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Convert kinematic viscosity from centistokes (cSt) to square meters per second (m²/s) instantly. Ideal for engineering calculations, lubricant specifications, and fluid dynamics research.
Conversion Formula
m²/s = cSt ÷ 1,000,000
cSt = m²/s × 1,000,000
This table covers the most frequently encountered kinematic viscosity values, from thin solvents to extremely viscous materials, with real-world context for each value.
| Centistokes (cSt) | m²/s | Real-World Example |
|---|---|---|
| 0.01 | 1 × 10⁻⁸ | Very light solvents |
| 0.1 | 1 × 10⁻⁷ | Acetone, diethyl ether |
| 0.5 | 5 × 10⁻⁷ | Gasoline / petrol |
| 1 | 1 × 10⁻⁶ | Water at 20 °C |
| 2.2 | 2.2 × 10⁻⁶ | ISO VG 2 instrument oil |
| 5 | 5 × 10⁻⁶ | Kerosene / jet fuel |
| 10 | 1 × 10⁻⁵ | ISO VG 10 spindle oil |
| 22 | 2.2 × 10⁻⁵ | ISO VG 22 hydraulic oil |
| 32 | 3.2 × 10⁻⁵ | ISO VG 32 hydraulic oil |
| 46 | 4.6 × 10⁻⁵ | ISO VG 46 general hydraulics |
| 68 | 6.8 × 10⁻⁵ | ISO VG 68 gearbox oil |
| 100 | 1 × 10⁻⁴ | ISO VG 100 heavy-duty gear oil |
| 220 | 2.2 × 10⁻⁴ | ISO VG 220 industrial gear oil |
| 460 | 4.6 × 10⁻⁴ | ISO VG 460 large gearboxes |
| 1,000 | 1 × 10⁻³ | Heavy gear oil / castor oil |
| 10,000 | 1 × 10⁻² | Honey (approx.) |
| 100,000 | 1 × 10⁻¹ | Thick adhesives |
| 1,000,000 | 1 | Extremely viscous materials |
Kinematic viscosity is a measure of a fluid's resistance to flow under the influence of gravity. It is defined as the ratio of a fluid's dynamic viscosity to its density: v = μ / ρ, where v is kinematic viscosity, μ is dynamic viscosity, and ρ is fluid density. Unlike dynamic viscosity, which measures only internal friction, kinematic viscosity accounts for how heavy the fluid is, making it the preferred metric for gravity-driven flow applications.
The centistoke (cSt) belongs to the CGS (centimeter-gram-second) system and equals one hundredth of a stoke (St). The stoke is named after Sir George Gabriel Stokes, the Irish-born mathematician who made foundational contributions to fluid dynamics. One centistoke is equivalent to one square millimeter per second (mm²/s). The centistoke is the standard unit used in the petroleum industry for grading lubricating oils, hydraulic fluids, and fuel specifications.
The square meter per second (m²/s) is the SI unit for kinematic viscosity. Because the square meter is much larger than the square millimeter, numerical values in m²/s tend to be very small for common fluids. For example, water at 20 °C has a kinematic viscosity of approximately 1.004 cSt, which equals 1.004 × 10⁻⁶ m²/s. Despite the inconvenient scale, m²/s is essential in scientific and engineering calculations where SI unit consistency is mandatory, such as computing the Reynolds number or solving the Navier-Stokes equations.
In practice, engineers and technicians most often work in centistokes for daily specifications and testing, then convert to m²/s when plugging values into equations or publishing research. Understanding both units and how to convert between them is a fundamental skill in fluid mechanics, tribology, and petroleum engineering.
m²/s = cSt ÷ 1,000,000
cSt = m²/s × 1,000,000
This conversion works because 1 cSt = 1 mm²/s, and there are 1,000,000 mm² in 1 m² (1000 mm × 1000 mm = 10⁶ mm²).
A hydraulic system uses ISO VG 32 oil with a kinematic viscosity of 32 cSt at 40 °C.
Step 1: Start with 32 cSt
Step 2: Divide by 1,000,000
Step 3: 32 ÷ 1,000,000 = 0.000032 m²/s
Step 4: In scientific notation: 3.2 × 10⁻⁵ m²/s
A typical SAE 10W-30 motor oil has a kinematic viscosity of about 70 cSt at 40 °C.
Step 1: Start with 70 cSt
Step 2: Divide by 1,000,000
Step 3: 70 ÷ 1,000,000 = 0.00007 m²/s
Step 4: In scientific notation: 7.0 × 10⁻⁵ m²/s
Pure water at 20 °C has a kinematic viscosity of approximately 1.004 cSt.
Step 1: Start with 1.004 cSt
Step 2: Divide by 1,000,000
Step 3: 1.004 ÷ 1,000,000 = 0.000001004 m²/s
Step 4: In scientific notation: 1.004 × 10⁻⁶ m²/s
Simply move the decimal point 6 places to the left. For example, 46 cSt becomes 0.000046 m²/s. Alternatively, write the cSt value and multiply by 10⁻⁶. This is quick because the conversion factor is an exact power of ten.
ISO VG grades classify industrial lubricants by their midpoint kinematic viscosity at 40 °C.
| ISO VG Grade | Midpoint (cSt) | Midpoint (m²/s) | Application |
|---|---|---|---|
| VG 2 | 2.2 | 2.2 × 10⁻⁶ | Instrument oil |
| VG 10 | 10 | 1.0 × 10⁻⁵ | Spindle oil, sewing machines |
| VG 22 | 22 | 2.2 × 10⁻⁵ | Hydraulic systems, air tools |
| VG 32 | 32 | 3.2 × 10⁻⁵ | General machinery hydraulics |
| VG 46 | 46 | 4.6 × 10⁻⁵ | Circulation systems |
| VG 68 | 68 | 6.8 × 10⁻⁵ | Gearboxes, compressors |
| VG 100 | 100 | 1.0 × 10⁻⁴ | Heavy-duty gearboxes |
| VG 150 | 150 | 1.5 × 10⁻⁴ | Enclosed gears, bearings |
| VG 220 | 220 | 2.2 × 10⁻⁴ | Heavy industrial gears |
| VG 320 | 320 | 3.2 × 10⁻⁴ | Large gearboxes, cement mills |
| Fluid | cSt (approx.) | m²/s |
|---|---|---|
| Acetone | 0.41 | 4.1 × 10⁻⁷ |
| Gasoline | 0.7 | 7.0 × 10⁻⁷ |
| Water | 1.004 | 1.004 × 10⁻⁶ |
| Diesel fuel | 3.5 | 3.5 × 10⁻⁶ |
| Olive oil | 84 | 8.4 × 10⁻⁵ |
| SAE 30 motor oil | 100 | 1.0 × 10⁻⁴ |
| Glycerin | 1,180 | 1.18 × 10⁻³ |
| Honey | ~7,000 | ~7.0 × 10⁻³ |
| Temperature | cSt | m²/s |
|---|---|---|
| 0 °C | 1.787 | 1.787 × 10⁻⁶ |
| 10 °C | 1.307 | 1.307 × 10⁻⁶ |
| 20 °C | 1.004 | 1.004 × 10⁻⁶ |
| 30 °C | 0.801 | 8.01 × 10⁻⁷ |
| 40 °C | 0.658 | 6.58 × 10⁻⁷ |
| 60 °C | 0.475 | 4.75 × 10⁻⁷ |
| 80 °C | 0.365 | 3.65 × 10⁻⁷ |
| 100 °C | 0.295 | 2.95 × 10⁻⁷ |
ISO VG grades and SAE classifications define oils by their centistoke values. Converting to m²/s is essential when these values feed into engineering equations for bearing design, pump sizing, or hydraulic system modeling.
Peer-reviewed papers and international standards require SI units. Converting cSt measurements to m²/s ensures dimensional consistency in the Navier-Stokes equations, Reynolds number calculations, and heat transfer analysis.
Diesel, jet fuel, and marine fuel specifications rely on kinematic viscosity at specific temperatures. Accurate conversion ensures proper atomization, combustion efficiency, and compliance with ASTM and ISO fuel standards.
Calculating pressure drops, flow regimes, and pump power requirements in pipelines demands kinematic viscosity in m²/s for consistent results with velocity in m/s and pipe diameter in meters.
Centistokes (cSt) measure kinematic viscosity; centipoise (cP) measure dynamic viscosity. They are numerically equal only for fluids with density 1 g/cm³ (like water). For oils, always check which type of viscosity you have before converting.
The factor of 1,000,000 means moving the decimal point 6 places. A common error is moving it 3 or 5 places. Double-check by confirming that 1 cSt = 10⁻⁶ m²/s.
Values in m²/s are typically very small. Writing 3.2 × 10⁻⁵ is much clearer than 0.000032 and reduces the risk of transcription errors in engineering documents.
This identity is exact and can simplify multi-step conversions. If you know mm²/s, you already know centistokes, and vice versa.
Kinematic viscosity is highly temperature-dependent. A viscosity value without a stated temperature is nearly useless. Standard reference temperatures are 40 °C for industrial oils and 100 °C for engine oil classifications.
One centistoke equals 0.000001 (1 × 10⁻⁶) square meters per second. Conversely, one square meter per second equals 1,000,000 centistokes. This large conversion factor reflects the difference between CGS and SI unit systems for kinematic viscosity.
Dynamic viscosity measures a fluid's internal friction in units like centipoise (cP) or pascal-seconds (Pa·s). Kinematic viscosity accounts for the fluid's density, expressed in centistokes (cSt) or square meters per second (m²/s). The relationship is: kinematic viscosity = dynamic viscosity / density.
Centistokes provide more convenient numerical values for everyday fluids. Water at 20°C has a kinematic viscosity of about 1 cSt, whereas in m²/s it would be 0.000001, which is cumbersome for routine work. However, scientific publications and engineering equations require SI units like m²/s for dimensional consistency.
Use the formula: kinematic viscosity (cSt) = dynamic viscosity (cP) / density (g/cm³). For water with density 1 g/cm³, 1 cP equals 1 cSt. For a lubricating oil with density 0.85 g/cm³, 1 cP equals approximately 1.18 cSt.
SUS is an older viscosity unit that measures the time for a specific volume of fluid to flow through a calibrated orifice. It is still used in some petroleum industries. For viscosities below 100 SUS, multiply SUS by 0.226 to get an approximate centistokes value.
For most liquids, kinematic viscosity decreases significantly as temperature rises. The Viscosity Index (VI) quantifies this temperature dependence: a higher VI means viscosity changes less with temperature. This is critical when selecting lubricants for engines and machinery that operate across wide temperature ranges.
Capillary viscometers such as Ubbelohde and Cannon-Fenske types measure the time for a fluid to flow through a calibrated glass tube. Automated kinematic viscometers use the same principle with electronic timing and temperature control. The ASTM D445 standard governs these measurements for petroleum products.
The Reynolds number (Re) is a dimensionless quantity that predicts whether fluid flow will be laminar or turbulent. It is calculated as Re = (velocity × length) / kinematic viscosity. Using m²/s for kinematic viscosity keeps the units consistent when velocity is in m/s and length is in meters.
This converter is provided for informational and educational purposes only. While we strive for accuracy, always verify critical calculations with authoritative references or certified instruments. UnitTables is not responsible for errors resulting from the use of this tool.