The water density calculator above returns the density of liquid water as a function of temperature, with additional first-order corrections for pressure and for dissolved salt. Density is the quantity that connects a volume to a mass, so it sits underneath a great deal of practical arithmetic: what a tank of water weighs, how much a pump has to lift, whether an object floats, and how a heated system behaves as it circulates.
Arb Digital builds free tools that state the boundary between what they compute properly and what they only approximate. Temperature is handled properly here, through a published polynomial for air-free water at atmospheric pressure that reproduces the standard tables to within a few thousandths of a kilogram per cubic metre. Pressure and salinity are handled as linear corrections, which is honest for ordinary engineering and not good enough for oceanography or for high-pressure steam work. Both limits are spelled out below.
What This Water Density Calculator Does
The temperature dependence comes from a rational polynomial fit for air-free water at one atmosphere, valid from 0 to about 150 °C. It gives 999.840 kg/m³ at 0 °C, 999.972 kg/m³ at 3.98 °C, 998.204 kg/m³ at 20 °C and 958.364 kg/m³ at 100 °C. Those are the numbers in the standard reference tables, and they come out of the fit rather than being pasted in.
The pressure term treats water as very slightly compressible, with an isothermal compressibility of about 4.5 × 10−10 per pascal. That amounts to roughly a 0.45 per cent increase in density per hundred bar, so at 100 metres depth the correction is about 0.45 kg/m³, which is small but not always negligible. The reference pressure is one standard atmosphere, so at 1.01325 bar the correction is exactly zero.
The salinity term adds about 0.759 kg/m³ for each gram of dissolved salt per kilogram of water. That constant is chosen so that standard seawater at 35 g/kg and 20 °C comes out at 1,024.8 kg/m³, matching the accepted value. Away from that point the linear approximation drifts, because the real haline contraction coefficient itself varies with temperature and pressure.
How to Use It
- Enter the temperature of the water itself, not the air around it. In a heated or stratified body these can be far apart, and the density follows the water.
- Set the pressure only if it is well above atmospheric. For anything at the surface, leave it at 1.01325 bar and the pressure correction vanishes.
- Enter salinity in grams per kilogram. Fresh water is zero; ocean water is near 35. Tap water and most process water is close enough to zero that the term does not matter.
- Give a volume to get a mass. This is the step people most often want, and it is where the density figure earns its keep: a thousand litres of cold water and a thousand litres of near-boiling water differ in mass by about forty kilograms.
- Check the validity note. Outside 0 to 150 °C the polynomial is being used beyond its range, and the tool says so rather than quietly returning a number.
The Anomaly at 4 °C and Why It Matters
Almost every substance gets steadily denser as it cools, right up to the point where it freezes. Water does not. It reaches its maximum density at about 3.98 °C and then becomes less dense as it cools further, so ice at 0 °C is around 8 per cent less dense than the liquid it forms from.
The cause is hydrogen bonding. As water cools towards freezing, its molecules increasingly arrange themselves into the open, tetrahedral network that becomes ice, and that network holds them further apart than random thermal packing does. Below about 4 °C that structural expansion outweighs the ordinary thermal contraction, and the density falls.
The consequences are large. Ice floats, so a frozen lake insulates the water beneath it instead of freezing solid from the bottom. Cooling surface water sinks only until it reaches 4 °C, after which further cooling makes it buoyant, which is why deep lakes sit at close to 4 °C all winter. And it is why freezing damages pipes: water expands as it turns to ice, and it does so with enough force to split metal.
Where the Approximations Stop Being Good Enough
Three situations call for something better than this page.
The first is high pressure and high temperature together, which is the domain of steam plant. There the compressibility is not a constant and the linear correction fails. The authoritative treatment is the IAPWS Industrial Formulation 1997 for the thermodynamic properties of water and steam, which covers 273.15 K to 2273.15 K at pressures up to 100 MPa and is the formulation the power industry uses.
The second is seawater in earnest. Ocean density depends on temperature, salinity and pressure in a coupled way that a single linear coefficient cannot capture, and the internationally endorsed treatment is the IAPWS 2008 formulation for the thermodynamic properties of seawater, valid for standard seawater up to 80 °C and 120 g/kg salinity, which became part of the Thermodynamic Equation of Seawater 2010 used in oceanography.
The third is dissolved or suspended material other than sea salt. Sugar, glycol, slurries and antifreeze change density far more than the salinity term here allows, and each needs its own data. Properties of pure water itself, including the phase change and heat capacity data, are tabulated in the NIST Chemistry WebBook entry for water.
Why the Thermal Change Is Bigger Than It Looks
A drop from 998 to 958 kg/m³ between 20 °C and 100 °C sounds like a rounding error. In a closed heating system it is not, because the water has nowhere to go.
Heat a hundred litres of water from 20 °C to 80 °C and its mass does not change, but its volume grows by about 2.9 per cent, or nearly three litres. In a sealed circuit that expansion has to be absorbed by an expansion vessel; without one the pressure rises until a relief valve opens. This is the entire reason heating systems have expansion vessels, and sizing one is a direct application of the density difference between the cold fill temperature and the maximum operating temperature.
The same density difference drives natural circulation. Warm water is lighter, so it rises, and the resulting convection loop is what made gravity-fed heating systems work before pumps. It is also why a hot water cylinder stratifies, holding usable hot water at the top long after the bottom has cooled.
How This Differs From the Adjacent Arb Digital Tools
The boundary in one sentence: the density calculator divides a mass you measured by a volume you measured for any substance, while this page computes the density of one specific substance, water, from its temperature and condition, with no measurement required. The two answer opposite questions, and the second is the one you need when you have no sample to weigh.
The specific gravity calculator handles the ratio of one density to a reference density, which is the quantity this page reports in its second grid item. The density converter rescales density units, and the temperature converter handles temperatures that arrive in the wrong scale. For what the density is used for, the buoyancy calculator and the hydrostatic pressure calculator both take a fluid density as their key input, and the water heating calculator uses the mass this page derives from a volume.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Assuming water is always 1,000 kg/m³ — that is true only near 4 °C. At 80 °C it is under 972, and in a large volume the difference is tonnes.
- Using the air temperature — density follows the temperature of the water, which in a tank or a lake can be far from the surrounding air.
- Applying the salinity term to other solutes — sugar, glycol and suspended solids change density by much more per gram than sea salt does.
- Extrapolating past 100 °C at atmospheric pressure — water is not liquid there, and the polynomial describes liquid water only.
- Ignoring thermal expansion in a closed system — the same mass occupies more volume when hot, and in a sealed circuit that shows up as pressure.
Related Free Tools From Arb Digital
For density from a measured mass and volume, use the density calculator, and for the ratio to a reference the specific gravity calculator. Rescale units with the density converter, the temperature converter or the volume converter. The buoyancy calculator and hydrostatic pressure calculator consume the density this page produces, the water heating calculator turns a volume into an energy requirement, and the pool volume calculator gives you the volume to start from. The complete free online tools hub lists everything else.
Frequently Asked Questions
At 20 degrees Celsius and atmospheric pressure, pure air-free water has a density of 998.20 kilograms per cubic metre, or 0.99820 grams per cubic centimetre. It is slightly below the round figure of 1,000 that most people remember.
At about 3.98 degrees Celsius, where it reaches 999.972 kilograms per cubic metre. Cooling it further makes it less dense, which is the anomaly that lets ice float and lets lakes freeze from the surface downwards.
Only near 4 degrees Celsius, and only for fresh water. At 20 degrees a litre weighs about 998.2 grams, and near boiling it weighs about 958 grams. The kilogram-per-litre rule is a convenient approximation, not an identity.
Very little at ordinary pressures. Water is nearly incompressible, with a density increase of roughly 0.45 per cent per hundred bar, so a hundred metres of depth adds about half a kilogram per cubic metre.
Standard seawater at 35 grams of salt per kilogram is about 1,024.8 kilograms per cubic metre at 20 degrees Celsius, some 2.7 per cent denser than fresh water at the same temperature. That difference is why floating is noticeably easier in the sea.
Because heating it lowers its density while its mass stays the same, so the same weight now occupies more volume and the surrounding cooler water pushes it upwards. That buoyancy drives convection in tanks, lakes and heating circuits.
Zero to about 150 degrees Celsius for the temperature term, at pressures high enough to keep water liquid. The pressure and salinity corrections are first-order and are intended for moderate conditions rather than for deep ocean or steam plant work.
Slightly. The polynomial used here is for air-free water, and water saturated with air at room temperature is a few thousandths of a kilogram per cubic metre less dense. For nearly every practical purpose the difference is irrelevant.
