# Water Density Calculator

By Wojciech Sas, PhD candidate
Last updated: Aug 10, 2021

With this water density calculator, you can quickly estimate the density of salt water. In this text, you will find the answer to the question "What is the density of water?", and how it changes depending on temperature, salinity, or pressure. Have you ever wondered what the relation is between the density of water in `kg/m³`, the density of water in `g/ml`, and the density of water in `lb/ft³`? Should eggs float or sink in salt water? Read on to find answers to these questions too!

## What is the density of water?

The definition of the density of water (or any other substance) is the ratio of its mass, `m`, to its volume, `V`. Density is usually denoted using the symbol `ρ`, so the formula for density is:

`ρ = m / V`.

It turns out that density isn't constant for most substances, but in fact changes when external parameters change, such as the temperature or pressure.

## Water density units

There are various units of water density. Actually, any combination of the units of mass and the units of volume are acceptable, but some of them are more prevalent than others. The most commonly used units are:

• [kg/m³] - kilogram per cubic meter,
• [lb/ft³] - pound per cubic foot,
• [g/ml] or [g/cm³] - gram per milliliter or gram per cubic centimeter, which are equivalent to each other.

The density of water in `kg/m³` is `1000` times greater than the density of water in `g/cm³` and circa `16.018` times smaller than the density of water in `lb/ft³`. If you are interested in the different units of density and want to know the relation between them, try our density converter.

## Temperature dependence of water density

You probably know of the phenomenon of the the density of water changing at different temperatures, even if you've never thought about it in scientific terms; ever wondered why ice floats? This change is mainly caused by thermal expansion - where the same amount of substance occupies more and more space as the temperature increase. As a result, the mass stays constant, but the volume increases, causing the density to decrease.

Qualitatively, it's fairly simple, but from a mathematical point of view estimating the outcome is a different story. Water has an intriguing property - it reaches its maximum density at about `4°C` or `40°F`. While there are tables of pure water density between water's freezing point (`0°C` or `32°F`) and its boiling point (`100°C` or `212°F`), there isn't a straightforward formula which yields the exact value for a given temperature. To get around this, our water density calculator uses an approximate equation, based on the 5th order polynomial:

`ρ(T) = ρ₀ + a₁*T + a₂*T² + a₃*T³ + a₄*T⁴ + a₅*T⁵`,

where the temperature `T` is in `°C`, and the values of coefficients are the following:

• `ρ₀ = 999.83311 kg/m³`,
• `a₁ = 0.0752 kg/(m³·°C)`,
• `a₂ = -0.0089 kg/(m³·°C²)`,
• `a₃ = 7.36413*10⁻⁵ kg/(m³·°C³)`,
• `a₄ = 4.74639*10⁻⁷ kg/(m³·°C⁴)`,
• `a₅ = 1.34888*10⁻⁹ kg/(m³·°C⁵)`,

We use scientific notation to express all of the small values in a clearer way. Although the outcome is an approximation, it's provided with sufficient precision.

## The density of salt water

The mixture of water and salt, hereafter referred to as salt water, has a different density than pure water. The basic parameter that tells us about the amount of salt in salt water is salinity, `S`, given as:

`S = m₁ / (m₁ + m₀)`,

where `m₀` is the mass of pure water and `m₁` is the mass of salt. In other words, mixing a mass of pure water, `m₀`, with a mass of salt, `m₁`, gives you the salinity `S` of salt water. This quantity is usually given in per mille `‰`, parts per thousand (ppt), or practical salinity units (psu), which are basically equivalent.

In our density of water calculator, we use a method proposed by Millero and his coworkers. The overall formula is complicated so that we won't show it here explicitly, but generally, it uses the same concept as the equation for the temperature dependence of density - a polynomial of mixed terms of temperature, salinity, and pressure:

`ρ(T,S,p) = ρ(T) + f(T,S,p)`.

Here `ρ(T)` is the density of pure water derived from the previous chapter.

However, we can spot some common properties - the density of salt water increases for higher salinity, and higher external pressure.

## How to use water density calculator?

What is the density of water at `20°C` of salinity `S = 35‰` and under the pressure of `1 atm`? Let's give our water density calculator a try and find out!

1. Set temperature to `20°C`.
2. Set salinity to `35‰`.
3. Set pressure to `1 atm`.
4. And that's it! The density of salt water is `1,024.9 kg/m³`.

The same density of water is `1.0249 g/ml`, or `63.982 lb/ft³`.

But this is not the end! Perform your own experiment at home - take a few objects with an unknown density (but more or less equal to the value for the density of water, i.e. `1000 kg/m³`). Although it is not so easy to change the external pressure, you can create a liquid with known salinity and control its temperature. Check out the Advanced mode to see how much pure water and salt you need to obtain salt water with a specific density.

You can start by heating your mixture (e.g. in a microwave), then submerging your objects in it. You can quickly evaluate the temperature of water while it is cooling down. At the beginning, the density of hot water is quite high, so everything should sink, but at some point the density will have decreased to the point that the object begins to float! Insert the value of salinity and temperature at which the object began to float into water density calculator, and you should be able to estimate those densities with relatively good precision!

You can also choose one of the objects from the list to see if it floats or sinks. We take into account some average values so the results may not be accurate in every case (especially for fruit).

## Should eggs float or sink?

Well, the most accurate answer is: it depends!

Firstly, there is a difference between fresh and rotten eggs. When you want to boil an egg, you can put it in pure lukewarm water before testing it by opening. If it sinks, it should be fresh, but if it floats, it's most probably stale. As an egg ages, some gases (e.g. hydrogen sulfide) are produced inside, and they escape the object through pores in the shell. As a result, the mass decreases, but the volume of the egg remains constant, so the density decreases.

The second factor is the salinity of the water. When we are cooking we most often use pure or slightly salty water, so the explanation above holds true. But if we put an egg into a really salty environment (like the Dead Sea which has a salinity of around `342‰`), both the fresh and rotten variety will float. It would therefore be impossible to decide whether the egg is fresh or not using this method. Check what is the critical value of salinity that makes it possible for a fresh egg to float for yourself with our density of water calculator!

## Speed of sound in water

There is a simple formula which tells about the speed of sound in air, `c`. It can be rewritten as:

`c = √(γ * p / ρ)`,

where `γ` is the adiabatic index, `p` is pressure, and `ρ` is the density of air. For most liquids, the relationship is usually not that simple, but in general, the speed of sound in the water rises when the density decreases over a wide range of temperatures. The knowledge of the speed of sound dependence in salt water is crucial for all research involving sonar measurements.

Wojciech Sas, PhD candidate
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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