Density Formula: ρ = m/V, SI Unit, Examples and Calculator

The density formula is $\rho = \frac{m}{V}$ : divide the mass of a sample by the volume it takes up. The Greek letter ρ (rho) is the usual symbol, though some school books simply write D or d. The answer tells you how many kilograms sit in one cubic metre of the material.

The same three letters solve every density question. Rearranged, they give the mass formula with density and volume, $m = \rho V$ , and the volume formula with mass and density, $V = \frac{m}{\rho}$ . Density is the starting point of the fluids and matter formulas, because pressure, buoyancy and floating all depend on it.

Quick facts

Formula
$\rho = \frac{m}{V}$
SI unit
kilogram per cubic metre (kg/m³)
Lab unit
g/cm³ or g/mL; 1 g/cm³ = 1000 kg/m³
Dimensional formula
[M¹ L⁻³ T⁰]
Type
Scalar, a property of the material, not of the object's size
Water
about 1000 kg/m³ (1.00 g/cm³) near 4 °C
Rearranged
$m = \rho V$ , $V = \frac{m}{\rho}$

What is the formula of density, symbol by symbol

The three quantities in ρ = m / V
Symbol	Quantity	SI unit	Common lab unit
$\rho$	Density	kg/m³	g/cm³
$m$	Mass	kg	g
$V$	Volume	m³	cm³ or mL

Mass is measured on a balance. Volume comes from a ruler for a regular shape (length × width × height for a block) or from the rise of water in a measuring cylinder for an irregular one. Because 1 mL equals 1 cm³, a cylinder reading can go straight into the formula in g/cm³.

Density does not change when you cut a sample in half: the mass halves and the volume halves, so the ratio stays the same. That is why a steel pin and a steel girder share one density. It does change with temperature, since most materials expand when heated, and gases change a lot with pressure too.

Density formula in physics and chemistry

Physics and chemistry use the same mass density formula. The only real difference is the unit habit. Physics answers are usually in kg/m³ because the rest of the working is in SI. Chemistry labs prefer g/cm³ or g/mL because samples are small. Moving between them is one step:

$1\ \text{g/cm}^3 = \frac{10^{-3}\ \text{kg}}{10^{-6}\ \text{m}^3} = 1000\ \text{kg/m}^3$

Typical densities at room temperature
Material	kg/m³	g/cm³
Air (sea level)	1.2	0.0012
Ice	917	0.917
Water	1000	1.00
Sea water	1025	1.025
Aluminium	2700	2.70
Iron	7870	7.87
Mercury	13 600	13.6

Comparing a density with that of water gives the relative density, a pure number. For powders and soils, the volume includes air gaps, which leads to bulk density and tapped density.

Density calculation formula in four steps

List mass and volume with their units exactly as the question gives them.
Choose one unit system. Either kg with m³, or g with cm³. Never divide grams by cubic metres.
Divide. Write $\rho = \frac{m}{V}$ , substitute and simplify.
Sense check. Most solids and liquids fall between 500 and 20 000 kg/m³. If you get 0.0027 kg/m³ for a metal, a conversion went wrong.

To find mass or volume instead, use the calculator above: choose the unknown, type the other two values in SI units and read off the answer.

Density formula examples

Example 1: an aluminium block

A small block has a mass of 54 g and a volume of 20 cm³. Find its density in kg/m³.

Convert: m = 0.054 kg, V = 20 × 10⁻⁶ m³ = 2.0 × 10⁻⁵ m³.

$\rho = \frac{0.054}{2.0 \times 10^{-5}} = 2700\ \text{kg/m}^3$

In lab units the same block is 54 ÷ 20 = 2.7 g/cm³, which matches aluminium.

Example 2: an irregular stone by displacement

Water in a measuring cylinder stands at 50 mL. A 150 g stone is lowered in and the level rises to 110 mL. Find the density of the stone.

Volume of stone = 110 − 50 = 60 mL = 60 cm³.

$\rho = \frac{150\ \text{g}}{60\ \text{cm}^3} = 2.5\ \text{g/cm}^3 = 2500\ \text{kg/m}^3$

Example 3: mass from density and volume

A can holds 5.0 L of cooking oil of density 920 kg/m³. What mass of oil is in it?

Convert: 5.0 L = 5.0 × 10⁻³ m³.

$m = \rho V = 920 \times 5.0 \times 10^{-3} = 4.6\ \text{kg}$

A litre is 1000 cm³, which is 10⁻³ m³. Most volume slips in density questions come from this conversion.

Units and dimensions of density

Mass has dimension [M] and volume is a length cubed, [L³]. Dividing them gives

$[\rho] = \frac{[\text{M}]}{[\text{L}^3]} = [\text{M}^1\,\text{L}^{-3}\,\text{T}^0]$

The SI unit follows directly: kilogram divided by cubic metre. The full derivation and the list of quantities that share these dimensions are on the dimensional formula of density page. Density then feeds into the hydrostatic part of the formula of pressure, $P = \rho g h$ , and into the buoyant force formula, $F_b = \rho_f V g$ .

Mistakes students make with density

Mixing g with m³. Keep mass and volume in matching systems before you divide.
Forgetting to cube the conversion. 1 m = 100 cm, but 1 m³ = 10⁶ cm³, not 100 cm³.
Using weight instead of mass. If the question gives newtons, divide by g = 9.8 m/s² first to get kilograms.
Thinking a heavier object is denser. A large log is heavier than a small iron nail, yet the nail is far denser and sinks.
Taking the outer volume of a hollow object. That gives an average density for the whole object, which is useful for floating questions but is not the density of the material.

Frequently asked questions

What is the formula for calculating density?

Divide mass by volume: ρ = m / V. Use kilograms and cubic metres for kg/m³, or grams and cubic centimetres for g/cm³.

What is the SI unit of density?

The SI unit is kilogram per cubic metre, kg/m³. Labs often quote g/cm³, and 1 g/cm³ equals 1000 kg/m³.

What is the volume formula with mass and density?

Rearrange ρ = m / V to get V = m / ρ. For example, 2.0 kg of water at 1000 kg/m³ takes up 0.0020 m³, which is 2.0 L.

What is the mass formula with density and volume?

Multiply density by volume: m = ρV. A 0.50 m³ block of ice at 917 kg/m³ has a mass of about 459 kg.

Is density a vector or scalar quantity?

Density is a scalar. It has a size and a unit but no direction, and it is the same at every point of a uniform material.

Why does ice float on water?

Ice has a density of about 917 kg/m³, less than the 1000 kg/m³ of liquid water. Anything less dense than the liquid around it floats.