1.000000e-6
m²/s
1
mm²/s
1
cSt
0.01
St
1.000000e+3
(m·s)/kg
1.000000e-3
m³/kg
1.000000e-6
m²/s
1
mm²/s
1
cSt
0.01
St
1.000000e+3
(m·s)/kg
1.000000e-3
m³/kg
The Kinematic Viscosity Calculator computes the kinematic viscosity of a fluid from its dynamic viscosity and density using the relationship: $$\nu = \frac{\mu}{\rho}$$ where $$\mu$$ is the dynamic viscosity in Pa·s, $$\rho$$ is the fluid density in kg/m³, and $$\nu$$ is the kinematic viscosity in m²/s.
Kinematic viscosity combines a fluid's resistance to flow with its density, representing the ratio of momentum diffusivity to inertial forces. It appears directly in the Reynolds number $$Re = VL/\nu$$ and is essential for predicting flow regimes, boundary layer behavior, and heat and mass transfer in fluid systems.
Kinematic viscosity relates dynamic viscosity to fluid density:
$$\nu = \frac{\mu}{\rho}$$
While dynamic viscosity $$\mu$$ measures the internal friction of a fluid (force per unit area per unit velocity gradient), kinematic viscosity $$\nu$$ incorporates the fluid's inertia through density. This makes kinematic viscosity the natural quantity in many fluid dynamics equations.
The Reynolds number, which determines whether flow is laminar or turbulent, is expressed as:
$$Re = \frac{VL}{\nu}$$
where V is the flow velocity, L is a characteristic length, and $$\nu$$ is the kinematic viscosity. A higher kinematic viscosity means the fluid is harder to set into turbulent motion — viscous diffusion dominates over inertial effects.
Key points about kinematic viscosity:
Kinematic viscosity is measured using capillary viscometers (e.g., Ubbelohde or Cannon-Fenske types), where the fluid flows under gravity and the time is proportional to $$\nu$$.
The calculated kinematic viscosity indicates how quickly momentum diffuses through the fluid. Water at 20°C has ν ≈ 1.004 cSt, air at 20°C has ν ≈ 15.1 cSt, and SAE 30 motor oil has ν ≈ 300–400 cSt at 20°C. Use the kinematic viscosity in Reynolds number calculations to determine whether your flow conditions are laminar or turbulent.
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Results
Water at 20°C: μ = 0.001002 Pa·s, ρ = 998.2 kg/m³ gives ν ≈ 1.004 cSt — the standard reference value.
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Results
Air at 20°C: μ = 1.81×10⁻⁵ Pa·s, ρ = 1.204 kg/m³ gives ν ≈ 15 cSt — about 15× greater than water despite much lower dynamic viscosity.
Kinematic viscosity (ν) is the ratio of a fluid's dynamic viscosity to its density: $$\nu = \mu/\rho$$. It represents the rate of momentum diffusion and has units of m²/s. It is the key viscosity quantity in the Reynolds number and other dimensionless groups used in fluid dynamics.
Kinematic viscosity appears in the Reynolds number $$Re = VL/\nu$$, which determines whether flow is laminar or turbulent. It also governs boundary layer thickness, friction coefficients, and momentum diffusion rates. Using kinematic viscosity simplifies many fluid dynamics equations by combining viscous and inertial effects into one parameter.
The stokes (St) is the CGS unit of kinematic viscosity: 1 St = 1 cm²/s = 10⁻⁴ m²/s. The centistokes (cSt) is 1/100 of a stokes: 1 cSt = 1 mm²/s = 10⁻⁶ m²/s. Centistokes is the most commonly used unit in engineering — water at 20°C has ν ≈ 1 cSt, providing a convenient reference.
Although air's dynamic viscosity (~0.018 cP) is much less than water's (~1 cP), air's density (~1.2 kg/m³) is about 830 times less than water's (~1000 kg/m³). Since $$\nu = \mu/\rho$$, the much lower density of air more than compensates for its lower dynamic viscosity, giving air a kinematic viscosity about 15 times greater than water's.
For liquids, kinematic viscosity decreases with temperature because dynamic viscosity drops significantly while density decreases only slightly. For gases, kinematic viscosity increases with temperature because dynamic viscosity increases and density decreases. Water's kinematic viscosity drops from 1.79 cSt at 0°C to 0.294 cSt at 100°C.
Capillary viscometers (Ubbelohde, Cannon-Fenske, Ostwald types) measure kinematic viscosity directly by timing gravity-driven flow through a calibrated capillary tube. The efflux time is proportional to ν. For opaque fluids, rotational viscometers measure dynamic viscosity, which is then divided by density.
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