Dynamic/kinematic viscosity conversion
Converts between kinematic viscosity nu (mm2/s, cSt) and dynamic viscosity eta (mPa*s, cP) via the lubricant's density -- only one of the two quantities is ever requested at a time.
Formula
eta = nu * rho (with eta in mPa*s, nu in mm2/s = cSt, rho in g/cm3)
eta and nu describe conceptually different things: eta is resistance to shear itself (force per area per velocity gradient), while nu is eta referred to the fluid's density and describes how the fluid behaves under gravity/inertia. Density is therefore not a side note but the actual conversion factor -- without it, no conversion is possible.
What this model does not show
The relation eta = nu*rho holds only for Newtonian fluids, where viscosity does not depend on shear rate. Highly additised multigrade oils or greases can be shear-thinning, for which this simple conversion is only approximate. Both values must also apply at the same temperature -- a density measured at 40 C must not be combined with a viscosity measured at 100 C.
Worked example
A gear oil ISO VG 46 has kinematic viscosity nu = 46 mm2/s (cSt) at 40 C and density rho = 870 kg/m3 = 0.87 g/cm3. Converted: eta = 46 cSt x 0.87 g/cm3 = 40.0 mPa*s = 40.0 cP = 0.0400 Pa*s. Conversely, eta = 40 mPa*s at the same density gives back nu = 40/0.87 ~ 46.0 cSt -- the conversion is exactly reversible at constant density.
Common mistakes
- Treating cSt and cP as the same unit -- they are numerically equal only at rho = 1 g/cm3 (pure water at 4 C), not for oils (rho approx. 0.85-0.90 g/cm3).
- Interpreting an ISO VG grade (e.g. VG 46) as a dynamic viscosity -- ISO VG grades always denote kinematic viscosity at 40 C.
- Combining density and viscosity measured at different temperatures without adjusting density to the viscosity's reference temperature.
Frequently asked questions
What is the difference between dynamic and kinematic viscosity?
Dynamic viscosity eta describes a fluid's internal shear resistance directly (force/area per velocity gradient). Kinematic viscosity nu = eta/rho relates that resistance to density and describes how the fluid moves under gravity and inertia, e.g. when draining from a capillary viscometer.
Why isn't cSt the same as cP?
cSt (centistokes) measures kinematic viscosity, cP (centipoise) dynamic viscosity. The two are numerically equal only when the fluid's density is exactly 1 g/cm3. Mineral oils typically have rho approx. 0.85-0.90 g/cm3, so the numeric values differ noticeably.
Why does ISO VG always refer to kinematic viscosity?
ISO 3448 historically defines viscosity grades (ISO VG) via kinematic viscosity at 40 C, because it was directly measurable with simple efflux viscometers. Datasheets therefore state nu, even though calculations such as the Sommerfeld number need eta.
Does eta = nu*rho hold for every grease?
Only approximately. Greases and many highly additised oils are not strictly Newtonian; their apparent viscosity depends on shear rate. The formula is useful for a quick conversion, not for an exact rheological characterization.
Which density should I use if I only know a 15 C value?
Mineral-oil density falls with rising temperature by roughly 0.00065 to 0.0007 g/(cm3*K). For an accurate conversion at operating temperature, density should be corrected to that temperature or measured there directly, rather than reusing an unadjusted 15 C value.
What comes after this conversion?
With dynamic viscosity at operating temperature you can calculate the Sommerfeld number (calculator 58). If instead the viscosity is needed at a different temperature, the viscosity-vs-temperature calculator (calculator 52) provides that value first.