The water viscosity calculator above turns a temperature into a viscosity. It does not look the answer up in a table and interpolate between rows; it evaluates the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance, the release known as R12-08, which is the reference correlation that the published tables themselves are generated from. Give it a temperature and it produces dynamic viscosity in pascal seconds, millipascal seconds and centipoise, kinematic viscosity in square metres per second and centistokes, and the density those two are linked by.
Arb Digital publishes this alongside two adjacent pages, and the boundary between them is worth stating before you use any of them. The air viscosity calculator uses Sutherland's law, an empirical two-constant relation for gases that works well for air across a very wide temperature range and does not describe a liquid at all. The viscosity converter rescales a viscosity you already have between poise, stokes, pascal seconds and their relatives; it changes units, never conditions. This page is the one that produces the number in the first place, from a temperature, for water.
What This Water Viscosity Calculator Does
Viscosity is a fluid's resistance to shearing. Dynamic viscosity, μ, is the constant of proportionality between shear stress and velocity gradient, in pascal seconds. Kinematic viscosity, ν, is dynamic viscosity divided by density, in square metres per second. They describe the same fluid and are not interchangeable: μ governs the force a shear takes, ν governs how fast momentum diffuses, and the Reynolds number is built from ν.
Water at 20 °C has a dynamic viscosity almost exactly 1.0016 mPa·s, which is where the old habit of calling water "one centipoise" comes from. That single figure is quoted so often that it gets used at temperatures where it is badly wrong. At 0 °C water is about 1.79 mPa·s, nearly eighty per cent thicker. At 100 °C it is about 0.28 mPa·s, less than a third of the room-temperature value. The whole point of this page is that the temperature you actually have is rarely 20 °C.
How to Use It
- Enter the temperature and pick its unit. Use the temperature of the water itself, not the ambient air, which in a buried pipe or a heat exchanger can be a long way apart.
- Leave the density on automatic for ordinary work. That covers liquid water at atmospheric pressure: pipework, open channels, cooling loops, laboratory viscometry.
- Switch to a manual density for anything pressurised. Viscosity depends on temperature and density, so if you are working at high pressure or with steam, take the density from a steam table and enter it here.
- Set a comparison temperature. The second figure is what tells you whether a temperature change matters. A ten-degree swing near freezing changes viscosity far more than a ten-degree swing near boiling.
- Take the kinematic value into any Reynolds calculation. That is the one the Reynolds number calculator and the friction factor calculator want, and using the dynamic value there is the most common single error in pipe work.
The Formula: How IAPWS R12-08 Is Built
The formulation writes viscosity as a product of three factors rather than a single polynomial: μ = μ0(T) × μ1(T, ρ) × μ2(T, ρ), all in reduced form against the critical constants Tc = 647.096 K, ρc = 322 kg/m³ and a reference viscosity of 1 μPa·s.
The first factor, μ0, is the dilute-gas limit — the viscosity water vapour would have if the molecules were far enough apart to ignore each other. It is a function of reduced temperature alone: μ0 = 100√T̄ ÷ Σ(Hi / T̄i) over four coefficients. The second factor, μ1, carries everything that finite density does, as an exponential of a double sum in (1/T̄ − 1) and (ρ̄ − 1) with twenty-one non-zero coefficients. In the liquid region this factor is doing almost all the work: at room temperature it multiplies the dilute-gas value by roughly ninety.
The third factor, μ2, is the critical enhancement, which accounts for viscosity diverging at the critical point. The release states that it contributes more than two per cent only inside a narrow window, roughly 645.91 K to 650.77 K and 245.8 to 405.3 kg/m³, and that outside it the enhancement is smaller than the uncertainty of the correlation itself. IAPWS explicitly permits setting μ2 = 1 outside the critical region, and this tool does that. It is the one deliberate simplification on the page.
The density that μ1 needs, in automatic mode, comes from the standard fifth-order density correlation for air-free liquid water at atmospheric pressure, which reproduces the familiar maximum density of 999.972 kg/m³ at just under 4 °C. Kinematic viscosity is then simply ν = μ ÷ ρ. Working the default through: at 20 °C the density correlation gives 998.204 kg/m³, the formulation returns 1001.6 μPa·s, and dividing gives 1.0034 × 10−6 m²/s, or 1.0034 cSt. The value at 20 °C matters because it is the one the international standard fixes as the anchor for water viscometry.
Where the Formulation Stops Being Valid
R12-08 covers the stable fluid region from the melting curve to 1173 K, at pressures to 300 MPa in the lower part of that range, with declared uncertainties from about one per cent in the ordinary liquid region to several per cent at extreme conditions. That envelope is not the envelope of this page.
The limiting factor here is the density. In automatic mode the tool supplies the density of liquid water at one atmosphere, which is only meaningful between the freezing and boiling points; ask it for 150 °C and it will say so, because water at one atmosphere is not liquid there. If you need viscosity at 200 °C in a pressurised loop, take the density from a steam table at your actual pressure and switch the density source to manual. The formulation itself handles the temperature perfectly well.
A second boundary is dissolved content. Everything here is ordinary pure water. Seawater at typical salinity is several per cent more viscous at the same temperature, glycol mixtures are dramatically more viscous, and a slurry is not Newtonian at all. For those fluids the temperature dependence still shows the shape of the curve, but the magnitude is yours to establish.
Why the Kinematic Value Is the One Pipe Work Wants
The Reynolds number is ρVD/μ, which is identically VD/ν. Both forms are correct, and the second is less error-prone because it needs one fluid property instead of two. That is why fluids handbooks tabulate kinematic viscosity for water and why almost every pipe-flow chart is drawn against it.
The consequence is larger than people expect. Take a 50 mm line carrying water at 1 m/s. At 5 °C the kinematic viscosity is about 1.518 cSt and the Reynolds number is around 32,900. At 60 °C it is about 0.474 cSt and the Reynolds number is around 105,500 — more than three times higher, same velocity, same pipe. The pipe flow calculator and the friction loss calculator both take viscosity as an input, and feeding either a room-temperature default when the line runs at 60 °C is a common source of error.
It cuts the other way in cold conditions. A gravity-fed or low-head system designed on 20 °C properties can fail to deliver in winter, not because anything broke but because the water got thicker.
Viscosity Is Not Density, and the Two Move Differently
People often reach for viscosity when what they actually want is density, and the two behave nothing alike over the same temperature range. Between 0 °C and 100 °C the density of water falls by about four per cent, from roughly 999.8 to 958.4 kg/m³, and it does so non-monotonically, rising slightly to a maximum near 4 °C before falling. Over the same interval the dynamic viscosity falls by a factor of about 6.4, monotonically and steeply.
That is why hydrostatic calculations can usually get away with a fixed water density while viscous ones cannot get away with a fixed viscosity. If the density itself is what you need, the water density calculator is the dedicated page, and the density converter handles the unit side.
Reading Centipoise, Centistokes and the Older Units
Water work is full of legacy units, and the arithmetic linking them is worth memorising. One centipoise is exactly one millipascal second. One centistokes is exactly one square millimetre per second, or 10−6 m²/s. Because water near room temperature has a density close to 1000 kg/m³, its viscosity in centipoise and in centistokes are numerically close — convenient, and a trap, because for any other fluid they differ by the density ratio.
Two families of empirical scales appear on older equipment and are deliberately not produced here. Saybolt Universal Seconds and Engler degrees come from timed efflux through a standard orifice, and their relationship to kinematic viscosity is non-linear, so no single multiplier converts them. For the pressure and temperature units that sit alongside viscosity on a typical data sheet, the pressure converter and the temperature converter cover the rest.
Where a Small Temperature Error Costs You Most
Viscometry is the obvious case. Capillary viscometers are calibrated against water, and a bath that drifts by a degree near 20 °C introduces roughly a 2.3 per cent viscosity error — more than an order of magnitude larger than the uncertainty of the formulation itself. That is why standards fix the bath temperature so tightly.
The sensitivity is not constant. Near freezing, one degree changes viscosity by about 2.7 per cent; near boiling, about 1.2 per cent. The same instrument tolerance therefore means very different things at different working points, and a cold-water rig needs tighter temperature control than a hot-water one for the same accuracy. For an independent cross-check of any value here, the NIST Chemistry WebBook thermophysical properties of fluid systems generates the same quantities from the same underlying formulations.
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Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using 1 cP for every temperature — that figure belongs to water near 20 °C and is out by a factor of six at the ends of the liquid range.
- Feeding dynamic viscosity into a Reynolds number that wants kinematic — they differ by the density, roughly a factor of a thousand in SI units, so the mistake is usually obvious in the result and occasionally is not.
- Asking for a temperature outside the liquid range on automatic density — the correlation for atmospheric liquid water stops at the freezing and boiling points, and beyond them you must supply a density yourself.
- Assuming Sutherland's law works for water — it is a gas relation, it predicts viscosity rising with temperature, and liquids do the opposite.
- Treating seawater, glycol or a slurry as water — dissolved and suspended content changes the magnitude, and a slurry may not be Newtonian at all, so no single viscosity describes it.
Related Free Tools From Arb Digital
For the gas equivalent of this page, use the air viscosity calculator, which applies Sutherland's law; to move an existing figure between poise, stokes and SI units, use the viscosity converter. The water density calculator covers the other temperature-dependent property, and the Reynolds number calculator is where the kinematic value goes next. For pipework, the flow rate calculator turns a velocity into a delivered volume. Open channels are handled by the open channel flow calculator, and everything Arb Digital publishes is indexed on the free online tools hub. The viscous-flow and boundary-layer theory behind all of it is developed in MIT OpenCourseWare's 2.25 Advanced Fluid Mechanics.
Frequently Asked Questions
About 1001.6 micropascal seconds, which is 1.0016 millipascal seconds or 1.0016 centipoise. Divided by the density of 998.204 kilograms per cubic metre it gives a kinematic viscosity close to 1.0034 square millimetres per second, or 1.0034 centistokes. This is the value international standards fix as the anchor point for water viscometry, which is why so many data sheets quote water as one centipoise.
The IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance, release R12-08. It expresses viscosity as a dilute-gas term in temperature alone, multiplied by a finite-density term with twenty-one coefficients, multiplied by a critical enhancement term. The critical enhancement is set to one, which the release itself permits for use outside the narrow region around the critical point where it matters.
The underlying formulation is valid from the melting curve to 1173 kelvin. This page is narrower because of its density source: on automatic it uses a correlation for liquid water at atmospheric pressure, which is meaningful only between the freezing and boiling points. Switch the density source to manual and enter a density from a steam table, and the formulation will handle temperatures well beyond that range.
Dynamic viscosity relates shear stress to velocity gradient and is measured in pascal seconds. Kinematic viscosity is dynamic viscosity divided by density, measured in square metres per second, and it describes how quickly momentum diffuses through the fluid. The Reynolds number is built from the kinematic value, so that is the one most pipe and channel calculations want.
Because the mechanisms are different. In a gas, viscosity comes from molecules carrying momentum between layers, and hotter molecules move faster and carry more, so viscosity rises with temperature. In a liquid, viscosity comes from molecules having to break free of their neighbours to slide past, which is an activated process that gets easier as temperature rises. That is why Sutherland's law works for air and would be badly wrong for water.
The converter takes a viscosity you already have and rescales it between poise, stokes, pascal seconds and their relatives. It changes units and never changes conditions, so it cannot tell you what water is doing at 60 degrees. This page produces the value itself from a temperature. Use this one to get the number and that one to express it in whatever unit your data sheet expects.
No. Everything here is ordinary pure water. Seawater at typical salinity is several per cent more viscous than fresh water at the same temperature, and glycol mixtures are far more viscous and have a quite different temperature curve. The shape of the temperature dependence is still informative, but the magnitude is not, so for those fluids use a property source specific to the mixture.
Very little at ordinary pressures. The formulation depends on temperature and density, and liquid water is nearly incompressible, so going from atmospheric pressure to a few tens of bar barely moves the density and therefore barely moves the viscosity. It becomes significant only at the hundreds of megapascals the full formulation is designed to cover, at which point you should supply the density yourself.
This page evaluates a published reference correlation for pure water and omits the critical enhancement term, which the release permits outside the near-critical region. Property values for a real system should be confirmed against the source appropriate to that fluid.
