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Density

What is density, and how do you measure it?

BeginnerFoundationsLast reviewed 5 October 2026
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What is it?

Density is the mass of a substance per unit volume. It tells you how tightly matter is packed:

ρ=mV\rho = \frac{m}{V}

where ρ\rho (the Greek letter rho) is density, mm is mass and VV is volume. In chemistry, density is usually given in g/cm³ for solids and g/mL for liquids (these are the same, since 1 mL = 1 cm³). The SI unit is kg/m³, and 1 g/cm³ = 1000 kg/m³.

Substance (20 °C)Density (g/cm³)
Air0.00120
Ethanol0.789
Ice (0 °C)0.917
Water0.998
Aluminium2.70
Iron7.87
Copper8.96
Lead11.3
Gold19.3

Key idea

Density is a property of the substance, not of the object. A paper clip and a steel girder have very different masses, but the same density. That’s why density helps to identify a substance.

Why does it matter?

  • Identifying substances. Measuring density is a quick test of what a material is, or whether it is pure: an alloy or a diluted liquid has a different density.
  • Floating and sinking. An object floats in a liquid if it is less dense than the liquid. Ice floats on water, oil floats on vinegar, and a ship floats because its average density, including the air inside, is less than that of water.
  • Converting between mass and volume. Density is a conversion factor: from a volume of liquid you can find its mass without weighing it, and the reverse.

How does it work?

1. Calculating density

Measure the mass on a balance and the volume by one of the methods below, then divide. Rearranging the formula gives the other two forms:

m=ρ×VV=mρm = \rho \times V \qquad V = \frac{m}{\rho}

2. Measuring volume

  • Regular solid (cube, block, cylinder): measure the dimensions and calculate. For a block, V=length×width×heightV = \text{length} \times \text{width} \times \text{height}.
  • Irregular solid (a stone, a key): use displacement. Part-fill a measuring cylinder with water, read the volume, lower the object in and read again. The rise in volume equals the volume of the object.
  • Liquid: measure a volume accurately with a pipette or measuring cylinder, and weigh it.

3. Floating and sinking

Compare densities. If ρobject<ρliquid\rho_\text{object} < \rho_\text{liquid} the object floats; if ρobject>ρliquid\rho_\text{object} > \rho_\text{liquid} it sinks. Liquids that don’t mix form layers, with the densest at the bottom.

4. Replicate measurements

As with any measurement, repeat it at least three times (triplicate), then report the mean and the standard deviation. Compare the mean with the accepted value to judge accuracy, and use the standard deviation to judge precision (see Significant Figures and Measurement).

Think of it like this

Think of a lift. Ten people in a big lift and ten people in a small lift are the same “mass”, but the small lift is more crowded. Density is how crowded the matter is: the same mass squeezed into a smaller volume means a higher density.

More precisely

Density changes with temperature, because most substances expand when heated: their volume increases while their mass stays the same. That’s why careful work states the temperature. Water is unusual: it is densest at about 4 °C (1.000 g/mL), and ice is less dense than liquid water, so lakes freeze from the top down and fish survive the winter underneath. Gases are about a thousand times less dense than liquids, and their density depends strongly on pressure too.

Visualise it

Two measuring cylinders. The first holds water up to 25.0 mL. In the second, a stone has been lowered in and the water level has risen to 32.4 mL. The rise of 7.4 mL is the volume of the stone.
Measuring the volume of an irregular solid by displacement: the rise in the water level is the volume of the object.

Worked example

Worked example: A regular solid

Question: A metal block measures 2.00 cm × 3.00 cm × 5.00 cm and has a mass of 81.0 g. Find its density and suggest which metal it is.

  1. Volume:

    V=2.00 cm×3.00 cm×5.00 cm=30.0 cm3\begin{aligned} &V = 2.00\ \text{cm} \times 3.00\ \text{cm} \\[4pt] &\quad \times 5.00\ \text{cm} \\[4pt] &= 30.0\ \text{cm}^3 \end{aligned}

  2. Density:

    ρ=mV=81.0 g30.0 cm3=2.70 g/cm3\begin{aligned} &\rho = \frac{m}{V} = \frac{81.0\ \text{g}}{30.0\ \text{cm}^3} \\[4pt] &= 2.70\ \text{g/cm}^3 \end{aligned}

  3. This matches aluminium (2.70 g/cm³).

Worked example: An irregular solid, by displacement

Question: A measuring cylinder holds 25.0 mL of water. A stone of mass 18.5 g is lowered in and the level rises to 32.4 mL. Find the density of the stone.

  1. Volume of the stone = rise in level:

    V=32.4 mL−25.0 mL=7.4 mL=7.4 cm3\begin{aligned} &V = 32.4\ \text{mL} - 25.0\ \text{mL} \\[4pt] &= 7.4\ \text{mL} = 7.4\ \text{cm}^3 \end{aligned}

  2. Density:

    ρ=18.5 g7.4 cm3=2.5 g/cm3\rho = \frac{18.5\ \text{g}}{7.4\ \text{cm}^3} = 2.5\ \text{g/cm}^3

  3. The volume has only 2 significant figures, so the answer is 2.5 g/cm³.

Worked example: Using density to find a volume

Question: What volume does 500. g of gold occupy? (density 19.3 g/cm³)

V=mρ=500. g19.3 g/cm3=25.9 cm3\begin{aligned} &V = \frac{m}{\rho} = \frac{500.\ \text{g}}{19.3\ \text{g/cm}^3} \\[4pt] &= 25.9\ \text{cm}^3 \end{aligned}

Half a kilogram of gold is smaller than a matchbox.

Worked example: Replicate measurements of a liquid

Question: A student weighs three separate 10.00 mL samples of a colourless liquid at 20 °C and calculates densities of 0.791 g/mL, 0.789 g/mL and 0.792 g/mL. Report the result and decide whether the liquid could be ethanol (0.789 g/mL).

  1. Mean:

    ρˉ=13 (0.791+0.789+0.792) g/mL=2.372 g/mL3=0.7907 g/mL\begin{aligned} &\bar{\rho} = \tfrac{1}{3}\,(0.791 + 0.789 \\[4pt] &\qquad + 0.792)\ \text{g/mL} \\[4pt] &= \frac{2.372\ \text{g/mL}}{3} \\[4pt] &= 0.7907\ \text{g/mL} \end{aligned}

  2. Standard deviation, from the deviations +0.0003 g/mL, −0.0017 g/mL and +0.0013 g/mL:

    s=∑(ρi−ρˉ)2n−1s2=4.67×10−6 g2/mL22s2=2.33×10−6 g2/mL2s=0.0015 g/mL\begin{aligned} &s = \sqrt{\frac{\sum (\rho_i - \bar{\rho})^2}{n - 1}} \\[4pt] &s^2 = \frac{4.67 \times 10^{-6}\ \text{g}^2/\text{mL}^2}{2} \\[4pt] &\phantom{s^2} = 2.33 \times 10^{-6}\ \text{g}^2/\text{mL}^2 \\[4pt] &s = 0.0015\ \text{g/mL} \end{aligned}

  3. Result: 0.791 ± 0.002 g/mL (n = 3). The difference from ethanol, 0.791 g/mL − 0.789 g/mL = 0.002 g/mL, is about the size of the standard deviation, so the result is consistent with ethanol.

Worked example: Will it float?

Question: A plastic toy has a mass of 50.0 g and a volume of 62.5 cm³. Does it float in water (0.998 g/cm³)?

ρ=50.0 g62.5 cm3=0.800 g/cm3\rho = \frac{50.0\ \text{g}}{62.5\ \text{cm}^3} = 0.800\ \text{g/cm}^3

0.800 g/cm³ is less than 0.998 g/cm³, so it floats.

Common mistake

Common mistake: Dividing the wrong way round

Density is mass ÷ volume, not volume ÷ mass. Check the units: the answer must come out in g/cm³ (mass on top). If you get cm³/g, the fraction is upside down.

Common mistake: Using the final reading as the volume

In displacement, the volume of the object is the difference between the two readings (32.4 mL − 25.0 mL), not the final reading of 32.4 mL.

Common mistake: Confusing heavy with dense

A large log is heavier than a small iron nail, yet the log floats and the nail sinks. Floating depends on density, not on mass.

Notation note

  • g/cm³ can also be written g cm⁻³; g/mL and g/cm³ are numerically identical.
  • Always state the temperature with a precise density, for example “0.998 g/mL at 20 °C”.

Remember this

Remember this

  • ρ=m/V\rho = m/V; rearranged, m=ρVm = \rho V and V=m/ρV = m/\rho.
  • 1 mL = 1 cm³, so g/mL = g/cm³; 1 g/cm³ = 1000 kg/m³.
  • Volume of an irregular solid = rise in level when it is submerged (displacement).
  • Less dense than the liquid: floats. Denser: sinks.
  • Density depends on temperature: state it, and measure in replicate (mean ± standard deviation).

Test yourself

Check your understanding before moving on.

Flashcards

10 cards

  1. Question
    What is density?
    Answer

    Mass per unit volume: ρ=mV\rho = \dfrac{m}{V}

  2. Question
    Rearrange ρ=m/V\rho = m/V to give mass and volume.
    Answer

    m=ρVm = \rho V and V=mρV = \dfrac{m}{\rho}

  3. Question
    Which units are used for density in chemistry?
    Answer

    g/cm³ for solids and g/mL for liquids (the same, since 1 mL = 1 cm³). SI unit: kg/m³.

  4. Question
    Convert 1 g/cm³ to kg/m³.
    Answer

    1 g/cm³ = 1000 kg/m³

  5. Question
    How do you measure the volume of an irregular solid?
    Answer

    By displacement: the rise in the water level in a measuring cylinder when the object is submerged.

  6. Question
    When does an object float in a liquid?
    Answer

    When its density is less than the density of the liquid.

  7. Question
    A block of 81.0 g measures 2.00 cm × 3.00 cm × 5.00 cm. What is its density?
    Answer

    81.0 g ÷ 30.0 cm³ = 2.70 g/cm³ (aluminium)

  8. Question
    Why must you state the temperature with a precise density?
    Answer

    Most substances expand when heated, so their volume rises and their density falls.

  9. Question
    At what temperature is water densest?
    Answer

    About 4 °C (1.000 g/mL). Ice (0.917 g/cm³) is less dense than water, so it floats.

  10. Question
    How should a measured density be reported?
    Answer

    As the mean ± standard deviation of replicate measurements (at least three), with n and the temperature.

Quiz

7 questions

  1. Question 1EasyWhich formula gives density?
    Show answer

    Answer: ρ = m / V

    Density is mass per unit volume, so ρ = m / V. Check the units: g ÷ cm³ gives g/cm³.

  2. Question 2EasyA 54.0 g sample has a volume of 20.0 cm³. What is its density?
    Show answer

    Answer: 2.70 g/cm³

    ρ = 54.0 g ÷ 20.0 cm³ = 2.70 g/cm³. 0.370 is the fraction upside down (cm³/g).

  3. Question 3EasyWater in a measuring cylinder rises from 30.0 mL to 45.2 mL when a metal piece is added. What is the volume of the metal?
    Show answer

    Answer: 15.2 mL

    The volume of the object is the rise in level: 45.2 mL − 30.0 mL = 15.2 mL (= 15.2 cm³).

  4. Question 4MediumWhich object will float in water (0.998 g/cm³)?
    Show answer

    Answer: Mass 20.0 g, volume 25.0 cm³

    20.0 g ÷ 25.0 cm³ = 0.800 g/cm³, less than water, so it floats. The others are 1.20 g/cm³, 5.00 g/cm³ and 3.00 g/cm³: all sink.

  5. Question 5MediumEthanol has a density of 0.789 g/mL. What is the mass of 200. mL of ethanol?
    Show answer

    Answer: 158 g

    m = ρV = 0.789 g/mL × 200. mL = 157.8 g, which is 158 g to 3 significant figures. 253 g comes from dividing (200. ÷ 0.789).

  6. Question 6MediumWhy does ice float on liquid water?
    Show answer

    Answer: Ice is less dense than liquid water

    Ice (0.917 g/cm³) is less dense than liquid water (about 1.00 g/mL) because water molecules are held further apart in the ice structure. Floating depends on density, not on mass.

  7. Question 7HardFive measurements of a metal density are 2.68, 2.71, 2.69, 2.72 and 2.70 g/cm³. Which is the best report?
    Show answer

    Answer: 2.70 ± 0.02 g/cm³ (n = 5)

    Mean = 13.50 g/cm³ ÷ 5 = 2.70 g/cm³. Sample standard deviation s = 0.016 g/cm³, which rounds to 0.02 g/cm³. ±0.04 is the range (2.72 − 2.68), not the standard deviation.

Notes and downloads

  • Worksheet

    Density Worksheet

    8 questions on calculating density, displacement, floating and sinking, using density as a conversion factor and replicate measurements. Answer key included.

    BeginnerFree

References

  1. Bureau International des Poids et Mesures (BIPM). The International System of Units (SI), 9th ed.; BIPM, 2019. Link
  2. Brown, T. L.; LeMay, H. E., Jr.; Bursten, B. E.; Murphy, C. J.; Woodward, P. M.; Stoltzfus, M. W. Chemistry: The Central Science, 15th ed.; Pearson, 2022.

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