🌀 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

20+ Units ISO VG & SAE Guide All Units at Once Free & Instant

🔄 Kinematic Viscosity Converter

1 St = 100 cSt
Formula: value × 100

📊 All Units at Once

💡 How it works: All conversions use m²/s as the SI pivot unit. Formula: \( \nu_{\text{to}} = \nu_{\text{from}} \times \dfrac{f_{\text{from}}}{f_{\text{to}}} \) where \(f\) is each unit's exact m²/s equivalent.

📖 How to Use the Kinematic Viscosity Converter

  1. 1
    Filter 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.

  2. 2
    Enter 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.

  3. 3
    Select 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.

  4. 4
    Use 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.

  5. 5
    View 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

FromToMultiply ByMath 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 cStmm²/s1 (exact)\( 1\,\text{cSt} = 1\,\text{mm}^2/\text{s} \)
1 m²/sStokes (St)10,000\( 1\,\text{m}^2/\text{s} = 10^4\,\text{St} \)
1 m²/scSt1,000,000\( 1\,\text{m}^2/\text{s} = 10^6\,\text{cSt} \)
1 ft²/sm²/s0.0929030\( 1\,\text{ft}^2/\text{s} = 0.09290304\,\text{m}^2/\text{s} \)
1 m²/sft²/s10.7639\( 1\,\text{m}^2/\text{s} \approx 10.7639\,\text{ft}^2/\text{s} \)
1 ft²/scSt92,903.04\( 1\,\text{ft}^2/\text{s} = 92{,}903.04\,\text{cSt} \)
1 in²/scSt645.16\( 1\,\text{in}^2/\text{s} = 645.16\,\text{cSt} \)

🌀 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.

Kinematic Viscosity — Definition
\[ \nu = \frac{\mu}{\rho} \]
\(\nu\) = kinematic viscosity (m²/s or St or cSt)  ·  \(\mu\) = dynamic viscosity (Pa·s or cP)  ·  \(\rho\) = fluid density (kg/m³)  ·  For water at 20°C: \(\nu = 1.002\,\text{cP} \div 0.998\,\text{g/cm}^3 = 1.004\,\text{cSt}\)

📐 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.

SI Dimensional Analysis
\[ [\nu] = \frac{[\mu]}{[\rho]} = \frac{\text{Pa·s}}{\text{kg/m}^3} = \frac{\text{kg/(m·s)}}{\text{kg/m}^3} = \frac{\text{m}^2}{\text{s}} \]
Key multiples: \(1\,\text{m}^2/\text{s} = 10^4\,\text{St} = 10^6\,\text{cSt} = 10^6\,\text{mm}^2/\text{s}\)

🌀 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 & Centistokes — Exact Definitions
\[ 1\,\text{St} = 1\,\frac{\text{cm}^2}{\text{s}} = 10^{-4}\,\frac{\text{m}^2}{\text{s}} \] \[ 1\,\text{cSt} = 10^{-2}\,\text{St} = 10^{-4}\,\frac{\text{cm}^2}{\text{s}} = 10^{-6}\,\frac{\text{m}^2}{\text{s}} = 1\,\frac{\text{mm}^2}{\text{s}} \]
Note: 1 cSt = 1 mm²/s exactly — this SI-compatible notation is increasingly preferred in modern engineering standards
💡 Key identity to remember: \(1\,\text{cSt} = 1\,\text{mm}^2/\text{s}\) exactly. Many modern standards (ISO 3448, DIN 51519) now express kinematic viscosity in mm²/s rather than cSt, but they are numerically identical — an oil rated at 46 mm²/s is the same as 46 cSt.

⚗️ 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.

Stokes' Law — Terminal Settling Velocity (Re < 1)
\[ v_t = \frac{2 r^2 (\rho_p - \rho_f) g}{9 \mu} = \frac{2 r^2 (\rho_p - \rho_f) g}{9 \rho_f \nu} \]
\(v_t\) = terminal velocity (m/s)  ·  \(r\) = particle radius (m)  ·  \(\rho_p\) = particle density (kg/m³)  ·  \(\rho_f\) = fluid density (kg/m³)  ·  \(g\) = 9.80665 m/s²  ·  \(\nu\) = kinematic viscosity (m²/s)  ·  Valid for Re = \(v_t d/\nu\) < 1
📌 Example 1 — Settling Velocity of a Silt Particle in Water

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 Definition
\[ \text{ISO VG}\,N \implies \nu_{40°C} \in \left[ 0.9N,\; 1.1N \right]\,\text{cSt} \]
Example: ISO VG 46 → viscosity at 40°C must be between 41.4 and 50.6 cSt. Midpoint = 46 cSt.
ISO VG GradeKinematic Viscosity at 40°C (cSt)Typical Applications
ISO VG 21.98–2.42Precision spindles, air tools
ISO VG 54.14–5.06Dental handpieces, instrument oil
ISO VG 109.00–11.0Light hydraulics, some spindles
ISO VG 2219.8–24.2Pneumatic tools, air compressors
ISO VG 3228.8–35.2Hydraulic systems (most common)
ISO VG 4641.4–50.6Hydraulic systems, vane pumps
ISO VG 6861.2–74.8Gear boxes, hydraulics (heavy)
ISO VG 10090.0–110Gear oils, compressors
ISO VG 150135–165Industrial gearboxes
ISO VG 220198–242Heavy gear, worm gear drives
ISO VG 320288–352Enclosed gear drives, rolling mills
ISO VG 460414–506Open gear, heavy machinery
ISO VG 680612–748Extreme-load gear drives
ISO VG 15001,350–1,650Very 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.

SAE Multi-Grade Oil — Viscosity Requirements (SAE J300)

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

"W" = winter; number before W = cold performance; number after W = high-temp viscosity at 100°C
SAE Grade\(\nu\) at 100°C (cSt)\(\nu\) at 40°C (typical cSt)Typical Use
SAE 205.6–9.3~30–55Warm climates, older engines
SAE 309.3–12.5~80–110Small engines, lawnmowers
SAE 4012.5–16.3~110–150Diesel engines, hot climates
SAE 5016.3–21.9~150–220Racing, high-load diesel
SAE 5W-4012.5–16.3~75–110Modern passenger cars (most common)
SAE 10W-4012.5–16.3~90–120General purpose engine oil
SAE 0W-206.9–9.3~35–60Fuel-efficient modern engines
SAE 10W-309.3–12.5~70–100Older 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.

Walther's Equation (ASTM D341) — Viscosity vs Temperature
\[ \log\log(\nu + 0.7) = A - B \cdot \log T \]
\(\nu\) = kinematic viscosity (cSt)  ·  \(T\) = temperature (Kelvin)  ·  \(A, B\) = fluid-specific constants determined from two known viscosity-temperature data points  ·  Basis of the ASTM viscosity-temperature chart

📈 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.

Viscosity Index Formula (ASTM D2270)
\[ VI = \frac{L - U}{L - H} \times 100 \]
\(U\) = kinematic viscosity at 40°C of the oil being tested  ·  \(L\) = viscosity at 40°C of a reference oil with VI = 0 having the same \(\nu\) at 100°C  ·  \(H\) = viscosity at 40°C of a reference oil with VI = 100 having the same \(\nu\) at 100°C
VI RangeClassificationTypical Oil Type
Below 0Very Low VINaphthenic base oils, extreme cases
0–35Low VINaphthenic base oils
35–80Medium VIParaffinic base oils (Group I)
80–110High VIRefined paraffinic (Group II)
110–150Very High VI (VHVI)Group III hydrocracked oils (most modern synthetics)
Above 150Ultrahigh VIPAO (Group IV) and ester synthetics

📊 Kinematic Viscosity Reference Table for Common Fluids

FluidTemperatureKinematic Viscosity (cSt)In m²/s
Air20°C15.11\(1.511 \times 10^{-5}\)
Air100°C23.02\(2.302 \times 10^{-5}\)
Water20°C1.004\(1.004 \times 10^{-6}\)
Water40°C0.658\(6.58 \times 10^{-7}\)
Water100°C0.294\(2.94 \times 10^{-7}\)
Ethanol (20°C)20°C1.52\(1.52 \times 10^{-6}\)
SAE 10W motor oil40°C35–40\(≈3.7 \times 10^{-5}\)
SAE 30 motor oil40°C90–110\(≈1.0 \times 10^{-4}\)
SAE 40 motor oil40°C130–150\(≈1.4 \times 10^{-4}\)
SAE 5W-40 (modern)100°C13–15\(≈1.4 \times 10^{-5}\)
ISO VG 32 hydraulic oil40°C28.8–35.2\(≈3.2 \times 10^{-5}\)
ISO VG 68 hydraulic oil40°C61.2–74.8\(≈6.8 \times 10^{-5}\)
Olive oil25°C84\(8.4 \times 10^{-5}\)
Honey25°C2,500–10,000\(≈5 \times 10^{-3}\)
Castor oil25°C985\(9.85 \times 10^{-4}\)
🌡️ Air has higher kinematic viscosity than water! Air's kinematic viscosity (~15 cSt at 20°C) is about 15× greater than water's (~1 cSt). This seems counterintuitive but results from air's extremely low density — even though air's dynamic viscosity is about 55× lower than water's, the density ratio (998 kg/m³ for water vs 1.2 kg/m³ for air) reverses the comparison. This is why aerodynamic Reynolds numbers are much lower than hydraulic ones for the same geometry and speed.
📌 Example 2 — Converting Kinematic to Dynamic Viscosity (SAE 30 Oil)

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).

N
Written & Reviewed by Num8ers Editorial Team — Fluid Mechanics & Tribology Specialists Last updated: April 2026 · Conversion factors verified against NIST SP 811 (2008), ISO 3448 (Industrial Lubricants — ISO Viscosity Classification), SAE J300 (Engine Oil Viscosity Classification), ASTM D2270 (Viscosity Index Calculation) & ASTM D341

❓ Frequently Asked Questions About Kinematic Viscosity

What is kinematic viscosity and how does it differ from dynamic viscosity?
Kinematic viscosity (\(\nu\)) = dynamic viscosity (\(\mu\)) ÷ fluid density (\(\rho\)): \(\nu = \mu/\rho\). It describes how a fluid flows under the influence of gravity — relevant when density matters (e.g., settling, gravity-driven flow). Dynamic viscosity measures raw shear resistance, relevant for pump design and forced flow. Units: kinematic = m²/s, cSt, mm²/s; dynamic = Pa·s, cP.
How do I convert stokes to centistokes?
Multiply by 100 (exact). \(1\,\text{St} = 100\,\text{cSt}\). Reverse: \(1\,\text{cSt} = 0.01\,\text{St}\). Example: 1.5 St = 150 cSt. Both are CGS units derived from the stoke (1 cm²/s). The centistoke is preferred because water at 20°C ≈ 1 cSt — a convenient reference.
How do I convert centistokes to m²/s?
Multiply by \(10^{-6}\) (exact). \(1\,\text{cSt} = 10^{-6}\,\text{m}^2/\text{s}\). Example: 100 cSt = \(10^{-4}\,\text{m}^2/\text{s}\). Reverse: multiply by \(10^6\). Note also: \(1\,\text{cSt} = 1\,\text{mm}^2/\text{s}\) exactly — same number, different notation.
Why does 1 cSt = 1 mm²/s?
By definition: \(1\,\text{cSt} = 10^{-2}\,\text{St} = 10^{-2}\,\text{cm}^2/\text{s}\). Now \(1\,\text{cm} = 10\,\text{mm}\), so \(1\,\text{cm}^2 = 100\,\text{mm}^2\). Therefore: \(10^{-2}\,\text{cm}^2/\text{s} = 10^{-2} \times 100\,\text{mm}^2/\text{s} = 1\,\text{mm}^2/\text{s}\). This exact equality makes mm²/s an SI-friendly alternative to cSt — modern standards like ISO 3448 increasingly use mm²/s.
What is the kinematic viscosity of water at different temperatures?
Water kinematic viscosity varies significantly: 0°C → 1.787 cSt; 10°C → 1.307 cSt; 20°C → 1.004 cSt; 30°C → 0.801 cSt; 40°C → 0.658 cSt; 60°C → 0.474 cSt; 80°C → 0.365 cSt; 100°C → 0.294 cSt. Water's kinematic viscosity drops nearly 6× from 0°C to 100°C — demonstrating the strong temperature dependence captured by Walther's equation.
What does cSt mean in lubrication and motor oil?
cSt = centistokes — the standard unit for lubricant kinematic viscosity. ISO VG grades: the VG number is the nominal viscosity in cSt at 40°C (e.g., ISO VG 46 = ~46 cSt at 40°C). SAE grades: determined by viscosity in cSt at 100°C (e.g., SAE 40 = 12.5–16.3 cSt at 100°C). Higher cSt = thicker oil.
How do I convert kinematic viscosity to dynamic viscosity?
Multiply by density: \(\mu = \nu \times \rho\). If \(\nu\) is in cSt and \(\rho\) in g/cm³, then \(\mu\) is in cP (= mPa·s). Example: SAE 30 with \(\nu = 100\,\text{cSt}\) and \(\rho = 0.87\,\text{g/cm}^3\): \(\mu = 100 \times 0.87 = 87\,\text{cP}\). For water (ρ ≈ 1 g/cm³): cSt ≈ cP numerically.
What is ISO VG grade and how is it determined?
ISO VG (Viscosity Grade) per ISO 3448 — the number is the nominal kinematic viscosity in cSt at 40°C, with ±10% tolerance band. There are 18 grades from VG 2 to VG 1500. VG 32 and VG 46 are the most common hydraulic oil grades. VG 220 and VG 320 are typical for industrial gearboxes. Always specify both the ISO VG grade and the base oil type (mineral, synthetic, PAO, etc.).
What is SAE viscosity grade for motor oil?
SAE J300 classifies engine oils by high-temperature and low-temperature viscosity. The "W" (winter) number reflects cold-temperature performance; the second number reflects viscosity at 100°C. SAE 5W-40: low-temp cranking OK to −30°C; \(\nu_{100°C} = 12.5\)–16.3 cSt. Most modern passenger cars use SAE 5W-30, 5W-40, or 0W-20 for fuel efficiency.
Why is kinematic viscosity of air so high compared to water?
Air at 20°C has \(\nu \approx 15.1\,\text{cSt}\) — about 15× more than water (1.004 cSt). This seems surprising since air "flows" so easily. The reason: \(\nu = \mu/\rho\). While air's dynamic viscosity is ~55× lower than water, air's density (1.2 kg/m³) is ~830× lower than water's. The density ratio dominates, so: \(\nu_{\text{air}} = 1.82 \times 10^{-5}/1.2 \approx 1.5 \times 10^{-5}\,\text{m}^2/\text{s}\) vs \(\nu_{\text{water}} = 1.002 \times 10^{-3}/998 \approx 1.0 \times 10^{-6}\,\text{m}^2/\text{s}\).
What is viscosity index (VI) and why does it matter?
Viscosity Index (VI) per ASTM D2270 — a dimensionless number describing how much kinematic viscosity changes between 40°C and 100°C. High VI (above 110) = oil maintains stable viscosity across temperatures. High-VI oils (Group III/IV synthetics, VI > 150) are preferred for multi-grade motor oils and hydraulic systems operating across wide temperature ranges. Low-VI oils thin out rapidly when hot.
What is the ASTM D341 equation used for?
Walther's equation (ASTM D341) predicts how a petroleum oil's kinematic viscosity changes with temperature from two known data points (typically at 40°C and 100°C): \(\log\log(\nu + 0.7) = A - B\log T\). Used to: generate the ASTM viscosity-temperature chart; estimate viscosity at intermediate temperatures; calculate Viscosity Index; predict cold-start and high-temperature performance.
How accurate is the Num8ers Kinematic Viscosity Converter?
Uses exact conversion factors per NIST SP 811: 1 St = 10⁻⁴ m²/s exactly (CGS definition); 1 ft²/s = 0.09290304 m²/s (from exact 1959 foot definition). JavaScript double-precision arithmetic provides ~15 significant digits. The "All Units at Once" panel shows your value in all 20+ units simultaneously. Actual fluid viscosity depends on temperature, pressure, and composition — always use values measured under the conditions relevant to your application.

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