This kinematic viscosity converter changes a kinematic viscosity between square meters per second, square millimeters per second, stokes, centistokes, square feet per second and square inches per second. Formula: 1 cSt = 1 mm²/s = 0.000001 m²/s; ν = μ/ρ in SI units. The SI unit is m²/s. 1 cSt is exactly 1 mm²/s (10⁻⁶ m²/s), and 1 stokes (St) is 100 cSt.
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How to use the kinematic viscosity converter
- Enter the value, for example 46 cSt from an oil data sheet.
- In the kinematic viscosity converter, choose its unit and the target unit.
- Read the kinematic viscosity converter result: 46 cSt = 46 mm²/s = 0.000046 m²/s.
cSt to mm²/s is one-to-one; cSt to m²/s is divide by 1,000,000. Saybolt seconds (SUS) are an empirical scale and are not included.
What is kinematic viscosity?
Kinematic viscosity is dynamic viscosity divided by density, in square meters per second. Motor oil and lubricant specifications use centistokes (cSt), and 1 cSt = 1 mm²/s.
Conversion formula
The kinematic viscosity converter stores every unit as a multiple of the base unit, the square meter per second (m²/s). To convert:
value in target unit = value × (factor of source unit ÷ factor of target unit)
where each factor is the size of the unit in square meters per second.
Common kinematic viscosity conversions
| From | To | 1 unit equals |
|---|---|---|
| centistokes (cSt) | square meter per second (m²/s) | 1 × 10−6 m²/s |
| stokes (St) | square millimeter per second (mm²/s) | 100 mm²/s |
| square foot per second (ft²/s) | square meter per second (m²/s) | 0.09290304 m²/s |
Kinematic viscosity converter worked example
Convert 25 stokes to square millimeters per second:
- Factor of St = 0.0001 m²/s
- Factor of mm²/s = 1 × 10−6 m²/s
- 25 × 0.0001 ÷ 1 × 10−6 = 2,500 mm²/s
Kinematic viscosity unit reference
| Unit | Symbol | Group | Equals (m²/s) |
|---|---|---|---|
| Square Meter per Second | m²/s | SI | 1 |
| Square Millimeter per Second | mm²/s | SI | 1 × 10−6 |
| Stokes | St | CGS | 0.0001 |
| Centistokes | cSt | Common | 1 × 10−6 |
| Square Foot per Second | ft²/s | US/Imperial | 0.09290304 |
| Square Inch per Second | in²/s | US/Imperial | 0.00064516 |
Reverse factors for each kinematic viscosity unit
The reference table gives each unit in square meter per seconds. To go the other way, divide by that factor; the list below does the division for you.
- Square Millimeter per Second (mm²/s), SI: 1 mm²/s = 1 × 10−6 m²/s, so 1 m²/s = 1,000,000 mm²/s.
- Stokes (St), CGS: 1 St = 0.0001 m²/s, so 1 m²/s = 10,000 St.
- Centistokes (cSt), Common: 1 cSt = 1 × 10−6 m²/s, so 1 m²/s = 1,000,000 cSt.
- Square Foot per Second (ft²/s), US/Imperial: 1 ft²/s = 0.09290304 m²/s, so 1 m²/s = 10.76391 ft²/s.
- Square Inch per Second (in²/s), US/Imperial: 1 in²/s = 0.00064516 m²/s, so 1 m²/s = 1,550.003 in²/s.
ISO VG viscosity grades
Industrial oils are graded by ISO 3448, where the ISO VG number is the midpoint kinematic viscosity at 40 °C in cSt and the allowed range is ±10 %:
| ISO VG grade | Midpoint at 40 °C (cSt) | Allowed range (cSt) |
|---|---|---|
| VG 10 | 10 | 9 to 11 |
| VG 22 | 22 | 19.8 to 24.2 |
| VG 32 | 32 | 28.8 to 35.2 |
| VG 46 | 46 | 41.4 to 50.6 |
| VG 68 | 68 | 61.2 to 74.8 |
| VG 100 | 100 | 90 to 110 |
| VG 150 | 150 | 135 to 165 |
| VG 220 | 220 | 198 to 242 |
Stokes to cSt is multiply by 100.
Kinematic viscosity from dynamic viscosity
ν = μ ÷ ρ. An oil with dynamic viscosity 40 mPa·s and density 870 kg/m³ has ν ≈ 46 cSt. Convert μ first with the dynamic viscosity converter and ρ with the density converter.
Reynolds number with kinematic viscosity
With kinematic viscosity the Reynolds number is just Re = vD ÷ ν, with no density needed. Take an ISO VG 46 hydraulic oil at 40 °C, about 46 cSt or 46 × 10⁻⁶ m²/s, flowing at 2 m/s in a 20 mm line. Re = 2 × 0.02 ÷ 0.000046 ≈ 870, so the flow is laminar. Water at 20 °C, about 1.0 cSt, would be turbulent in the same pipe.
US references sometimes use ft²/s. The kinematic viscosity converter turns 46 cSt into about 0.000495 ft²/s. One cSt equals one mm²/s exactly, which is the unit most data sheets now print.
Kinematic viscosity is dynamic viscosity divided by density. If a data sheet gives only mPa·s, divide by the density in g/cm³ to get cSt. For water that barely changes the number; for a light oil at 0.85 g/cm³, 40 mPa·s becomes about 47 cSt. Note the test temperature too, usually 40 °C or 100 °C for lubricants.
Related converters and calculators
Related fluid tools:
- Viscosity converter: cP and Pa·s
- Density converter: kg/m³ and g/cm³
- Surface tension converter: mN/m and dyn/cm
- Flow rate converter: gpm, L/min, m³/h
Sources
NIST Special Publication 811, Appendix B; ISO 3448: Industrial liquid lubricants, ISO viscosity classification.
Questions about this calculator
What is the SI unit of kinematic viscosity?
Square meter per second (m²/s).
Is cSt the same as mm²/s?
Yes. One centistokes equals exactly one square millimeter per second.
How do I convert cSt to m²/s?
Divide by 1,000,000. For example, 100 cSt = 0.0001 m²/s.
What does ISO VG 46 mean?
An oil with kinematic viscosity of 46 cSt at 40 °C, within ±10 % (41.4 to 50.6 cSt).
How do I get kinematic viscosity from dynamic viscosity?
Divide by density: ν = μ ÷ ρ, with μ in Pa·s and ρ in kg/m³ giving m²/s.
Check the assumptions and units before relying on a result. Financial, tax and health estimates do not replace advice for your individual circumstances.
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