Water-Cement Ratio

Also known as w/c ratio · w/cm ratio · water cementitious ratio · water to cement ratio · wcm · water binder ratio · how to calculate water cement ratio

wc=mwmc\dfrac{w}{c} = \dfrac{m_w}{m_c}

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Two weights and a division. It is the simplest calculation in concrete technology and the one that governs almost everything: compressive strength, tensile strength, permeability, chloride resistance, sulphate resistance, freeze-thaw durability, drying shrinkage and creep. When a durability specification wants to say something serious, it says it as a maximum water-cement ratio, because that one number reaches further into the finished material than any other.

Permeability is where the ratio earns its place in a specification more than strength does. As the ratio rises, the capillary pore network in the paste goes from disconnected pockets to a continuous, interconnected system — and the transition is not gradual. Below roughly 0.40 to 0.45, with reasonable curing, the capillaries in a mature paste are largely segmented and the concrete is very difficult for water and dissolved ions to move through. Above it they join up, and permeability climbs by orders of magnitude over a narrow band. Everything that destroys concrete slowly — chloride reaching the reinforcement, sulphate reaching the paste, water freezing where it should not be — is a transport problem first, and the ratio is what decides whether the transport happens. This is why a low water-cement ratio is worth specifying even where the strength is not needed.

Now the numerator, because it is where the mistake lives. The free water is not the water on the mix design and it is not the water that came out of the meter. It is the batched water, plus the surface moisture riding on wet sand and stone, minus the water a dry aggregate will absorb out of the mix, plus the water content of any liquid admixture dosed in quantity. A sand at six percent moisture in an ordinary mix carries enough surface water on its own to move the ratio by around 0.05, which on Abrams' curve is several megapascals of strength that nobody ordered. Automated plants with moisture probes handle this continuously; plants without them handle it on a technician's judgement, and judgement is worse after rain.

The denominator carries a convention too. Where supplementary cementitious materials are used the ratio is normally written w/cmw/cm, over the total cementitious mass — cement plus fly ash plus slag plus silica fume. But not every specification counts them the same way. Some durability provisions credit only a fraction of the supplementary material, or cap how much may be counted, precisely because a kilogram of fly ash does not do the same work as a kilogram of portland cement at early ages. Two engineers can compute two different ratios from the same batch ticket and both be right about their own document. Read which one yours means before arguing about a second decimal place.

One more thing worth knowing. There is a floor on how low the ratio can usefully go, and it is around 0.35 to 0.40 depending on how you count. Below that, there is not enough water present to hydrate all the cement even in principle, so some of it stays unreacted forever, acting as a very expensive fine filler. Mixes are run below the floor on purpose — the unhydrated cement is dense and strong and the pore structure is superb — but they are unforgiving. There is no spare water in them, so a curing lapse does not merely slow the strength gain; it stops it permanently in the surface layer that dried.

Water-Cement Ratio
wc=mwmc\dfrac{w}{c} = \dfrac{m_w}{m_c}
mwmcwc
Where
  • w/cw/c= Water-cement ratio
  • mwm_w= Free water mass (kg)
  • mcm_c= Cementitious mass (kg)
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