How this instrument works
Density is mass packed into a given volume, and for water it is not a constant — it is a function of temperature, ρ(T). The Kell equation captures that function as a rational curve: a fifth-degree polynomial in temperature divided by a simple linear term, fitted directly to painstaking pycnometer measurements rather than derived from first principles. It is not a law of physics in the Newton's-second-law sense; it is the most trusted empirical map from a thermometer reading to a density figure that liquid water actually obeys.
The curve is not monotonic. Cool water from room temperature and it gets denser, as intuition expects, but only down to about 4°C — this calculator's own reference points put the true maximum at 999.972 kg/m³, not the tidy 1000 kg/m³ once used to define the kilogram itself. Below that point density falls again as the water approaches freezing, the hydrogen-bonding anomaly that makes ice float and lets a lake's coldest water rise toward the surface in winter instead of sinking.
The fit is only as good as its calibration range: valid from 0°C to 100°C at ordinary atmospheric pressure, the liquid range of water at sea level. Push past either edge — supercooled water below 0°C, superheated water under pressure, or seawater carrying dissolved salts — and this particular curve no longer applies; those regimes need the fuller IAPWS-95 formulation or a salinity-corrected equation of state, not this one.
- Enter the Water temperature in °C — or switch the field's unit menu to °F if that is what your thermometer reads.
- Leave it at the default, 20°C, to see standard room-temperature water, or set any value from 0°C to 100°C.
- Read the result in the Water density field, reported in kg/m³ to six decimal places.
- Toggle Water density to g/cm³ if you need the figure a hydrometer or lab balance would recognize.
- Watch for the range warning below 0°C — it flags that the Kell fit is no longer valid there.
Worked example — calibrating a pipette at 20°C
Set the Water temperature field to 20°C — the reference condition ISO 4787 specifies for testing volumetric glassware — and the Kell equation returns 998.204132201 kg/m³. That is about 1.8 kg/m³, roughly 0.18 percent, below the schoolbook 1000 kg/m³ figure: a small gap, but one a metrology lab cannot ignore when it is weighing water to certify a pipette's delivered volume.
Switch Water density to g/cm³ and the same figure reads 0.998204 g/cm³, the number a lab balance and a temperature-corrected weighing table both use to convert a measured mass of water into the volume it actually occupies — the working principle behind gravimetric calibration of glassware worldwide.
Questions
Why isn't water density exactly 1000 kg/m³?
Because 1000 kg/m³ was always an approximation. The kilogram was originally defined, in 1799, as the mass of one liter of water at its densest point, but later, more precise measurement — the basis of the Kell equation — puts that true maximum at 999.972 kg/m³, not 1000. At 20°C, room temperature, the figure drops further to 998.204 kg/m³.
Why does water get denser as it cools, then reverse near 4°C?
Most liquids just keep contracting as they cool. Water does too, until it nears 4°C, where hydrogen bonds start locking molecules into the more open, cage-like arrangement that becomes ice. That structure takes up more room per molecule, so density peaks around 999.972 kg/m³ near 4°C and falls on both sides of it — which is why ice floats and a pond freezes from the top down.
What is the Kell equation and who developed it?
It is a curve fit, published by George Kell in 1975 in the Journal of Chemical & Engineering Data, built from precision pycnometer measurements of pure water rather than derived from theory. It expresses density as a fifth-degree polynomial in temperature divided by a linear term and has served since as the metrology community's working reference for liquid water's density at atmospheric pressure.
What temperature range does this calculator cover?
0°C to 100°C at standard atmospheric pressure — water's liquid range at sea level, and the span the Kell fit was calibrated against. Enter a value below 0°C and the instrument flags it: the correlation was never fitted to supercooled or frozen water, so results outside that window are not something a Kell-equation calculator can vouch for.
Does dissolved salt change the density this calculator reports?
Yes, and this instrument does not account for it. Seawater at typical ocean salinity is about 2.5 percent denser than pure water at the same temperature because dissolved ions add mass without adding much volume. Salinity-corrected density needs a different equation of state, such as the oceanographic TEOS-10 standard — this page's Kell equation assumes pure water throughout.