Density – Mass, Volume and Formula Rearrangement | GCSE Maths

Density describes how much mass is contained within a particular volume. The relationship between density, mass and volume can be expressed using one formula, which can then be rearranged depending on the quantity that needs to be found.

Density

Density is calculated by dividing mass by volume:

Density = mass / volume

d = m / v

What the Symbols Mean

d = density

m = mass

v = volume

Finding Volume

Start with the density formula:

d = m / v

⇒ dv = m

v = m / d
Volume = mass / density

Finding Mass

Starting again with:

d = m / v

⇒ dv = m

m = dv
Mass = density × volume

The Three Forms of the Density Formula

d = m / v

v = m / d

m = dv

Units of Density

Two common units of density are:

* Grams per cubic centimetre: g/cm³

* Kilograms per cubic metre: kg/m³

Understanding the Units

The units of density follow directly from the formula:

density = mass / volume

If mass is measured in grams and volume is measured in cubic centimetres, the density is measured in:

g/cm³

If mass is measured in kilograms and volume is measured in cubic metres, the density is measured in:

kg/m³

Summary

Density:
d = m / v

Volume:
v = m / d

Mass:
m = dv

Common density units:
g/cm³ and kg/m³

Notes and workings: Tiago Hands.

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