Math & Science
Mass from Density Calculator
Mass, volume or density for fourteen common materials — or any density you enter yourself.
Mass from Density Calculator
About the Mass from Density Calculator
Density links mass and volume. Know any two and the third follows: mass equals density times volume. This calculator solves in all three directions and comes with fourteen common materials built in, so you rarely need to look a density up.
Water, iron, steel, aluminium, copper, gold, silver, lead, concrete, oak, ice, petrol, milk and air are all preloaded. Pick one and enter a volume to get the mass — or enter your own density for anything not listed.
Units are flexible in both directions. Volume goes in as cubic metres, litres, cubic centimetres, millilitres, cubic feet or gallons; mass comes back in kilograms, grams, tonnes, pounds or ounces.
How to use the Mass from Density Calculator
- Choose which variable to solve for.
- Pick a material, or Custom to type your own density.
- Enter the values you have, in any supported unit.
- Select Calculate.
- The float/sink note compares the density against water.
Mass from density formula: mass, volume and density
m = ρ × V (mass from density and volume)
ρ = m ÷ V (density from mass and volume)
V = m ÷ ρ (volume from mass and density)
ρ is the Greek letter rho, the standard symbol for density.
Worked example
What does a solid iron cube of side 10 cm weigh?
Volume: 10 × 10 × 10 = 1,000 cm³ = 0.001 m³.
Iron's density is 7,874 kg/m³.
m = 7,874 × 0.001 = 7.874 kg
7.87 kg — about 17.4 pounds
The same cube in aluminium would be 2.7 kg, and in gold 19.3 kg. Same size, wildly different mass.
Reference densities
Values in kilograms per cubic metre, at ordinary room conditions:
| Material | kg/m³ | g/cm³ | Relative to water |
|---|---|---|---|
| Air (sea level) | 1.225 | 0.001225 | 0.001× |
| Petrol | 745 | 0.745 | 0.75× |
| Oak wood | 750 | 0.750 | 0.75× |
| Ice | 917 | 0.917 | 0.92× |
| Water (4 °C) | 1,000 | 1.000 | 1× |
| Milk | 1,030 | 1.030 | 1.03× |
| Concrete | 2,400 | 2.400 | 2.4× |
| Aluminium | 2,700 | 2.700 | 2.7× |
| Steel | 7,850 | 7.850 | 7.85× |
| Iron | 7,874 | 7.874 | 7.87× |
| Copper | 8,960 | 8.960 | 8.96× |
| Silver | 10,490 | 10.490 | 10.5× |
| Lead | 11,340 | 11.340 | 11.3× |
| Gold | 19,320 | 19.320 | 19.3× |
Density changes with temperature and, for gases, dramatically with pressure. These are reference figures for typical conditions. Alloys vary with composition — "steel" covers a range from about 7,750 to 8,050 kg/m³ — so use a supplier's figure when precision matters.
Why ice floats
Almost everything contracts as it freezes, so the solid form is denser than the liquid and sinks. Water is the famous exception. Ice is 917 kg/m³ against liquid water's 1,000, so it floats with about 92% of its bulk submerged — hence the tip of the iceberg.
The cause is hydrogen bonding. As water freezes, its molecules lock into an open hexagonal lattice that holds them further apart than they sit in the liquid. Expanding on freezing is why pipes burst in a cold snap and why bottles crack in the freezer.
It also matters biologically. Because ice floats, lakes freeze from the top down and insulate the water beneath, letting fish survive winters that would otherwise freeze a lake solid.
Converting density units
| From | To | Multiply by |
|---|---|---|
| g/cm³ | kg/m³ | 1,000 |
| kg/m³ | g/cm³ | ÷ 1,000 |
| kg/m³ | lb/ft³ | 0.062428 |
| lb/ft³ | kg/m³ | 16.0185 |
| g/mL | g/cm³ | 1 (identical) |
The g/cm³ to kg/m³ factor of 1,000 is worth memorising, because it is the conversion you meet most. Water is 1 g/cm³ and 1,000 kg/m³ — the same fact twice, and a handy way to check you have not slipped a factor of a thousand.
Finding the density of an irregular object
Weigh it, then measure its volume by displacement:
- Weigh the object on a balance and record the mass.
- Part-fill a measuring cylinder with water and note the level.
- Lower the object in fully and note the new level.
- The difference is the volume — 1 mL of displacement is 1 cm³.
- Divide mass by volume for the density.
This is Archimedes' method, and it still works. Two cautions: the object must sink, and it must not absorb water. For the volume of a regular shape, the volume calculator is quicker.
Other ways to use this calculator
- Mass calculator from density and volume — mass = density × volume.
- How to calculate mass from volume and density — multiply them, keeping the units consistent.
- How to calculate volume from mass and density — divide the mass by the density.
- Water mass calculator and iron mass calculator — water is 1,000 kg/m³ and iron about 7,874 kg/m³.
Frequently asked questions
Density is mass divided by volume: ρ = m ÷ V. Rearranged, mass equals density times volume, and volume equals mass divided by density. An iron cube of side 10 cm has a volume of 0.001 m³, and at 7,874 kg/m³ it weighs 7.87 kg. Keep units consistent — kg with m³, or grams with cm³ — and the arithmetic stays simple.
Iron has a density of about 7,874 kg/m³, or 7.874 g/cm³ — nearly eight times that of water. Steel is very slightly lower at around 7,850 kg/m³, though it varies with alloy composition from roughly 7,750 to 8,050. For engineering work, use the figure your supplier publishes for the specific grade rather than a generic value.
Because ice is less dense than liquid water — 917 kg/m³ against 1,000 — so it floats with about 92% submerged. Water is unusual in this: most substances contract when they freeze. Hydrogen bonding forces freezing water into an open hexagonal lattice that holds molecules further apart than in the liquid. It is also why pipes burst in winter and why lakes freeze from the top down.
Multiply g/cm³ by 1,000 to get kg/m³, or divide to go back. Water is 1 g/cm³ and 1,000 kg/m³ — a useful check that you have not slipped a factor of a thousand. For imperial, multiply kg/m³ by 0.062428 for lb/ft³. Note that g/mL and g/cm³ are numerically identical, since one millilitre is exactly one cubic centimetre.
Multiply the volume by the density, using matching units. 2 m³ of steel at 7,850 kg/m³ has a mass of 2 × 7,850 = 15,700 kg. To find volume instead, divide mass by density.
Sources and further reading
- NIST — Guide for the Use of the International System of Units — SI units for density, mass and volume
- NIST Chemistry WebBook — reference densities and material property data
- Density — Encyclopaedia Britannica — the density relationship and Archimedes' displacement method