Kinematic Viscosity Converter (St, cSt, m²/s)

Understanding the kinematic viscosity converter — concept and principle

Kinematic viscosity describes how easily a fluid flows under its own weight. It is the property quoted for lubricating, hydraulic and gear oils, fuels and many industrial liquids. This converter switches between stokes (St), centistokes (cSt, equal to mm²/s), square metres per second (m²/s) and square feet per second (ft²/s).

How it is calculated

The value is converted to centistokes and then to the target unit: result = value × (cSt per source unit) ÷ (cSt per target unit).

• 1 St = 1 cm²/s = 100 cSt
• 1 cSt = 1 mm²/s = 10⁻⁶ m²/s
• 1 m²/s = 1,000,000 cSt
• 1 ft²/s = 0.09290304 m²/s = 92,903.04 cSt

The principle

Kinematic viscosity ν is dynamic viscosity μ divided by density ρ: ν = μ ÷ ρ. Dynamic viscosity (in Pa·s or centipoise) measures resistance to shearing; dividing by density gives a quantity in units of area per time, which governs how quickly momentum spreads through the fluid. It is measured naturally in a capillary viscometer: a fixed volume flows through a thin tube under gravity, and because the driving force is the fluid's own weight, the flow time multiplied by the tube's constant gives kinematic viscosity directly. The stokes is named after George Gabriel Stokes. Viscosity changes strongly with temperature, so a value always needs its temperature.

Worked example

1. Inputs: 100 cSt, convert to stokes.
2. 1 St = 100 cSt, so 100 ÷ 100 = 1 St.
3. In m²/s: 100 × 10⁻⁶ = 0.0001 m²/s.
4. In ft²/s: 0.0001 ÷ 0.09290304 = 0.001076391 ft²/s.

How to read the result

Water at 20 °C is about 1.0 cSt. Industrial oils are graded by ISO viscosity grade at 40 °C: ISO VG 46, a common hydraulic oil, has a midpoint of 46 cSt with a tolerance of ±10%. Engine oil hot grades in SAE J300 are defined by kinematic viscosity at 100 °C; for example SAE 30 covers 9.3 to below 12.5 cSt.

Common mistakes

• Confusing kinematic viscosity (cSt) with dynamic viscosity (cP); converting between them needs density.
• Comparing values measured at different temperatures.
• Mixing up cSt and St, a factor of 100.
• Reading an ISO VG number as a value at 100 °C; it refers to 40 °C.

Frequently asked questions

Is cSt the same as mm²/s?

Yes, exactly.

How do I convert cSt to cP?

Multiply by the density in g/cm³. Oil of 0.87 g/cm³ at 100 cSt is about 87 cP.

What is the viscosity index?

A number describing how little an oil's viscosity changes between 40 °C and 100 °C; a higher index means a smaller change.

Sources: ISO 3448, Industrial liquid lubricants: ISO viscosity classification · SAE J300, Engine Oil Viscosity Classification · ASTM D445, Standard Test Method for Kinematic Viscosity of Transparent and Opaque Liquids