Why Is Water Densest at 4°C? A Deep Dive Into the Anomaly
Deep dive: This is the expert companion to our plain-language guide. For the short version — water’s strange chemistry in everyday terms — see: Why Is Water So Weird? The Chemistry That Makes Life Possible.
Our Complete guide gave the one-sentence answer to the density puzzle: cooling water packs its molecules closer together, until hydrogen bonds start building open structures that take up more room, and the two effects cross at about 4 °C. That answer is correct, but it leaves the interesting questions unasked. Exactly how dense, at exactly what temperature? What is the number that changes sign at 4 °C? Why does pressure erase the effect, and why does salt water not have it at all? And what do physicists still argue about? This Deep dive answers those questions, with the numbers researchers actually use.
The numbers first: density from 0 °C to 100 °C
For pure water at normal atmospheric pressure, the measured densities are:
| Temperature | Density (kg/m³) |
|---|---|
| 0 °C (liquid) | 999.84 |
| 3.98 °C — the maximum | 999.97 |
| 10 °C | 999.70 |
| 20 °C | 998.21 |
| 30 °C | 995.65 |
| 100 °C | 958.37 |
| 0 °C (ice) | 916.7 |
Two things stand out. First, the whole anomaly lives in a sliver: water at 0 °C is only 0.13 kg/m³ less dense than water at 4 °C, a difference of about one part in eight thousand. The peak is real and precisely measured — precision dilatometry puts the temperature of maximum density at 3.98 °C — but it is small. Second, the jump on freezing is enormous by comparison. A litre of water becomes about 1.09 litres of ice, a volume expansion of roughly 9%. That is the part that bursts pipes in winter and puts an insulating lid on lakes.
Two forces, one crossing point
The density maximum is a crossing point between two effects that pull in opposite directions. Cool any liquid and its molecules slow down and pack closer together, which raises the density. Water does this too, down to about 4 °C. But water molecules also attract each other through hydrogen bonds, and those bonds favour open, spacious arrangements. As the water cools, more of these open arrangements survive, which lowers the density. Above 4 °C the packing effect wins; below 4 °C the open-structure effect wins; at 3.98 °C they balance exactly.
Thermodynamics gives this balance a single number: the isobaric thermal expansion coefficient, αP, which measures how much a fixed mass of water expands when warmed at constant pressure. For almost every liquid it is positive. For water it is positive above 4 °C (about +2.1 × 10−4 per °C at 20 °C), exactly zero at the density maximum, and negative below it (about −0.7 × 10−4 per °C at 0 °C). A negative expansion coefficient means the liquid expands as it cools — the signature of the anomaly, written as one number. Cho, Singh and Robinson showed in 1996 that this behaviour follows from a competition between open, low-density molecular arrangements and collapsed, high-density ones, with temperature shifting the balance between them.
The molecule that builds open space
The open arrangements exist because of the shape of the water molecule. Two hydrogen atoms sit on the same side of one oxygen atom, bent at an angle of about 104.5 degrees, and oxygen pulls the shared electrons toward itself. The result is a polar molecule: the oxygen end slightly negative, the hydrogen ends slightly positive. The positive hydrogen of one molecule is attracted to the negative oxygen of a neighbour. That attraction is a hydrogen bond, worth roughly 20–25 kJ/mol — about a twentieth of the covalent bond inside the molecule, but there are vast numbers of them, constantly breaking and reforming on picosecond timescales.
Each water molecule can form up to four hydrogen bonds: two through its hydrogen atoms, two through the lone pairs on its oxygen. Four bonds pointing outward in roughly tetrahedral directions is what makes the open structure possible. In ordinary ice (ice Ih), every molecule is bonded to four neighbours in a hexagonal lattice full of empty channels — which is why ice is less dense than the liquid it came from. In the liquid, the same tetrahedral tendency survives as a flickering, local order. Cooling lets more of it persist, and the liquid opens up. Looked at shell by shell, the first shell of neighbours around a molecule contracts on cooling while the second shell expands; around 4 °C the two changes cancel, and the density peaks.
A tale of two liquids
The fullest modern picture of this competition comes from a 2016 review by Gallo and colleagues, “Water: A Tale of Two Liquids”. It describes liquid water as a fluctuating mixture of two kinds of local environment: a low-density liquid (LDL) of open, well-bonded, tetrahedral arrangements, favoured by enthalpy, and a high-density liquid (HDL) of collapsed, disordered arrangements, favoured by entropy. Warm water is mostly HDL-like; cold water carries more LDL-like patches. The density maximum is where the trade-off between them tips over.
The idea goes further. The review argues that if the two forms could be separated, they would meet at a liquid–liquid critical point deep in the supercooled region — water so cold it should have frozen, but held liquid. That region, roughly between 150 K and 233 K, is called “no-man’s land” because bulk water crystallises there faster than it can be measured. The best evidence comes from droplets cooled so fast they stay liquid: in 2017, Kim and colleagues cooled microscopic droplets to 227.7 K and found maxima in water’s thermodynamic response functions, exactly where the two-liquid picture says the influence of the hidden critical point should be strongest. X-ray studies reviewed by Nilsson and Pettersson in 2015 point the same way, showing fluctuating tetrahedral patches in the liquid at ordinary temperatures.
The quantum twist
There is a subtlety that classical pictures miss: hydrogen is the lightest atom, and its nuclei do not sit still. Their zero-point motion and quantum delocalisation change the effective strength and geometry of hydrogen bonds. Ceriotti and colleagues reviewed these nuclear quantum effects in 2016 and showed they are not a small correction — they shift the balance between open and collapsed structures. Water models that treat hydrogen nuclei as classical point particles put the density maximum several degrees too warm; including the quantum motion brings the models into line with the measured 4 °C. The anomaly is, in part, a quantum effect visible in a glass of water.
Pressure and salt: the anomaly is fragile
The density maximum is a creature of ordinary pressure. Squeeze water and the open structures collapse: the temperature of maximum density falls with pressure, reaching about −28 °C at 1,000 bar, and the maximum disappears altogether above roughly 1,800 bar, after which water behaves like a normal liquid. At the pressures of the deep ocean, the anomaly is gone, and density is governed by temperature, salinity and compression alone.
Salt kills it too. At the salinity of typical seawater, about 35 grams per litre, the temperature of maximum density is pushed down to about −3.8 °C — below seawater’s freezing point of −1.9 °C. Liquid seawater therefore has no density maximum at all: it just gets denser as it cools, right up to freezing. That is one reason the ocean behaves so differently from a freshwater lake, and why seawater chemistry deserves its own treatment — see our guide to ocean acidification.
Why lakes freeze from the top
The anomaly is the reason a lake in winter has liquid water under its ice. In autumn, the surface water cools, grows denser and sinks, and warmer water rises to take its place. This overturn continues until the whole lake reaches 4 °C. Cool the surface further and the pattern reverses: water below 4 °C is less dense, so it stays on top, cools to 0 °C and freezes. The ice, lighter still, floats as an insulating lid, while the densest water — at about 4 °C — sits at the bottom all winter. Fish survive underneath it. In spring the process runs in reverse: the ice melts, the surface warms toward 4 °C, grows denser and sinks, and the lake mixes again. Lakes that do this twice a year are called dimictic, and the twice-yearly turnover carries oxygen down and nutrients up.
If water behaved like an ordinary liquid, lakes would freeze from the bottom up, and cold-climate lakes would freeze solid each winter. The 4 °C maximum is a small number with outsized consequences: it is the difference between a lake that keeps a living refuge through winter and one that does not.
Not unique — but rare
Textbooks often say water is the only substance that expands when it freezes. That is not true: bismuth, silicon, germanium and gallium all expand on freezing too. What is rare about water is the density maximum in the liquid itself, just above freezing, at everyday pressure. A handful of other liquids show density maxima under some conditions, but none of them is the liquid that covers most of the planet’s surface and fills every living cell. The anomaly matters because it happens in the most ordinary substance there is.
What the model gets wrong
The density maximum itself is settled fact, measured to a hundredth of a degree. The explanation is not finished. The liquid–liquid critical point has never been observed directly in bulk water, because no-man’s land blocks the measurement; the evidence is indirect, from droplets, glasses and simulations. Two-state models fit the thermodynamics well, but a 2026 review notes that a simple mixture of two states cannot reconcile every property at once — some properties follow the two-state fractions and others run against them. And the exact microscopic picture is still argued over: fluctuating patches of two distinct structures, or one continuous distribution of local environments that merely looks two-state in some measurements. The honest summary is that the competition between open and collapsed arrangements explains the density maximum, while the deeper question — whether liquid water is truly two liquids in one — remains open. That is a good place for a science to be: the number is certain, and the reason is still being worked out.
Sources
- Gallo, P., et al. (2016). Water: A Tale of Two Liquids. Chemical Reviews, 116, 7463–7500. Full text (PDF, Boston University)
- Nilsson, A., & Pettersson, L. G. M. (2015). The structural origin of anomalous properties of liquid water. Nature Communications, 6, 8998. nature.com
- Gallo, P., & Stanley, H. E. (2017). Supercooled water reveals its secrets. Science, 358, 1543–1544. Full text (PDF, Boston University)
- Kim, K. H., et al. (2017). Maxima in the thermodynamic response and correlation functions of deeply supercooled water. Science, 358, 1589–1593.
- Cho, C. H., Singh, S., & Robinson, G. W. (1996). An explanation of the density maximum in water. Physical Review Letters, 76, 1651–1654. doi.org
- Kell, G. S. (1977). Effects of isotopic composition, temperature, pressure, and dissolved gases on the density of liquid water. Journal of Physical and Chemical Reference Data, 6, 1109. doi.org
- Ceriotti, M., et al. (2016). Nuclear quantum effects in water and aqueous systems: Experiment, theory, and current challenges. Chemical Reviews, 116, 7529–7550. doi.org
- Mallamace, F., et al. (2012). A singular thermodynamically consistent temperature at the origin of the anomalous behavior of liquid water. Scientific Reports, 2, 993. nature.com
- U.S. Geological Survey. Water density. Water Science School. usgs.gov
- World Ocean Review. Water – a unique molecule. worldoceanreview.com