Last updated: 2026-05-18

Density, mass, and volume

This calculator computes density from mass and volume using the formula ρ = m ÷ V. It also runs the formula in reverse — enter a known density and volume to find mass, or enter mass and density to find volume. Useful for chemistry labs, material identification, shipping calculations, and everyday science problems.

Definition

Density is the amount of mass contained in a given volume of a substance. It is an intensive property — it does not change with sample size. A small pebble and a large boulder of the same granite have identical density; only their mass and volume differ.

The SI unit of density is kg/m³. For everyday materials, g/cm³ is more convenient — water's density of 1,000 kg/m³ becomes the memorable benchmark value of 1 g/cm³.

The density formula

$$\rho = \frac{m}{V}$$

Symbol	Meaning	SI unit
ρ (rho)	Density	kg/m³
m	Mass	kg
V	Volume	m³

Rearranging for the other two quantities:

• Mass from density and volume: m = ρ × V
• Volume from density and mass: V = m ÷ ρ

Worked example

Common material densities

Material	Density (kg/m³)	Density (g/cm³)
Air (20 °C)	1.2	0.0012
Water (4 °C)	1,000	1.000
Seawater	~1,025	~1.025
Ice	917	0.917
Aluminium	2,700	2.70
Iron	7,874	7.874
Copper	8,960	8.96
Lead	11,340	11.34
Gold	19,300	19.30
Osmium (densest element)	22,590	22.59

Buoyancy and relative density

Archimedes' principle states that a submerged object experiences an upward buoyant force equal to the weight of the fluid it displaces. An object floats when its average density is less than that of the surrounding fluid and sinks when it is greater.

• Steel ship floats: The hollow hull makes the ship's average density (mass of steel + enclosed air + cargo, divided by total displaced volume) less than water. Remove the air — collapse the hull — and the dense steel sinks.
• Ice floats on water: At 917 kg/m³, ice is about 8% less dense than liquid water. This is why icebergs float with roughly 90% of their volume submerged.
• Hot air balloons rise: Heating air reduces its density. When the air inside the envelope becomes lighter than the cooler air outside, net buoyancy lifts the balloon.

Unit conversions

The two most common density units are numerically related by a factor of 1,000:

$$1\text{ g/cm}^3 = 1{,}000\text{ kg/m}^3$$

This follows directly from the definitions: 1 g = 0.001 kg and 1 cm³ = 0.000001 m³, so 1 g/cm³ = 0.001 ÷ 0.000001 kg/m³ = 1,000 kg/m³.

g/mL and g/cm³ are identical because 1 mL = 1 cm³ by definition.

Frequently Asked Questions (FAQ)

What is the formula for density?

Density equals mass divided by volume: ρ = m ÷ V. In SI units, mass is measured in kilograms (kg), volume in cubic metres (m³), and density in kg/m³. For everyday use, the equivalent unit g/cm³ (grams per cubic centimetre) is common — water has a density of exactly 1 g/cm³ at 4 °C.

How do you find volume if you know density and mass?

Rearrange the density formula: V = m ÷ ρ. For example, if you have 500 g of a material with density 2.5 g/cm³, the volume is 500 ÷ 2.5 = 200 cm³. Use the "Find Volume" mode above to do this automatically.

What is the density of water?

Pure water has a density of 1,000 kg/m³ (1 g/cm³ or 1 g/mL) at 4 °C, which is its point of maximum density. At 20 °C (room temperature) water is about 998 kg/m³. Saltwater is denser — seawater averages about 1,025 kg/m³. Common reference densities: air ≈ 1.2 kg/m³, ice ≈ 917 kg/m³, aluminum ≈ 2,700 kg/m³, iron ≈ 7,874 kg/m³, lead ≈ 11,340 kg/m³.

Why do objects float or sink?

An object floats when its average density is less than the fluid it displaces (Archimedes' principle). A steel ship floats because its hollow hull makes its average density less than water — the ship displaces a weight of water equal to its own weight. A solid steel block sinks because steel's density (~7,874 kg/m³) greatly exceeds water's (1,000 kg/m³). Hot air balloons rise because heated air is less dense than the cooler air surrounding it.