Water density: definition and core idea
Water density is the amount of mass packed into a given volume of water. The physical definition of density is:
\[ \rho = \frac{m}{V} \]Here, \(\rho\) is density, \(m\) is mass, and \(V\) is volume. For liquid water, density depends strongly on temperature and weakly on pressure (near everyday conditions).
Common units for water density
In chemistry and lab work, water density is often expressed in \(\mathrm{g/mL}\). In physics and engineering, \(\mathrm{kg/m^3}\) is common. These two units are numerically connected by:
\[ 1\ \mathrm{g/mL} = 1000\ \mathrm{kg/m^3} \]Practical shortcut. A density written in \(\mathrm{g/mL}\) can be converted to \(\mathrm{kg/m^3}\) by multiplying by \(1000\).
\[ 0.997\ \mathrm{g/mL} = 997\ \mathrm{kg/m^3} \]How water density changes with temperature
Unlike most liquids, pure water reaches its maximum density near \(4^\circ\mathrm{C}\). Above about \(4^\circ\mathrm{C}\), water density decreases as temperature increases because thermal expansion increases volume more than mass changes.
Reference values for liquid water density (approx., 1 atm)
The table below lists typical water density values across a useful temperature range. Values are approximate for pure liquid water at standard pressure.
| Temperature | Water density (g/mL) | Water density (kg/m3) |
|---|---|---|
| 0 °C | 0.99984 | 999.84 |
| 4 °C | 0.99997 | 999.97 |
| 10 °C | 0.99970 | 999.70 |
| 20 °C | 0.99821 | 998.21 |
| 25 °C | 0.99705 | 997.05 |
| 30 °C | 0.99565 | 995.65 |
| 40 °C | 0.99222 | 992.22 |
| 60 °C | 0.98320 | 983.20 |
| 80 °C | 0.97180 | 971.80 |
| 100 °C | 0.95837 | 958.37 |
Worked example: compute water density from mass and volume
Step 1. Use the definition of density.
\[ \rho = \frac{m}{V} \]Step 2. Substitute a sample measurement (e.g., \(m=250.0\ \mathrm{g}\), \(V=251.0\ \mathrm{mL}\)).
\[ \begin{aligned} \rho &= \frac{250.0\ \mathrm{g}}{251.0\ \mathrm{mL}} \\ &= 0.996\ \mathrm{g/mL} \end{aligned} \]Step 3. Convert to \(\mathrm{kg/m^3}\) if needed.
\[ \begin{aligned} \rho &= 0.996\ \mathrm{g/mL} \\ &= 996\ \mathrm{kg/m^3} \end{aligned} \]Interpretation and common pitfalls
Report water density with the temperature and (if relevant) the pressure. For typical lab conditions, temperature is the main factor: using \(1.000\ \mathrm{g/mL}\) as a universal constant can introduce noticeable error for warm water.