Why is centipoise the most used viscosity unit?

Water at 20°C has a viscosity of approximately 1 cP, making it an intuitive calibration reference. A fluid at 100 cP is simply 100 times more viscous than water.

What is the viscosity of water at 20°C?

Water at 20°C has a dynamic viscosity of approximately 1.002 cP = 0.001002 Pa·s = 1.002 mPa·s.

1 reyn = 1 lbf·s/in² = 6,894.76 Pa·s. Named after Osborne Reynolds. Used in US lubrication engineering. Extremely large unit — about 6.9 million times the viscosity of water.

🌊 Dynamic Viscosity Conversion Calculator

Convert between pascal seconds, poise, centipoise, mPa·s, reyn and 20+ dynamic viscosity units — SI, CGS & Imperial — with Poiseuille & Navier–Stokes formulas

20+ Units MathJax Formulas Category Filter Real-Fluid Reference Free & Instant

🔄 Dynamic Viscosity Converter

Enter Value From Unit

Result To Unit

1 Pa·s = 10 P

Formula: value × 10

📊 All Units at Once

💡 How it works: All conversions pivot through the pascal second (Pa·s) — the SI base unit. Formula: \( \mu_{\text{to}} = \mu_{\text{from}} \times \dfrac{f_{\text{from}}}{f_{\text{to}}} \) where \(f\) is each unit's exact Pa·s equivalent.

📖 How to Use the Dynamic Viscosity Converter

1

Filter by Unit System (Optional)
Click SI Units, CGS (Poise), or Imperial to narrow the dropdown to units from that system. Click "All Units" to see every available viscosity unit across all systems.
2

Enter Your Viscosity Value
Type your viscosity number into the "Enter Value" field. Both very small values (e.g., 0.0182 for air in cP) and very large values (e.g., 250,000 for peanut butter in cP) are supported. Results update live.
3

Select Source & Target Units
Choose your input unit from "From Unit" and the desired output unit from "To Unit." The exact conversion result and multiplication factor appear instantly in the dark result panel.
4

Use Quick-Convert Buttons
Click a preset button (Pa·s→P, cP→Pa·s, P→Pa·s, etc.) for the most common viscosity conversions. Both dropdowns are pre-set and the answer appears immediately.
5

View All Units & Copy
The "All Units at Once" panel displays your viscosity value simultaneously in every supported unit. Click "📋 Copy Result" to copy the primary conversion to your clipboard.

📐 Dynamic Viscosity Conversion Factors

From	To	Multiply By	Math Expression
1 Pa·s	Poise (P)	10	\( 1\,\text{Pa·s} = 10\,\text{P} \)
1 Pa·s	Centipoise (cP)	1,000	\( 1\,\text{Pa·s} = 10^3\,\text{cP} \)
1 Pa·s	mPa·s	1,000	\( 1\,\text{Pa·s} = 10^3\,\text{mPa·s} \)
1 Poise (P)	Pa·s	0.1	\( 1\,\text{P} = 10^{-1}\,\text{Pa·s} \)
1 Centipoise (cP)	Pa·s	0.001	\( 1\,\text{cP} = 10^{-3}\,\text{Pa·s} \)
1 cP	mPa·s	1 (exact)	\( 1\,\text{cP} = 1\,\text{mPa·s} \)
1 kg/(m·s)	Pa·s	1 (exact)	\( 1\,\text{kg/(m·s)} = 1\,\text{Pa·s} \)
1 lb/(ft·s)	Pa·s	1.48816	\( 1\,\text{lb/(ft·s)} \approx 1.488\,\text{Pa·s} \)
1 lbf·s/ft²	Pa·s	47.8803	\( 1\,\text{lbf·s/ft}^2 \approx 47.88\,\text{Pa·s} \)
1 reyn	Pa·s	6,894.76	\( 1\,\text{reyn} = 1\,\text{lbf·s/in}^2 \approx 6{,}895\,\text{Pa·s} \)
1 kgf·s/m²	Pa·s	9.80665	\( 1\,\text{kgf·s/m}^2 = g_n \approx 9.807\,\text{Pa·s} \)

🌊 Understanding Dynamic Viscosity — A Complete Guide

Dynamic viscosity — also called absolute viscosity — is one of the most important physical properties of any fluid. It quantifies a fluid's internal resistance to deformation under an applied shear stress: in simple terms, how "thick" or "resistant to flow" a fluid is. Understanding viscosity is fundamental to fluid mechanics, chemical engineering, petroleum engineering, food science, biomedical applications, and countless other disciplines.

The challenge for engineers, scientists, and technicians is that viscosity is expressed in a variety of units across different measurement systems — pascal seconds (Pa·s) in SI, poise (P) and centipoise (cP) in the CGS system, and several obscure imperial units like the reyn. Our Num8ers dynamic viscosity converter handles over 20 units instantly, with all conversion factors traceable to internationally defined physical constants.

Newton's Law of Viscosity — The Defining Equation

\[ \tau = \mu \frac{du}{dy} \]

\(\tau\) = shear stress (Pa) · \(\mu\) = dynamic viscosity (Pa·s) · \(\dfrac{du}{dy}\) = velocity gradient (shear rate, s\(^{-1}\)) · Valid for Newtonian fluids (water, air, most oils)

This equation, formulated by Isaac Newton in 1687, defines what we mean by dynamic viscosity. A fluid with high \(\mu\) requires a large shear stress to produce a given shear rate — it resists flow. A fluid with low \(\mu\) flows easily under small stresses. The SI unit of shear stress is the pascal (Pa = N/m²) and the shear rate is in s⁻¹, so the SI unit of dynamic viscosity is Pa·s = N·s/m² = kg/(m·s).

📐 SI Dynamic Viscosity Units

Pascal Second — SI Unit Derivation

\[ 1\,\text{Pa·s} = 1\,\frac{\text{N·s}}{\text{m}^2} = 1\,\frac{\text{kg}}{\text{m·s}} = 1\,\text{kg·m}^{-1}\text{s}^{-1} \]

All four expressions are dimensionally equivalent — these are all the same SI unit just written differently

💧

Pascal Second (Pa·s)

The SI base unit of dynamic viscosity. Water at 20°C ≈ 0.001 Pa·s. Honey: 2–10 Pa·s. Motor oil SAE 30: 0.15–0.20 Pa·s. Glass (at room temperature): ≈ \(10^{21}\) Pa·s!

🔬

Millipascal Second (mPa·s)

1 mPa·s = 0.001 Pa·s = 1 cP (exactly). Convenient for low-viscosity fluids. Water ≈ 1 mPa·s at 20°C. Used in clinical/pharmaceutical contexts alongside cP.

⚖️

kg/(m·s)

Identical to Pa·s by dimensional analysis: \(\text{Pa} = \text{kg/(m·s}^2)\), so \(\text{Pa·s} = \text{kg/(m·s)}\). Sometimes written in fundamental SI base units to make dimensional analysis explicit.

🏋️

kgf·s/m² — Technical Unit

Uses kilogram-force instead of newton: \(1\,\text{kgf·s/m}^2 = 9.80665\,\text{Pa·s}\) (exactly, using standard gravity \(g_n\)). Used in older German and Italian engineering literature.

🧪 CGS Viscosity Units — Poise & Centipoise

Before SI, the CGS (centimetre-gram-second) system was the dominant scientific measurement system. In CGS, the unit of dynamic viscosity is the poise (P), named after the French physicist Jean Léonard Marie Poiseuille (1797–1869), whose experimental and theoretical work on viscous flow through capillary tubes laid the groundwork for modern fluid mechanics.

The poise is defined in CGS units as \(1\,\text{P} = 1\,\text{g/(cm·s)} = 1\,\text{dyn·s/cm}^2\). Since 1 Pa = 10 dyn/cm², and 1 m = 100 cm, the relationship is: \(1\,\text{P} = 0.1\,\text{Pa·s}\). The centipoise (cP) — one hundredth of a poise — became vastly more common because it gives water a convenient viscosity of approximately 1 cP at 20°C.

Poise & Centipoise — Exact SI Relationships

\[ 1\,\text{P} = \frac{1\,\text{g}}{\text{cm·s}} = \frac{1\,\text{dyn·s}}{\text{cm}^2} = 0.1\,\text{Pa·s} \] \[ 1\,\text{cP} = 10^{-2}\,\text{P} = 10^{-3}\,\text{Pa·s} = 1\,\text{mPa·s} \]

These are exact conversions. Named after Jean Léonard Marie Poiseuille (1797–1869), who derived Hagen–Poiseuille flow in capillaries.

Hagen–Poiseuille Equation — Laminar Flow in a Pipe

\[ Q = \frac{\pi r^4 \Delta P}{8 \mu L} \]

\(Q\) = volumetric flow rate (m³/s) · \(r\) = pipe radius (m) · \(\Delta P\) = pressure difference (Pa) · \(\mu\) = dynamic viscosity (Pa·s) · \(L\) = pipe length (m) · Valid only for laminar flow (Re < 2,300)

🔬 Why centipoise is the most used unit: Water near room temperature has a viscosity of exactly 1.002 cP — making centipoise a naturally calibrated scale where water = approximately 1 unit. This makes relative viscosity immediately intuitive: motor oil at 150 cP is 150× more viscous than water.

🔧 Imperial & Engineering Viscosity Units

Several imperial viscosity units remain in use in American engineering practice, particularly in the petroleum, aerospace, and mechanical engineering sectors. These units are based on the pound-force (lbf), pound-mass (lb), foot (ft), inch (in), and second (s) — and their conversions to SI involve the exact 1959 inch definition and standard gravity \(g_n = 9.80665\,\text{m/s}^2\).

Imperial Viscosity Unit Conversions to Pa·s

\( 1\,\text{lb/(ft·s)} = 1.48816\,\text{Pa·s} \quad \text{(slug-related, used in aerodynamics)} \)

\( 1\,\text{lbf·s/ft}^2 = 47.8803\,\text{Pa·s} \quad \text{(force-based)} \)

\( 1\,\text{reyn} = 1\,\text{lbf·s/in}^2 = 6{,}894.76\,\text{Pa·s} \quad \text{(named after Osborne Reynolds)} \)

Derived from: 1 lb = 0.453592 kg, 1 ft = 0.3048 m, 1 in = 0.0254 m, \(g_n = 9.80665\,\text{m/s}^2\)

🌀 Navier–Stokes Equations & Viscosity

Dynamic viscosity \(\mu\) appears directly in the Navier–Stokes equations — the governing equations of fluid motion, which were developed by Claude-Louis Navier (1827) and George Gabriel Stokes (1845). For an incompressible Newtonian fluid:

Navier–Stokes Equation (Incompressible Newtonian Fluid)

\[ \rho \left( \frac{\partial \mathbf{u}}{\partial t} + \mathbf{u} \cdot \nabla \mathbf{u} \right) = -\nabla p + \mu \nabla^2 \mathbf{u} + \rho \mathbf{g} \]

\(\rho\) = density (kg/m³) · \(\mathbf{u}\) = velocity field (m/s) · \(p\) = pressure (Pa) · \(\mu\) = dynamic viscosity (Pa·s) · \(\mathbf{g}\) = gravitational acceleration (m/s²)

⚖️ Dynamic vs Kinematic Viscosity

Dynamic viscosity \(\mu\) and kinematic viscosity \(\nu\) are closely related but measure different aspects of fluid flow. Dynamic viscosity (also called absolute viscosity) measures the force required to shear a fluid at a given rate — it is relevant when external forces drive flow (e.g., pump pressure). Kinematic viscosity additionally accounts for the fluid's density — it is relevant for flows driven by gravity or inertia.

Dynamic vs Kinematic Viscosity Relationship

\[ \nu = \frac{\mu}{\rho} \]

\(\nu\) = kinematic viscosity (m²/s or stokes, St) · \(\mu\) = dynamic viscosity (Pa·s) · \(\rho\) = fluid density (kg/m³) · 1 stoke (St) = 1 cm²/s = 10⁻⁴ m²/s

📌 Example — Dynamic to Kinematic Viscosity (Water at 20°C)

Given: Water at 20°C: \(\mu = 1.002\,\text{mPa·s} = 1.002 \times 10^{-3}\,\text{Pa·s}\), \(\rho = 998.2\,\text{kg/m}^3\)

\[ \nu = \frac{\mu}{\rho} = \frac{1.002 \times 10^{-3}}{998.2} = 1.004 \times 10^{-6}\,\text{m}^2/\text{s} = 1.004\,\text{cSt (centistokes)} \]

Answer: Water at 20°C has a kinematic viscosity of approximately 1.004 cSt — very close to 1 centistoke, which makes water the calibration reference for kinematic viscosity.

🌀 Reynolds Number — Viscosity in Flow Regime Classification

The Reynolds number (Re) is a dimensionless quantity that characterises whether a flow is laminar (smooth, orderly) or turbulent (chaotic). It is a ratio of inertial forces to viscous forces, and dynamic viscosity \(\mu\) appears in its denominator — meaning more viscous fluids are more likely to flow laminarly for the same velocity and geometry.

Reynolds Number — Named After Osborne Reynolds (1883)

\[ Re = \frac{\rho v L}{\mu} = \frac{v L}{\nu} \]

\(v\) = flow velocity (m/s) · \(L\) = characteristic length (m, e.g., pipe diameter) · \(\mu\) = dynamic viscosity (Pa·s) · \(\nu\) = kinematic viscosity (m²/s)
Re < 2,300 → Laminar · 2,300 < Re < 4,000 → Transitional · Re > 4,000 → Turbulent

📌 Example — Reynolds Number for Water in a Pipe

Problem: Water flows at 2 m/s through a 5 cm (0.05 m) diameter pipe at 20°C. Is it laminar or turbulent?

\[ Re = \frac{\rho v D}{\mu} = \frac{998.2 \times 2 \times 0.05}{1.002 \times 10^{-3}} = \frac{99.82}{0.001002} \approx 99{,}620 \]

Answer: Re ≈ 99,620 ≫ 4,000, so the flow is highly turbulent. Reynolds number is the reason viscosity matters for pipe sizing and pump design.

🌡️ How Temperature Affects Dynamic Viscosity

One of the most practically important — and often counterintuitive — aspects of viscosity is its temperature dependence. For liquids, viscosity decreases with increasing temperature (heating makes them flow more easily). For gases, viscosity increases with temperature (more molecular collisions increase internal friction). These opposing trends arise from completely different molecular mechanisms.

Arrhenius Equation — Liquid Viscosity vs Temperature

\[ \mu = A \cdot e^{\,B/T} \]

\(A, B\) = fluid-specific constants · \(T\) = absolute temperature (Kelvin) · As \(T\) increases, \(\mu\) decreases exponentially for liquids

Sutherland's Formula — Gas Viscosity vs Temperature

\[ \mu = \mu_0 \left(\frac{T}{T_0}\right)^{3/2} \frac{T_0 + S}{T + S} \]

\(\mu_0\) = reference viscosity at \(T_0\) · \(S\) = Sutherland constant (for air: S = 120 K, \(\mu_0 = 1.716 \times 10^{-5}\,\text{Pa·s},\, T_0 = 273.15\,\text{K}\))

📊 Real-World Fluid Viscosity Reference (at 20°C unless noted)

Fluid	Viscosity (cP)	Viscosity (Pa·s)	Viscosity (P)
Air (20°C)	0.0182	\(1.82 \times 10^{-5}\)	\(1.82 \times 10^{-4}\)
Ethanol (20°C)	1.074	0.001074	0.01074
Water (0°C)	1.791	0.001791	0.01791
Water (20°C)	1.002	0.001002	0.01002
Water (40°C)	0.653	0.000653	0.00653
Water (100°C)	0.282	0.000282	0.00282
Milk (20°C)	2–3	0.002–0.003	0.02–0.03
Olive oil (20°C)	84	0.084	0.84
Motor oil SAE 10 (40°C)	65–90	0.065–0.090	0.65–0.90
Motor oil SAE 30 (40°C)	90–110	0.090–0.110	0.90–1.10
Motor oil SAE 40 (40°C)	140–170	0.140–0.170	1.40–1.70
Castor oil (25°C)	985	0.985	9.85
Honey (25°C)	2,000–10,000	2–10	20–100
Chocolate syrup	10,000–25,000	10–25	100–250
Peanut butter	150,000–250,000	150–250	1,500–2,500
Glass (25°C)	≈ \(10^{24}\)	≈ \(10^{21}\)	≈ \(10^{22}\)

🌡️ Temperature matters enormously. Engine oil can vary from over 1000 cP at cold start (−20°C) to under 10 cP at full operating temperature (150°C). This 100:1 range is exactly why multi-grade oils (e.g., SAE 5W-40) were developed — their viscosity index is high enough to remain pumpable when cold yet protective when hot.

🔬 Newtonian vs Non-Newtonian Fluids

Newton's law of viscosity (\(\tau = \mu\,du/dy\)) assumes that \(\mu\) is constant regardless of the applied shear rate. Fluids obeying this assumption are called Newtonian fluids. Those that don't are non-Newtonian, and their apparent viscosity changes with shear rate. This distinction is critical in food engineering, polymer processing, cosmetics, pharmaceuticals, and biological fluid mechanics.

Type	Behaviour	Examples	Model
Newtonian	Constant μ at any shear rate	Water, air, most oils, ethanol	\(\tau = \mu \dot{\gamma}\)
Shear-thinning (pseudoplastic)	μ decreases with shear rate	Ketchup, paint, blood, shampoo	Power-law: \(\tau = K\dot{\gamma}^n\), \(n < 1\)
Shear-thickening (dilatant)	μ increases with shear rate	Cornstarch in water (oobleck)	Power-law: \(\tau = K\dot{\gamma}^n\), \(n > 1\)
Bingham plastic	Yield stress required to flow	Toothpaste, mayonnaise, drilling mud	\(\tau = \tau_y + \mu_p\dot{\gamma}\)
Thixotropic	μ decreases with time at const. shear	Gels, some paints, yogurt	Time-dependent

⚠️ Important: Our calculator converts between unit systems for a given viscosity number. For non-Newtonian fluids, viscosity is not a single fixed value — it is measured at a specific shear rate and temperature. Always check the measurement conditions when using viscosity data in engineering calculations.

Written & Reviewed by Num8ers Editorial Team — Fluid Mechanics & Chemical Engineering Specialists Last updated: April 2026 · Conversion factors verified against NIST Special Publication 811 (2008), BIPM SI Brochure 9th ed. (2019), and CRC Handbook of Chemistry and Physics (103rd ed.)

❓ Frequently Asked Questions About Dynamic Viscosity Conversion

What is dynamic viscosity and what does it measure?

Dynamic viscosity (μ, absolute viscosity) measures a fluid's resistance to flow under an applied shear stress. Defined by Newton's law: \( \tau = \mu\,\frac{du}{dy} \) — shear stress = viscosity × shear rate. High μ → thick, slow-flowing fluid (honey, molasses). Low μ → thin, fast-flowing fluid (water, acetone). The SI unit is the pascal second (Pa·s).

How do I convert poise to pascal second?

Divide by 10 (or multiply by 0.1). \( 1\,\text{P} = 0.1\,\text{Pa·s} \) (exact). Example: 5 P = 0.5 Pa·s. Reverse: \( 1\,\text{Pa·s} = 10\,\text{P} \). This relationship comes from the CGS-to-SI unit conversion: \( 1\,\text{g/(cm·s)} = 0.1\,\text{kg/(m·s)} = 0.1\,\text{Pa·s} \).

How do I convert centipoise to pascal second?

Divide by 1,000 (or multiply by 0.001). \( 1\,\text{cP} = 10^{-3}\,\text{Pa·s} \) (exact). Also: \(1\,\text{cP} = 1\,\text{mPa·s}\). Example: 100 cP (motor oil) = 0.1 Pa·s. Water at 20°C = 1.002 cP = 0.001002 Pa·s.

Why is centipoise the most commonly used viscosity unit?

Because water at 20°C has a viscosity of approximately 1 cP (exactly 1.002 cP) — making it an intuitive reference point. Any fluid's viscosity in cP directly tells you how many times more viscous it is than room-temperature water. Honey at 5,000 cP is 5,000× more viscous than water. This makes centipoise extremely practical across industries.

What is the viscosity of water at different temperatures?

Water viscosity varies significantly with temperature: 0°C → 1.791 cP; 10°C → 1.307 cP; 20°C → 1.002 cP; 30°C → 0.798 cP; 40°C → 0.653 cP; 60°C → 0.467 cP; 80°C → 0.354 cP; 100°C → 0.282 cP. Water becomes nearly 6× less viscous from 0°C to 100°C — demonstrating the strong Arrhenius-type dependence of liquid viscosity on temperature.

What is the difference between dynamic and kinematic viscosity?

Dynamic viscosity (μ): absolute resistance to shear, Pa·s or cP. Depends on fluid composition and temperature. Kinematic viscosity (ν): \(\nu = \mu/\rho\) — dynamic viscosity divided by density, m²/s or centistokes (cSt). Kinematic viscosity naturally arises in flows driven by gravity or inertia (like Stokes settling law, pipe flow under gravity). Water at 20°C: μ = 1.002 cP, ν = 1.004 cSt.

How does temperature affect viscosity of liquids vs gases?

Liquids (e.g., water, oil): Viscosity DECREASES with temperature. Molecular cohesive forces weaken as thermal energy increases — molecules slip past each other more easily: \(\mu \propto e^{B/T}\). Gases (e.g., air): Viscosity INCREASES with temperature. More molecular collisions at higher temperatures transfer more momentum perpendicular to flow, increasing resistance: \(\mu \propto T^{3/2}/(T+S)\) (Sutherland's formula).

What is a reyn and where is it used?

1 reyn = 1 lbf·s/in² = 6,894.76 Pa·s. Named after Osborne Reynolds (1842–1912), who introduced the Reynolds number. The reyn is an imperial engineering unit used in lubrication engineering and tribology in the United States. It is an extremely large unit — 1 reyn is about 6.9 million times the viscosity of water!

What is a Newtonian fluid?

A Newtonian fluid obeys Newton's law of viscosity: \(\tau = \mu\,\dot{\gamma}\) — shear stress is directly proportional to shear rate, with a constant proportionality coefficient μ. Water, air, pure oils, and ethanol are Newtonian. Non-Newtonian fluids (ketchup, blood, toothpaste, paint) have shear-rate-dependent apparent viscosity — our converter handles fixed viscosity values, not shear-rate profiles.

What is the Hagen–Poiseuille equation?

The Hagen–Poiseuille equation describes laminar flow through a cylindrical pipe: \[ Q = \frac{\pi r^4 \Delta P}{8 \mu L} \] where Q = flow rate, r = radius, ΔP = pressure drop, μ = dynamic viscosity, L = pipe length. It shows flow rate is inversely proportional to viscosity — doubling viscosity halves the flow rate for a given pressure. Valid only for Re < 2,300 (laminar flow).

What does SAE motor oil viscosity grade mean?

SAE (Society of Automotive Engineers) grades classify motor oil by viscosity. Single grades: SAE 30 means viscosity ≈ 90–110 cP at 40°C. Multi-grades: SAE 5W-40 — "5W" = viscosity performance at −25°C (W = winter), "40" = viscosity at 100°C must be 12.5–16.3 mm²/s (cSt). Multi-grades were developed to remain fluid in cold starts and protective at operating temperature.

How do I measure dynamic viscosity?

Several viscometer types: Capillary viscometer — measures flow time through a tube (Hagen–Poiseuille, gives kinematic ν). Rotational viscometer (e.g., Brookfield) — measures torque on a rotating spindle (direct μ, used for non-Newtonian). Falling-ball viscometer — measures ball descent time (Stokes law: \(\mu = \frac{2r^2(\rho_b - \rho_f)g}{9v}\)). Vibrating viscometer — uses resonant frequency shift.

Is 1 cP exactly equal to 1 mPa·s?

Yes — exactly. \(1\,\text{cP} = 10^{-2}\,\text{P} = 10^{-2} \times 0.1\,\text{Pa·s} = 10^{-3}\,\text{Pa·s} = 1\,\text{mPa·s}\). This equality is mathematically exact, not an approximation. Many modern scientific publications use mPa·s because it is an SI-coherent unit, while industries often use cP for its practical convenience (water ≈ 1).

How accurate is the Num8ers Dynamic Viscosity Converter?

The converter uses exact or best-available conversion factors per NIST SP 811 and BIPM SI Brochure standards — e.g., 1 cP = 0.001 Pa·s (exact), 1 lb/(ft·s) = 1.48816394... Pa·s (from exact 1959 yard definitions). JavaScript double-precision arithmetic provides ~15 significant digits. The "All Units at Once" panel gives results simultaneously across all 20+ units.

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