# Density of Water Calculator

Created by Luis Hoyos
Last updated: Nov 05, 2022

If you're searching for how to calculate water density, this is the right place. With this calculator, you'll be able to:

• Know what the density of water at different temperatures is;
• Account for the effect of salt in water density in case you need it; and
• As a bonus, you can select among different objects and, according to their density, know if they'll float or sink in water (visit our immersed weight calculator to understand why objects float or sink in different liquids).

🔎 To know the density of many other substances or materials, look at our density calculator.

## How to calculate the density of water at different temperatures

Like with any other substance, the density of water changes with temperature mainly because of the thermal expansion phenomenon.

To calculate the density of water at different temperatures, this calculator uses the following approximate equation based on the 5th-order polynomial of a set of experimental values:

$\begin{split} \!\rho(T) &\!=\! \rho_0 + a_1 T - a_2 T^2 + a_3 T^3 \\ &- a_4 T^4 + a_5 T^5 \end{split}$

In the previous formula, the temperature ($T$) is in degrees celsius ($\degree C$), and the values of coefficients are the following:

• $\rho_0 = 999.83311\ \mathrm{kg/m^3}$;
• $a_1 = 0.0752\ \mathrm{ kg/(m³ \cdot \degree C)}$;
• $a_2 = 0.0089\ \mathrm{ kg/(m³ \cdot \degree C^2)}$;
• $a_3 = 7.36413 × 10⁻⁵\ \mathrm{ kg/(m³ \cdot \degree C^3)}$;
• $a_4 = 4.74639 × 10⁻⁷\ \mathrm{ kg/(m³ \cdot \degree C^4)}$; and
• $a_5 = 1.34888 × 10⁻⁹\ \mathrm{ kg/(m³ \cdot \degree C^5)}$.

## Accounting for pressure and salt in water density

Adding salt to the water is a way to modify its density. To characterize the water density as a function of its salt content, we use its salinity ($S$), which is the percentage of salt in the saltwater:

$S = \frac{m_1}{m_1 + m_0}$

In the previous equation, $m_0$ is the mass of pure water (unsalted), and $m_1$ is the mass of salt. This calculator also accepts "per mile" and "basis points," other common percentage units used for salinity.

Once the salinity is known, this calculator accounts for it similarly to how it does with the temperature: using a polynomial approximation of experimental data. The approximation $f(T, S, p)$ is a function of salinity, temperature, and pressure; it adds up to $\rho(T)$ to calculate the water density:

$\rho(T,S,p) = \rho(T) + f(T,S,p)$

The approximation polynomial is a bit complicated, and we don't deal with it in this article, but you can look at it in the paper of

Luis Hoyos
Temperature
°C
Salinity
Pressure
atm
Density
998.34
kg/m³
Choose an object and see if it floats or sinks in the water
Object
Egg
It will sink.
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