Density Calculator
Give the density calculator any two of density, mass and volume and it finds the third. It also says whether the thing floats, which is density against water.
Density
- The formula
- density = mass / volume
- Density in every unit g/cm3 and kg/L are the same number, which is the most useful coincidence in the metric system.
- 2.7 g/cm3 2,700 kg/m3 168.555 lb/ft3
- Specific gravity Density relative to water at 20 C. It is dimensionless, which is why it is the figure quoted in geology, brewing and anything comparing materials across unit systems.
- 2.70487
- In water it would Anything denser than water displaces less than its own weight and sinks.
- sink
- Closest common material Within 5%, so that is probably what it is.
- Aluminum (2.7 g/cm3)
- Mass and volume used
- 2.7 kg in 1 liters
| Material | g/cm3 | kg/m3 | Floats in water? |
|---|---|---|---|
| Water (4 C) | 1 | 1,000 | no |
| Water (20 C) | 0.9982 | 998.2 | no |
| Ice | 0.917 | 917 | yes |
| Seawater | 1.025 | 1,025 | no |
| Ethanol | 0.789 | 789 | yes |
| Olive oil | 0.915 | 915 | yes |
| Milk | 1.03 | 1,030 | no |
| Air (20 C, sea level) | 0.001204 | 1.204 | yes |
| Aluminum | 2.7 | 2,700 | no |
| Steel | 7.85 | 7,850 | no |
| Iron | 7.874 | 7,874 | no |
| Copper | 8.96 | 8,960 | no |
| Lead | 11.34 | 11,340 | no |
| Gold | 19.3 | 19,300 | no |
| Concrete | 2.4 | 2,400 | no |
| Pine (dry) | 0.5 | 500 | yes |
| Oak (dry) | 0.75 | 750 | yes |
| Glass | 2.5 | 2,500 | no |
- Density changes with temperature and, for gases, enormously with pressure. The reference figures are at roughly room temperature and sea level, and metals vary by alloy and grade.
- Density and specific gravity are the same comparison expressed two ways. Specific gravity is dimensionless, so it carries across unit systems without conversion. That is why it is the one quoted in trades.
How the Density Calculator works
Density is mass divided by volume. A kilogram of lead and a kilogram of feathers weigh the same; the lead occupies far less space, and density is the number that says so.
The metric system contains a coincidence that makes this unusually easy: water has a density of almost exactly 1 g/cm3, because the gram was originally defined as the mass of one cubic centimeter of water. The consequences are that 1 g/cm3 equals 1 kg/L equals 1,000 kg/m3, and that a liter of water weighs a kilogram. Most density work in metric units is therefore a matter of moving a decimal point.
Specific gravity is density divided by the density of water, which makes it dimensionless. That is its entire point: a specific gravity of 2.7 is 2.7 whether you work in g/cm3 or lb/ft3, so it carries across unit systems without conversion. It is the figure quoted in geology, brewing, winemaking and the trades for exactly that reason.
It also answers the flotation question immediately. Anything with a specific gravity under 1 floats; anything over 1 sinks. And the fraction that sits below the surface is exactly the specific gravity. Ice at 0.917 floats with 91.7% of its volume submerged, which is where "the tip of the iceberg" comes from. That is Archimedes' principle restated: a floating object displaces its own weight of fluid, so the submerged volume times the fluid's density equals the object's total mass.
A few reference points worth carrying. Water is 1. Ice is 0.917, which is why it floats. That is an unusual property, since almost everything else is denser as a solid than as a liquid, and the fact that ice floats is why lakes freeze from the top and life survives under them. Aluminum is 2.7, steel about 7.85, lead 11.34, gold 19.3. Air at sea level is 0.0012, roughly 1/800th of water. Pine is about 0.5 and oak about 0.75, which is why both float.
Two things that change the answer and are routinely forgotten.
Temperature. Nearly everything expands when heated, so density falls. Water is the famous exception between 0 and 4 C, where it contracts as it warms. That is the other half of why ice floats and why lakes stratify. For liquids the effect is a fraction of a percent per degree; for gases it is large.
Pressure, for gases specifically. Liquids and solids are nearly incompressible and their density barely moves with pressure. A gas's density is proportional to pressure and inversely proportional to absolute temperature, so a figure for air is meaningless without both. The 1.204 kg/m3 quoted above is at 20 C and sea level.
One distinction worth keeping straight for materials sold in bulk: bulk density is not the same as material density. Gravel has a material density around 2.7 g/cm3 like the rock it came from, and a bulk density nearer 1.5 because a pile of it is substantially air. Which one applies depends on whether you are weighing the stone or filling a truck, and construction takeoff wants the bulk figure.
Density Calculator FAQ
How do I calculate density?
Divide mass by volume. 2,700 g in 1,000 cm3 is 2.7 g/cm3, which is aluminum. Rearranged, mass = density x volume and volume = mass / density: the same identity read three ways.
What is specific gravity?
Density divided by the density of water, which makes it a pure number with no units. That is why it is quoted in geology, brewing and the trades: a specific gravity of 2.7 is 2.7 whatever unit system you work in, so it needs no conversion.
Will it float in water?
It floats if its density is under 1 g/cm3 and sinks above it. The fraction sitting below the surface equals the specific gravity. Ice at 0.917 floats with 91.7% submerged, which is Archimedes' principle in a sentence and the origin of 'the tip of the iceberg'.
Why does ice float?
Because water is unusual: it expands when it freezes, so ice at 0.917 g/cm3 is less dense than the liquid at 1.0. Almost every other substance is denser as a solid. It matters more than it sounds: lakes freeze from the top down rather than solid, which is why things live in them through winter.