🌀 Kinematic Viscosity Conversion Calculator
Convert between stokes, centistokes, m²/s, mm²/s, ft²/s and 20+ kinematic viscosity units — with Stokes' law, ISO VG grades, SAE viscosity & ASTM D341 formulas
🔄 Kinematic Viscosity Converter
📊 All Units at Once
📖 How to Use the Kinematic Viscosity Converter
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1Filter by Category (Optional)
Click Common, Metric/SI, or Imperial to narrow your dropdown to units from that system. "Common" shows stokes, centistokes, and mm²/s — the units used most often in lubricant datasheets.
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2Enter Your Kinematic Viscosity Value
Type a value into the "Enter Value" field. Very small values (e.g., 1.004 for water in cSt) and large values (e.g., 100+ for motor oils) are fully supported. Results update live as you type.
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3Select Source & Target Units
Choose your input unit from "From Unit" and the desired output from "To Unit." The result and exact multiplication factor appear instantly in the result panel.
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4Use Quick-Convert Buttons
Click any preset button (St→cSt, cSt→m²/s, ft²/s→m²/s, etc.) for the most frequent conversions. Both dropdowns set automatically and the answer appears immediately.
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5View All Units & Copy
The "All Units at Once" panel shows your value simultaneously in every unit. Click "📋 Copy Result" to copy the primary conversion to your clipboard for use in engineering documents or reports.
📐 Kinematic Viscosity Conversion Factors
| From | To | Multiply By | Math Expression |
|---|---|---|---|
| 1 Stokes (St) | Centistokes (cSt) | 100 (exact) | \( 1\,\text{St} = 100\,\text{cSt} \) |
| 1 Stokes (St) | m²/s | \(10^{-4}\) (exact) | \( 1\,\text{St} = 10^{-4}\,\text{m}^2/\text{s} \) |
| 1 Centistokes (cSt) | m²/s | \(10^{-6}\) (exact) | \( 1\,\text{cSt} = 10^{-6}\,\text{m}^2/\text{s} \) |
| 1 cSt | mm²/s | 1 (exact) | \( 1\,\text{cSt} = 1\,\text{mm}^2/\text{s} \) |
| 1 m²/s | Stokes (St) | 10,000 | \( 1\,\text{m}^2/\text{s} = 10^4\,\text{St} \) |
| 1 m²/s | cSt | 1,000,000 | \( 1\,\text{m}^2/\text{s} = 10^6\,\text{cSt} \) |
| 1 ft²/s | m²/s | 0.0929030 | \( 1\,\text{ft}^2/\text{s} = 0.09290304\,\text{m}^2/\text{s} \) |
| 1 m²/s | ft²/s | 10.7639 | \( 1\,\text{m}^2/\text{s} \approx 10.7639\,\text{ft}^2/\text{s} \) |
| 1 ft²/s | cSt | 92,903.04 | \( 1\,\text{ft}^2/\text{s} = 92{,}903.04\,\text{cSt} \) |
| 1 in²/s | cSt | 645.16 | \( 1\,\text{in}^2/\text{s} = 645.16\,\text{cSt} \) |
🌀 Understanding Kinematic Viscosity — A Complete Guide
Kinematic viscosity (\(\nu\), Greek letter "nu") is one of the two principal ways to express a fluid's resistance to flow — the other being dynamic (absolute) viscosity (\(\mu\)). While dynamic viscosity describes the force required to shear a fluid at a given rate, kinematic viscosity describes how a fluid flows under the influence of gravity — making it the preferred parameter for lubricant classification, hydraulic fluid specification, and any gravity-driven flow analysis.
The distinction matters enormously in engineering. Two fluids with identical dynamic viscosity can have very different kinematic viscosities if their densities differ — and it is the kinematic viscosity that determines their behaviour in most real-world flow situations. This is why motor oil specifications, ISO hydraulic oil grades, and pipeline flow calculations all use kinematic viscosity (typically in centistokes, cSt) as the primary viscosity parameter.
📐 SI Unit of Kinematic Viscosity — m²/s
The SI unit of kinematic viscosity is the square meter per second (m²/s). This follows directly from the definition \(\nu = \mu/\rho\): dynamic viscosity in Pa·s = kg/(m·s), density in kg/m³, so kinematic viscosity = kg/(m·s) ÷ kg/m³ = m²/s. However, 1 m²/s is an enormous kinematic viscosity — water at 20°C has \(\nu \approx 1.004 \times 10^{-6}\,\text{m}^2/\text{s}\), so practical engineering uses sub-multiples.
🌀 Stokes (St) & Centistokes (cSt) — The Practical Units
The stokes (St) is the CGS (centimetre-gram-second) unit of kinematic viscosity, named after the Irish mathematician and physicist Sir George Gabriel Stokes (1819–1903), who made foundational contributions to fluid mechanics, including the law bearing his name that describes the drag on a sphere settling through a viscous fluid. The stokes is defined as 1 cm²/s = 10⁻⁴ m²/s.
The centistokes (cSt) — one hundredth of a stokes — became the engineering standard because it gives water a kinematic viscosity of approximately 1 cSt at 20°C, creating an intuitive reference. ISO oil viscosity grades are defined in cSt at 40°C; SAE motor oil grades are based on cSt at 100°C. An oil at 32 cSt is simply 32 times more viscous (kinematically) than water.
⚗️ Stokes' Law — Viscosity & Particle Settling
Sir George Stokes derived one of the most important equations in fluid mechanics in 1851 — the Stokes drag law, which describes the terminal velocity of a small sphere settling through a viscous fluid. This equation is foundational to sedimentation analysis, particle size measurement (by Stokes' settling method), blood cell separation in centrifuges, and hydrogeological modelling of aquifer materials.
Problem: How fast does a spherical silt particle (radius = 0.01 mm = 10⁻⁵ m, density = 2,650 kg/m³) settle in water at 20°C (ν = 1.004 × 10⁻⁶ m²/s, ρ = 998 kg/m³)?
\[ v_t = \frac{2 \times (10^{-5})^2 \times (2650 - 998) \times 9.80665}{9 \times 998 \times 1.004 \times 10^{-6}} \]
\[ v_t = \frac{2 \times 10^{-10} \times 1652 \times 9.807}{9 \times 1.004 \times 10^{-3}} = \frac{3.241 \times 10^{-7}}{9.036 \times 10^{-3}} \approx 3.59 \times 10^{-5}\,\text{m/s} \approx 0.036\,\text{mm/s} \]
Answer: A 0.01 mm silt particle settles at approximately 3.1 m/day in water at 20°C — demonstrating why silt stays suspended in slow-moving rivers for extended periods.
⚖️ Kinematic vs Dynamic Viscosity — Key Differences
Kinematic Viscosity (\(\nu\))
Ratio of dynamic viscosity to density: \(\nu = \mu/\rho\). Units: m²/s, cSt, mm²/s. Used for: lubricant grading, hydraulic oil specs, pipe flow under gravity. Water at 20°C: 1.004 cSt.
Dynamic Viscosity (\(\mu\))
Absolute shear resistance: \(\tau = \mu\,du/dy\). Units: Pa·s, cP, mPa·s. Used for: pump design, mixing, non-gravity flows. Water at 20°C: 1.002 cP.
Converting Between Them
\(\nu\,[\text{cSt}] = \mu\,[\text{cP}] / \rho\,[\text{g/cm}^3]\). For water (ρ ≈ 1 g/cm³): cSt ≈ cP. For oil (ρ ≈ 0.87): cSt = cP/0.87 — kinematic viscosity is higher.
Temperature Dependence
Both decrease with temperature for liquids. Kinematic drops faster because density also changes. Motor oil: ~100 cSt at 40°C → ~15 cSt at 100°C (a 6.7× change over 60°C).
⚙️ ISO Viscosity Grades (ISO VG) — International Standard
The ISO 3448 standard classifies industrial lubricants into 18 Viscosity Grades (VG). Each ISO VG number is the nominal kinematic viscosity in cSt at 40°C, and the actual viscosity must fall within ±10% of that nominal value. This standardised system allows engineers worldwide to specify hydraulic oils, gear oils, compressor oils, and turbine oils with a single universal number.
| ISO VG Grade | Kinematic Viscosity at 40°C (cSt) | Typical Applications |
|---|---|---|
| ISO VG 2 | 1.98–2.42 | Precision spindles, air tools |
| ISO VG 5 | 4.14–5.06 | Dental handpieces, instrument oil |
| ISO VG 10 | 9.00–11.0 | Light hydraulics, some spindles |
| ISO VG 22 | 19.8–24.2 | Pneumatic tools, air compressors |
| ISO VG 32 | 28.8–35.2 | Hydraulic systems (most common) |
| ISO VG 46 | 41.4–50.6 | Hydraulic systems, vane pumps |
| ISO VG 68 | 61.2–74.8 | Gear boxes, hydraulics (heavy) |
| ISO VG 100 | 90.0–110 | Gear oils, compressors |
| ISO VG 150 | 135–165 | Industrial gearboxes |
| ISO VG 220 | 198–242 | Heavy gear, worm gear drives |
| ISO VG 320 | 288–352 | Enclosed gear drives, rolling mills |
| ISO VG 460 | 414–506 | Open gear, heavy machinery |
| ISO VG 680 | 612–748 | Extreme-load gear drives |
| ISO VG 1500 | 1,350–1,650 | Very slow-speed, extreme-load |
🛢️ SAE Motor Oil Viscosity Grades
The Society of Automotive Engineers (SAE) J300 standard classifies engine oils by their kinematic viscosity at 100°C (for the hot viscosity number) and their low-temperature cranking and pumping viscosity (for the "W" winter grade). This system was developed because engine bearings operate at high temperatures while cold starts require adequate pumpability at very low temperatures.
High-temperature grade (e.g., "40" in SAE 5W-40): \( 12.5 \leq \nu_{100°C}\,[\text{cSt}] \leq 16.3 \)
Winter grade (e.g., "5W"): max cranking viscosity at −30°C and max pumping viscosity at −35°C
| SAE Grade | \(\nu\) at 100°C (cSt) | \(\nu\) at 40°C (typical cSt) | Typical Use |
|---|---|---|---|
| SAE 20 | 5.6–9.3 | ~30–55 | Warm climates, older engines |
| SAE 30 | 9.3–12.5 | ~80–110 | Small engines, lawnmowers |
| SAE 40 | 12.5–16.3 | ~110–150 | Diesel engines, hot climates |
| SAE 50 | 16.3–21.9 | ~150–220 | Racing, high-load diesel |
| SAE 5W-40 | 12.5–16.3 | ~75–110 | Modern passenger cars (most common) |
| SAE 10W-40 | 12.5–16.3 | ~90–120 | General purpose engine oil |
| SAE 0W-20 | 6.9–9.3 | ~35–60 | Fuel-efficient modern engines |
| SAE 10W-30 | 9.3–12.5 | ~70–100 | Older cars, moderate climates |
🔬 ASTM D341 — Walther's Equation for Viscosity vs Temperature
Engineers frequently need to predict how a lubricant's kinematic viscosity changes with temperature — for example, to estimate cold-start viscosity from 40°C and 100°C data. The ASTM D341 standard provides Walther's equation (a double-logarithm relationship), which accurately describes viscosity–temperature behaviour for petroleum oils over a wide temperature range.
📈 Viscosity Index (VI) — Measuring Temperature Stability
The Viscosity Index (VI) is an empirical dimensionless number that describes how much a lubricant's kinematic viscosity changes with temperature — specifically between 40°C and 100°C. A high VI means the oil's viscosity changes relatively little with temperature (desirable for most applications). A low VI means large viscosity swings that can cause poor lubrication at high temperatures or difficult cold starts.
| VI Range | Classification | Typical Oil Type |
|---|---|---|
| Below 0 | Very Low VI | Naphthenic base oils, extreme cases |
| 0–35 | Low VI | Naphthenic base oils |
| 35–80 | Medium VI | Paraffinic base oils (Group I) |
| 80–110 | High VI | Refined paraffinic (Group II) |
| 110–150 | Very High VI (VHVI) | Group III hydrocracked oils (most modern synthetics) |
| Above 150 | Ultrahigh VI | PAO (Group IV) and ester synthetics |
📊 Kinematic Viscosity Reference Table for Common Fluids
| Fluid | Temperature | Kinematic Viscosity (cSt) | In m²/s |
|---|---|---|---|
| Air | 20°C | 15.11 | \(1.511 \times 10^{-5}\) |
| Air | 100°C | 23.02 | \(2.302 \times 10^{-5}\) |
| Water | 20°C | 1.004 | \(1.004 \times 10^{-6}\) |
| Water | 40°C | 0.658 | \(6.58 \times 10^{-7}\) |
| Water | 100°C | 0.294 | \(2.94 \times 10^{-7}\) |
| Ethanol (20°C) | 20°C | 1.52 | \(1.52 \times 10^{-6}\) |
| SAE 10W motor oil | 40°C | 35–40 | \(≈3.7 \times 10^{-5}\) |
| SAE 30 motor oil | 40°C | 90–110 | \(≈1.0 \times 10^{-4}\) |
| SAE 40 motor oil | 40°C | 130–150 | \(≈1.4 \times 10^{-4}\) |
| SAE 5W-40 (modern) | 100°C | 13–15 | \(≈1.4 \times 10^{-5}\) |
| ISO VG 32 hydraulic oil | 40°C | 28.8–35.2 | \(≈3.2 \times 10^{-5}\) |
| ISO VG 68 hydraulic oil | 40°C | 61.2–74.8 | \(≈6.8 \times 10^{-5}\) |
| Olive oil | 25°C | 84 | \(8.4 \times 10^{-5}\) |
| Honey | 25°C | 2,500–10,000 | \(≈5 \times 10^{-3}\) |
| Castor oil | 25°C | 985 | \(9.85 \times 10^{-4}\) |
Problem: SAE 30 motor oil at 40°C has a kinematic viscosity of 100 cSt. Its density at 40°C is 870 kg/m³. What is its dynamic viscosity?
Step 1 — Convert ν to SI: \(100\,\text{cSt} = 100 \times 10^{-6}\,\text{m}^2/\text{s} = 10^{-4}\,\text{m}^2/\text{s}\)
Step 2 — Apply \(\mu = \nu \times \rho\):
\[ \mu = 10^{-4}\,\frac{\text{m}^2}{\text{s}} \times 870\,\frac{\text{kg}}{\text{m}^3} = 0.0870\,\text{Pa·s} = 87.0\,\text{mPa·s} = 87.0\,\text{cP} \]
Answer: SAE 30 at 40°C has a dynamic viscosity of approximately 87 cP (0.087 Pa·s).