals the displaced volume in millilitres. Divide the dry mass by that volume for the density. Gold is 19.3 g/cm³ and silver only 10.5, so even a modest amount of silver in the alloy drags the number down unmistakably.

Where this gets used

Freight and logistics work in density to decide whether a load cubes out or weighs out. Home brewers and winemakers read specific gravity, which is density relative to water, to track fermentation. Chemistry students convert between grams and millilitres of a solvent daily. Divers set buoyancy against the roughly 1.025 g/cm³ of seawater. Jewellers screen suspect gold. Even the bag of flour in your kitchen has a density near 0.53 g/cm³, which is why a cup of flour weighs about 125 g rather than the 240 g a cup of water would.

Limitations worth knowing

Three things quietly break density work. First, temperature: values are quoted at 20°C to 25°C, and hot liquids expand measurably — a few tenths of a percent per ten degrees for water, far more for oils. Second, gases: their density depends heavily on pressure, so a gas figure is meaningless without stating the conditions. Third, bulk versus true density: a scoop of sand or coffee grounds includes the air between the grains, so what you measure is bulk density, typically well under the density of the material itself. For solids with trapped voids, water displacement gives you the outside volume including the holes, which is exactly what you want for buoyancy and exactly what you do not want for identifying a metal.