Last updated: 2026-06-30

Kinematic Viscosity Units

Kinematic viscosity describes how readily a fluid flows under its own weight. It equals dynamic (absolute) viscosity divided by fluid density:

ν = μ / ρ

where ν is kinematic viscosity (m²/s), μ is dynamic viscosity (Pa·s), and ρ is density (kg/m³).

Conversion Reference

All conversions pivot on the SI base unit, the square meter per second (m²/s).

Unit	Symbol	Equivalent in m²/s	Notes
1 m²/s	m²/s	1	SI base unit
1 cm²/s	cm²/s	1 × 10⁻⁴	Equals 1 stokes (St)
1 mm²/s	mm²/s	1 × 10⁻⁶	Equals 1 centistoke (cSt)
1 St	St	1 × 10⁻⁴	CGS unit; 1 St = 1 cm²/s
1 cSt	cSt	1 × 10⁻⁶	Most common industrial unit; = 1 mm²/s
1 ft²/s	ft²/s	≈ 9.290 × 10⁻²	Imperial unit

cSt and mm²/s Are Identical

Centistokes (cSt) and square millimeters per second (mm²/s) are two names for the same unit. ISO viscosity grade tables list values in mm²/s at 40 °C; lubricant and hydraulic-fluid datasheets almost always print the same number with the cSt label. There is no conversion needed — they are numerically equal.

When Each Unit Appears

m²/s is the SI standard, used in scientific literature and fluid-dynamics simulations. Values for common liquids are very small (water ≈ 1 × 10⁻⁶ m²/s).

cSt (= mm²/s) is the workhorse unit for lubricants, hydraulic oils, and fuels. ISO viscosity grades (ISO VG 32, 46, 68 …) specify kinematic viscosity in mm²/s at 40 °C. Engine-oil grades (SAE 5W-30, 10W-40) are defined by ranges in cSt at 40 °C and 100 °C.

St (= cm²/s) is the original CGS unit, named after Sir George Gabriel Stokes. It is 100 times larger than the centistoke. Modern practice almost always uses cSt; stokes appear mainly in older references and some specialty polymer-processing applications.

ft²/s is used in US civil-engineering and hydraulics contexts (open-channel flow, dam spillways). One ft²/s ≈ 92,903 cSt — much larger than any common liquid at room temperature.

Viscosity of Common Fluids

Fluid	Kinematic viscosity at 20–25 °C
Air	≈ 15 cSt (1.5 × 10⁻⁵ m²/s)
Water (20 °C)	≈ 1.00 cSt
Diesel fuel	2–5 cSt
SAE 10W-30 motor oil (100 °C)	9.3–12.5 cSt
SAE 10W-30 motor oil (40 °C)	≈ 65–75 cSt
ISO VG 46 hydraulic oil (40 °C)	≈ 46 cSt
Honey	2,000–10,000 cSt

Temperature Dependence

Kinematic viscosity drops sharply as temperature rises. Engine oil at 100 °C is several times less viscous than at 40 °C. The viscosity index (VI) quantifies how much a lubricant's viscosity changes with temperature — a high VI means the viscosity changes less. Always state temperature when comparing or specifying kinematic viscosity.

Relationship to Dynamic Viscosity

If you know dynamic viscosity in mPa·s (= cP) and density in g/cm³, kinematic viscosity in cSt is:

ν (cSt) = μ (cP) / ρ (g/cm³)

For water at 20 °C: μ ≈ 1.002 cP, ρ ≈ 0.998 g/cm³, so ν ≈ 1.004 cSt — consistent with the measured value.

Frequently Asked Questions (FAQ)

Is cSt the same as mm²/s?

Yes — centistokes and square millimeters per second are numerically identical. One centistoke (cSt) is defined as exactly 1 mm²/s. Both are used interchangeably in lubrication and hydraulic oil specifications; the choice is mostly a matter of convention. ISO oil-grade viscosity tables, for example, list values in mm²/s at 40 °C, while many product datasheets print the same number with the cSt symbol.

What is the relationship between stokes (St) and cm²/s?

One stokes (St) equals exactly 1 cm²/s = 1 × 10⁻⁴ m²/s. It is the CGS unit of kinematic viscosity, named after Sir George Gabriel Stokes. Because the stokes is inconveniently large for most engineering fluids (water at 20 °C is about 0.01 St = 1 cSt), the centistoke is the practical everyday unit.

What is kinematic viscosity and how does it differ from dynamic viscosity?

Kinematic viscosity (ν) is dynamic viscosity (μ) divided by fluid density (ρ): ν = μ / ρ. It describes how fast a fluid flows under gravity alone, independent of the force applied.

Dynamic viscosity measures the internal friction force per unit area per unit velocity gradient. In SI, dynamic viscosity is measured in Pa·s (or mPa·s = cP), while kinematic viscosity is measured in m²/s (or cSt = mm²/s). Engine oil grades (e.g. SAE 5W-30) are defined by their kinematic viscosity at 100 °C.

What is the kinematic viscosity of water?

Water at 20 °C has a kinematic viscosity of approximately 1.004 cSt (1.004 mm²/s = 1.004 × 10⁻⁶ m²/s). This value decreases significantly with temperature — at 40 °C it is about 0.658 cSt, and at 60 °C about 0.475 cSt. The converter defaults to 1 × 10⁻⁶ m²/s (1 cSt) as a convenient near-water reference point.