Viscosity Converter (Dynamic and Kinematic)

Dynamic and kinematic viscosity are different quantities and ν = µ / ρ, so converting between them needs the fluid’s density — which is why water is 1.0016 cP and 1.0034 cSt and neither is exactly 1. Sixteen units plus Saybolt from the real ASTM D2161 equation, ISO 3448 and SAE J300 explained rather than conflated, and ASTM D341 for the one temperature conversion that can be done honestly.

ν = µ / ρ, and everything else follows from it

Two different quantities, and the bridge between them

Reference values, with the density that connects them

ISO 3448: the grade IS the viscosity, at 40 °C, ±10%

SAE J300: a grade is a range with several criteria, not a number

Three oils of the same ISO VG, and three different SAE answers

Saybolt: the constant is an asymptote, not a conversion

Two quantities, one density, and two standards measured sixty degrees apart

Dynamic and kinematic viscosity are different physical quantities, and ν = µ / ρ. That single equation is why this page exists and why a search engine’s unit widget cannot replace it: the conversion needs the fluid’s density, and nothing in the phrase “convert 40 cSt to cP” says what the fluid is. Dynamic viscosity is resistance to shear — stress per unit velocity gradient, in pascal-seconds. Kinematic viscosity is that divided by the density: a momentum diffusivity, in square metres per second, and the quantity that appears in the Reynolds number. They are measured by different instruments, which is most of why both exist. A rotational viscometer measures torque against speed and gives you µ. A capillary viscometer times a fluid falling through a tube under its own weight, so the density is already baked into what it measures, and gives you ν.

Inside each family the conversions are exact definitions. One centipoise is one millipascal-second, exactly, because the poise is defined as 0.1 Pa·s. One centistokes is one square millimetre per second, exactly. So water at 20 °C is 1.0016 cP and 1.0034 cSt — near 1 in both, exactly 1 in neither, and 0.18% apart. Verify that coincidence and it stops being mysterious: in these units you are dividing by water’s density expressed in grams per cubic centimetre, which is 0.9982, and dividing by something that close to 1 barely moves the number. The CGS units were built around water. That one accident is the reason people treat the two quantities as interchangeable, and it stops working the moment the fluid changes: for an engine oil at 870 kg/m³ the cSt number is 15% above the cP number, and for air, at 1.204, it is 830 times larger. Air is worth dwelling on. It is about fifty-five times LESS viscous than water dynamically and about fifteen times MORE viscous kinematically, because there is hardly any mass there to move. Both statements are true and they point opposite ways.

An SAE engine oil grade is not a number, it is a range with several criteria. The figure before the W is defined by low-temperature behaviour and by nothing else: a cranking viscosity on a cold-cranking simulator and a pumping viscosity on a mini-rotary viscometer, measured between −10 °C and −40 °C depending on the grade, with the pumping test always five degrees colder than the cranking one. The second figure is a kinematic viscosity band at 100 °C AND a high-shear-rate viscosity floor at 150 °C. Two criteria, so the band alone does not fix the grade — and since 2013 it fixes it even less, because the new SAE 8, 12 and 16 overlap their neighbours where the old ladder abutted exactly. A measured 7.0 mm²/s at 100 °C satisfies SAE 12, 16 and 20 simultaneously. An SAE 40 is not one specification either: its 150 °C floor is 3.5 mPa·s if it is a 0W-40, 5W-40 or 10W-40 and 3.7 otherwise.

ISO VG and SAE cannot be converted, and this is the page’s sharpest claim. ISO 3448 defines a viscosity grade as the kinematic viscosity at 40 °C, plus or minus ten per cent — so there is nothing to convert within it, the grade IS the viscosity. SAE’s second number is measured at 100 °C. Sixty degrees apart, and what happens in between is the oil’s viscosity index, a property neither number carries. Three oils can all be ISO VG 46, identical at 40 °C and indistinguishable by the ISO test, and be 5.4, 6.8 and 8.5 mm²/s at 100 °C, landing in different SAE bands. Every ISO-to-SAE chart on the web implies the conversion exists; what it has actually done is assume a viscosity index of about 100 without saying so. This page refuses the single-number conversion and offers the honest one instead: give it the 40 °C AND the 100 °C figures from a data sheet and it fits ASTM D341’s Walther relation — log log of viscosity against log of absolute temperature is a straight line — and reports the viscosity at whatever temperature you ask for, with the fitted slope shown.

Saybolt is not a constant either. Saybolt Universal seconds are still on American data sheets, and the conversion everyone quotes — divide by about 4.635 — is an asymptote rather than a factor. ASTM D2161 publishes a full equation, and the constant alone is 72% low at 2 cSt, 5.3% low at 20 cSt, and inside a tenth of a per cent only above about 80 cSt. This page uses the equation in both directions, inverting it numerically for Saybolt input, and it reproduces five rows of the standard’s own table to the digit printed. The standard’s number is 4.6324, not 4.635; and its 210 °F constant of 4.664 turns out to be the 100 °F one put through its own temperature correction, which is a satisfying thing to be able to check. For the density this page cannot do without, see the density and specific gravity converter, which also handles API gravity if that is what your data sheet gives you; for surface finish and hardness on the same components, the surface roughness converter and the hardness scale converter.

Frequently asked questions

Related calculators

References

1. ASTM D2161, Standard Practice for Conversion of Kinematic Viscosity to Saybolt Universal Viscosity or to Saybolt Furol Viscosity. The current edition is behind a paywall and was not fetched. The equation used here was read from the archived 1966 edition and then VERIFIED against five of that edition’s own Table 1 rows, which it reproduces to the digit printed: 2.0 cSt → 32.6 SUS, 4.0 → 39.2, 10 → 58.8, 20 → 97.8, 50 → 233. The temperature correction is U(t) = U(100 °F) × (1 + 0.000061(t − 100)), and the standard’s own 210 °F constant of 4.664 is recovered from its 100 °F constant of 4.6324 by exactly that factor, to 0.011%.
2. ISO 3448, Industrial liquid lubricants — ISO viscosity classification. Cited by number; the standard was not fetched. What was checked instead: the grade number IS the mid-point kinematic viscosity at 40 °C in mm²/s, the limits are that ±10%, and the eighteen grades from VG 10 upward are 10^(n/6) rounded — six steps to the decade — to within 2.2%. Grade list cross-read from Chevron Marine Products’ viscosity-class technical bulletin.
3. SAE J300, Engine Oil Viscosity Classification. An SAE standard and copyrighted; it was not fetched. The band limits used here were read from two independent secondary sources and cross-checked against each other: the Wikipedia article on SAE J300 (2021 revision) and Lubrita’s news item on the addition of SAE 8 and 12. Both give SAE 8 as 4.0 to below 6.1 mm²/s at 100 °C with a 1.7 mPa·s HTHS floor and SAE 12 as 5.0 to below 7.1 with 2.0, and they agree to the digit.
4. ASTM D341, Standard Practice for Viscosity-Temperature Equations and Charts for Liquid Petroleum or Hydrocarbon Products. Cited by number; not fetched. The form used — log₁₀ log₁₀ Z = A − B log₁₀ T with T in kelvin and Z = ν + 0.7 + exp(−1.47 − 1.84ν − 0.51ν²) — was read from Technical Toolboxes’ knowledge-base article on the practice, and is checked here by round-tripping: fitted to a pair of measured viscosities it reproduces both to a part in 10⁶.
5. Engineering ToolBox. Water — Dynamic and Kinematic Viscosity at Various Temperatures and Pressures. Water’s dynamic viscosity at 20 °C is 1.0016 mPa·s. Combined with Tanaka’s density that gives 1.0034 mm²/s, so water at 20 °C is 1.0016 cP and 1.0034 cSt — near 1 in both, and exactly 1 in neither.
6. Tanaka M, Girard G, Davis R, Peuto A, Bignell N. Recommended table for the density of water between 0 °C and 40 °C based on recent experimental reports. Metrologia 38 (2001) 301–309. doi:10.1088/0026-1394/38/4/3. The density used in every dynamic-to-kinematic conversion of water on this page.