How do I convert centipoise to pascal seconds?

Divide by 1,000 (exact). 1 cP = 0.001 Pa·s = 1 mPa·s. Example: 100 cP (motor oil at 40°C) = 0.1 Pa·s. Reverse: 1 Pa·s = 1,000 cP.

What do SAE motor oil numbers mean?

SAE 5W-30: '5W' = winter cold-performance grade (max 6,600 cP at -30°C cranking). '30' = hot viscosity grade at 100°C (9.3-12.5 cSt per SAE J300). W = winter, not weight.

What viscosity motor oil should I use?

Always follow your manufacturer's specification in the owner's manual. Modern cars typically require 5W-30, 0W-20, or 5W-40. Using the wrong grade can affect engine protection and fuel economy.

Is cP equal to mPa·s?

Yes, exactly. 1 cP = 1 mPa·s = 0.001 Pa·s. This is a mathematical identity, not an approximation.

Why can water not lubricate a car engine?

At 90°C, water = 0.315 cP while SAE 5W-30 = ~10 cP (32x more viscous). Water lacks adequate viscosity to maintain the hydrodynamic film needed between metal bearing surfaces.

How accurate is the Num8ers Oil and Water Viscosity Converter?

Uses exact conversion factors per NIST SP 811. Fluid reference values from NIST WebBook, CRC Handbook, SAE J300, and peer-reviewed literature. Actual viscosity depends on composition, exact temperature, and shear rate.

🛢️ Oil & Water Viscosity Conversion Calculator

Convert cP, Pa·s, poise, mPa·s & imperial units — plus compare motor oil, water, glycerin, honey & 20+ fluids at real temperatures with Arrhenius & SAE J300 formulas

Unit Converter Fluid Comparison Mode SAE Grade Guide Free & Instant

🔄 Oil & Water Viscosity Converter

Enter Value From Unit

Result To Unit

1 cP = 0.001 Pa·s

Formula: value × 0.001

📊 Common Fluid Viscosities at a Glance

💡 Newton's law: \( \tau = \mu \frac{du}{dy} \) — shear stress equals dynamic viscosity times shear rate. All units are expressions of this \(\mu\). Pivot unit: Pa·s.

📖 How to Use the Oil & Water Viscosity Converter

1

Choose a Mode: Unit Converter or Fluid Comparison
Click "🔢 Unit Converter" to convert a viscosity value between cP, Pa·s, poise, mPa·s, and imperial units. Click "🧪 Fluid Comparison" to look up the actual viscosity of water, motor oil, honey, glycerin and 20+ real fluids at specific temperatures.
2

Enter a Value or Select a Fluid
In Unit Converter mode, type your viscosity value. In Fluid Comparison mode, select a fluid and temperature from the dropdown. Both modes update the common fluid reference panel below.
3

Select Source & Target Units
Choose your starting unit from "From Unit" and desired output from "To Unit." The result appears live showing both the converted value and the multiplication factor used.
4

Use Quick-Convert Buttons
Click cP→Pa·s, P→cP, cP→mPa·s, or other preset buttons for the most frequent conversions. Both dropdowns set automatically — no manual selection needed.
5

Reference the Fluid Comparison Panel
The "Common Fluid Viscosities" panel always shows viscosities for water, motor oils, glycerin, honey, and more — useful for understanding the practical scale of your converted value.

📐 Viscosity Unit Conversion Reference

Unit	System	Exact Value in Pa·s	Math Expression
Pascal second (Pa·s)	SI	1 (base)	\( 1\,\text{Pa·s} = 1\,\text{kg/(m·s)} \)
Millipascal second (mPa·s)	SI	0.001	\( 1\,\text{mPa·s} = 10^{-3}\,\text{Pa·s} = 1\,\text{cP} \)
Centipoise (cP)	CGS	0.001 (exact)	\( 1\,\text{cP} = 10^{-3}\,\text{Pa·s} = 1\,\text{mPa·s} \)
Poise (P)	CGS	0.1 (exact)	\( 1\,\text{P} = 0.1\,\text{Pa·s} = 100\,\text{cP} \)
Millipoise (mP)	CGS	0.0001	\( 1\,\text{mP} = 10^{-4}\,\text{Pa·s} \)
N·s/m²	SI	1 (exact)	\( 1\,\text{N·s/m}^2 = 1\,\text{Pa·s} \)
kg/(m·s)	SI	1 (exact)	\( 1\,\text{kg/(m·s)} = 1\,\text{Pa·s} \)
kgf·s/m²	Technical	9.80665	\( 1\,\text{kgf·s/m}^2 = g_n \approx 9.807\,\text{Pa·s} \)
lb/(ft·s)	Imperial	1.48816	\( 1\,\text{lb/(ft·s)} \approx 1.488\,\text{Pa·s} \)
lbf·s/ft²	Imperial	47.8803	\( 1\,\text{lbf·s/ft}^2 \approx 47.88\,\text{Pa·s} \)
reyn (lbf·s/in²)	Imperial	6,894.76	\( 1\,\text{reyn} = 1\,\text{lbf·s/in}^2 \approx 6{,}895\,\text{Pa·s} \)

🌊 Oil & Water Viscosity — A Comprehensive Guide

When engineers, mechanics, food scientists, chemists, or everyday users need to understand fluid flow, viscosity is the central property. But viscosity is expressed in many different unit systems — centipoise (cP) in laboratories, Pa·s in SI engineering, poise in older CGS literature, cSt in lubricant datasheets, and SAE grades on motor oil bottles. The gap between these unit systems causes constant conversion errors that this tool eliminates instantly.

This page focuses specifically on the two most practically important liquids in everyday engineering and science: water (the universal reference fluid) and oil (the most commercially important category of viscous fluids, encompassing motor oils, hydraulic oils, industrial lubricants, food oils, and crude petroleum). Understanding how their viscosities compare — and how viscosity is affected by temperature — is essential knowledge for anyone working with fluids.

Newton's Law of Viscosity — The Foundation

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

\(\tau\) = shear stress (Pa) · \(\mu\) = dynamic viscosity (Pa·s) · \(du/dy\) = velocity gradient / shear rate (s⁻¹) · Valid for Newtonian fluids: water, clean oils, air, ethanol

💧 Water Viscosity — The Universal Reference

Water is the universal calibration standard for viscosity measurement. At 20°C, water has a dynamic viscosity of exactly 1.0020 centipoise (cP) = 1.0020 mPa·s = 0.0010020 Pa·s — so close to 1 cP that the centipoise system was historically designed around water as the reference. This is why 1 cP immediately tells you "this is roughly as thick as water."

Water's viscosity changes significantly with temperature — ranging from 1.792 cP at 0°C to just 0.282 cP at 100°C, a 6.35× decrease over the water's liquid temperature range. This temperature dependence follows an Arrhenius-type relationship and can be precisely modelled by Vogel–Fulcher–Tammann (VFT) or the Andrade equation.

Andrade Equation — Water Viscosity vs Temperature

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

For water: \(A \approx 2.414 \times 10^{-5}\,\text{Pa·s}\), \(B \approx 247.8\,\text{K}\), expressed with \(T\) in Kelvin. Viscosity decreases exponentially as temperature rises.

Temperature	μ (cP = mPa·s)	μ (Pa·s)	μ (Poise)	Relative to 20°C Water
0°C (32°F)	1.792	0.001792	0.01792	1.79×
20°C (68°F)	1.002	0.001002	0.01002	1.00× (reference)
25°C (77°F)	0.890	0.000890	0.00890	0.89×
37°C (body temperature)	0.690	0.000690	0.00690	0.69×
40°C (104°F)	0.653	0.000653	0.00653	0.65×
60°C (140°F)	0.467	0.000467	0.00467	0.47×
80°C (176°F)	0.355	0.000355	0.00355	0.35×
100°C (212°F)	0.282	0.000282	0.00282	0.28×

🩺 Blood vs water: Human blood at 37°C has a dynamic viscosity of approximately 3–4 cP — about 4–6× more viscous than water at the same temperature. Blood is a non-Newtonian fluid (Casson model), so its apparent viscosity changes with shear rate in capillaries vs large vessels — essential for cardiovascular modelling and pump design.

🛢️ Motor Oil Viscosity — Temperature, SAE Grades & Multigrade Oils

Motor oil viscosity is far more temperature-sensitive than water. The typical SAE 30 oil has a dynamic viscosity of ~100 cP at 40°C but drops to only ~10–12 cP at 100°C — a 10× change over 60°C, compared to water's 1.5× change over the same range. This dramatic sensitivity is why multi-grade oils like SAE 5W-40 were developed — they use polymer additives (viscosity index improvers) that coil at low temperatures and uncoil at high temperatures, creating a higher viscosity index.

ASTM D341 — Walther's Equation for Oil Viscosity vs Temperature

\[ \log\log(\nu + 0.7) = A - B \cdot \log T \]

\(\nu\) = kinematic viscosity (cSt) · \(T\) = temperature (K) · \(A, B\) = constants from two measured data points · Standard ASTM viscosity-temperature chart basis

SAE Grade	Cold Cranking (cP)	\(\nu\) at 40°C (cSt)	\(\nu\) at 100°C (cSt)	Best For
SAE 5W-20	≤ 6,600 at −30°C	35–50	6.9–9.3	New fuel-efficient engines
SAE 5W-30	≤ 6,600 at −30°C	50–75	9.3–12.5	Most modern passenger cars
SAE 5W-40	≤ 6,600 at −30°C	75–110	12.5–16.3	European engines, sporty driving
SAE 10W-40	≤ 7,000 at −25°C	90–120	12.5–16.3	General purpose, older engines
SAE 10W-30	≤ 7,000 at −25°C	65–90	9.3–12.5	Moderate climates
SAE 15W-40	≤ 7,000 at −20°C	100–120	12.5–16.3	Heavy-duty diesel engines
SAE 0W-20	≤ 6,200 at −35°C	25–45	6.9–9.3	Hybrid vehicles, best fuel economy
SAE 0W-16	≤ 6,200 at −35°C	20–35	6.1–8.2	Ultra-low viscosity, fuel economy

Decoding SAE Multi-Grade Oil: e.g. SAE 5W-40

\( \text{"5W"} \Rightarrow \text{Maximum cranking viscosity at cold temperature (W = Winter)} \)

\( \text{"40"} \Rightarrow \nu_{100°C} \in [12.5,\; 16.3]\,\text{cSt} \quad \text{per SAE J300} \)

\( VI = \frac{L - U}{L - H} \times 100 \geq 150 \quad \text{for most modern synthetics} \)

The W-number is NOT viscosity — it is a cold-performance classification. Lower W = better cold starting. The second number measures high-temperature/high-shear (HTHS) performance per ASTM D4683.

📈 Viscosity Index (VI) — The Stability Metric

The Viscosity Index is an empirical number defined by ASTM D2270 that quantifies how much a lubricant's kinematic viscosity changes between 40°C and 100°C. It was originally conceived in 1929 by Ernest Dean and G.H.B. Davis, who assigned a VI of 0 to naphthenic crude oils and VI = 100 to paraffinic crude oils — establishing a 0–100 scale. Modern lubricants with polymer additives routinely exceed VI = 150.

Viscosity Index Formula (ASTM D2270)

\[ VI = \frac{L - U}{L - H} \times 100 \]

\(U\) = kinematic viscosity (cSt) at 40°C of tested oil · \(L\) = reference VI=0 oil at same 100°C viscosity · \(H\) = reference VI=100 oil at same 100°C viscosity · All from ASTM D2270 lookup tables

🛢️

Mineral Oil (Group I)

VI typically 80–100. Naphthenic base stocks have lower VI (~40). Refined paraffinic stocks achieve VI ~100. Limited high-temperature performance. Being phased out for passenger cars.

⚙️

Hydrocracked (Group II/III)

VI 100–130+. Group III (VHVI) achieves VI 120–150. Used in "synthetic-blend" and some full-synthetic oils. Near-zero sulphur and aromatics for cleaner operation.

🔬

PAO Synthetic (Group IV)

VI 140–175. Polyalphaolefin (PAO) — true synthetic. Excellent temperature stability, very low pour point (−60°C possible). Used in aerospace, racing, and extended-drain intervals.

🌿

Ester-based (Group V)

VI 150–200+. Includes polyol esters, diesters. Biodegradable options available. Used in jet engines, food-grade lubrication, and environmentally sensitive applications.

📊 Viscosity Comparison — Water, Oils & Everyday Fluids

Fluid	Temperature	Viscosity (cP)	Viscosity (Pa·s)	Times More Viscous Than Water at 20°C
Air	20°C	0.0182	\(1.82 \times 10^{-5}\)	0.018×
Water	20°C	1.002	0.001002	1× (reference)
Water	0°C	1.792	0.001792	1.79×
Blood (human)	37°C	~3.5	~0.0035	~3.5×
Milk	20°C	2.0–3.0	0.002–0.003	~2.5×
Olive oil	25°C	84	0.084	84×
SAE 5W-30 oil	40°C	~60–80	~0.07	~70×
SAE 30 motor oil	40°C	~100	~0.10	~100×
SAE 40 motor oil	40°C	~140	~0.14	~140×
SAE 5W-30 oil	100°C	~10–12	~0.011	~11×
Glycerin	20°C	~1,490	1.490	~1,490×
Glycerin	40°C	~630	0.630	~630×
Honey	25°C	~3,000–10,000	3–10	~5,000×
Chocolate syrup	25°C	~10,000–25,000	10–25	~15,000×
Peanut butter	25°C	~200,000	200	~200,000×
Bitumen / asphalt	25°C	\(>10^8\)	\(>10^5\)	\(>10^8\times\)

🍯 The pitch drop experiment: Bitumen (asphalt) poured into a funnel in 1927 at the University of Queensland has produced only 9 drops in ~97 years — its viscosity at room temperature is approximately \(2 \times 10^8\,\text{Pa·s}\), about \(2 \times 10^{11}\) times that of water. This confirms that bitumen is indeed a liquid, just an extraordinarily viscous one.

⚖️ Water vs Oil — Key Viscosity Differences

Water and oil have profoundly different viscosity behaviours that reflect their completely different molecular structures. Water (H₂O, molecular weight 18 g/mol) forms a strong hydrogen-bonding network that reduces viscosity sharply with temperature. Hydrocarbon oils (molecular weights of 200–600 g/mol per chain) are held together by weaker van der Waals forces, but their long molecular chains create significantly more internal friction — hence higher viscosity for the same chain architecture.

Oil-Water Relative Viscosity at Engine Operating Temperature

\( \mu_{\text{water, 90°C}} \approx 0.315\,\text{cP} \)

\( \mu_{\text{SAE 5W-30, 100°C}} \approx 10\,\text{cP} \)

\( \dfrac{\mu_{\text{oil}}}{\mu_{\text{water}}} \approx \frac{10}{0.3} \approx 33 \quad \text{(oil is ~33× more viscous than water at engine temperature)} \)

This difference is why water cannot lubricate steel engine bearings — its viscosity is too low to maintain a hydrodynamic film at operating conditions.

📌 Worked Example — Converting Motor Oil Viscosity Across Unit Systems

Problem: A lubrication engineer needs SAE 5W-30 motor oil viscosity (100 cP at 40°C) expressed in Pa·s, poise, and lbf·s/ft² for an international compliance report.

Step 1 — cP to Pa·s: \( 100\,\text{cP} \times 0.001\,\text{Pa·s/cP} = 0.100\,\text{Pa·s} \)

Step 2 — cP to Poise: \( 100\,\text{cP} \div 100 = 1.00\,\text{P} \)

Step 3 — Pa·s to lbf·s/ft²: \( 0.100\,\text{Pa·s} \div 47.8803 = 0.002089\,\text{lbf·s/ft}^2 \)

Summary: \( 100\,\text{cP} = 0.100\,\text{Pa·s} = 1.00\,\text{P} = 100\,\text{mPa·s} = 0.002089\,\text{lbf·s/ft}^2 \approx 3.03 \times 10^{-5}\,\text{reyn} \)

❄️ Cold-Start Viscosity — Why It Matters for Engine Protection

The most dangerous moment for an internal combustion engine is the first few seconds after a cold start — when the oil is cold, thick, and has not yet circulated throughout the bearing surfaces. Data from the American Petroleum Institute (API) and SAE International shows that up to 80% of engine wear occurs during cold starts when oil has not yet reached components. This is why the SAE J300 standard specifies a maximum cold cranking viscosity (in cP, measured at the lower test temperature) in addition to the hot viscosity.

SAE J300 Cold Cranking vs Pumping Viscosity Requirements

\( \mu_{\text{cranking, max}} \leq 6{,}600\,\text{cP} \quad \text{for SAE xW-30/40 (x = 0, 5)} \)

\( \mu_{\text{pumping, max}} \leq 60{,}000\,\text{cP with no yield stress} \quad \text{(ensures oil reaches pump)} \)

Measured using: Cold Cranking Simulator (CCS, ASTM D2602) and Mini-Rotary Viscometer (MRV, ASTM D3829). Units in cP by convention.

Written & Reviewed by Num8ers Editorial Team — Lubrication Engineering & Fluid Science Specialists Last updated: April 2026 · Fluid viscosity data verified against NIST WebBook, CRC Handbook of Chemistry and Physics (103rd ed.), SAE J300 (2021), API 1509, ISO 3448, and ASTM D2270/D341 standards.

❓ Frequently Asked Questions — Oil & Water Viscosity

What is the viscosity of water at 20°C in cP, Pa·s, and poise?

Water at 20°C has dynamic viscosity of 1.002 cP = 0.001002 Pa·s = 0.01002 P = 1.002 mPa·s. This is why centipoise is so widely used — water at room temperature is approximately 1 unit. It decreases from 1.792 cP at 0°C to 0.282 cP at 100°C. The formula is: \(\mu_{\text{water}} \approx A\,e^{B/T}\) (Andrade equation).

How do I convert centipoise (cP) to pascal seconds (Pa·s)?

Divide by 1,000 (or multiply by 0.001). \(1\,\text{cP} = 0.001\,\text{Pa·s} = 1\,\text{mPa·s}\) (exact). Example: SAE 30 oil at 100 cP = 0.1 Pa·s. Reverse: 1 Pa·s = 1,000 cP. This exact relationship makes cP and mPa·s numerically identical — your choice of notation.

How do I convert poise to centipoise?

Multiply by 100 (exact). \(1\,\text{P} = 100\,\text{cP} = 0.1\,\text{Pa·s}\). Reverse: \(1\,\text{cP} = 0.01\,\text{P}\). Poise is the CGS unit (1 g/(cm·s)); centipoise became preferred because water ≈ 1 cP — an intuitive reference.

What do SAE oil grade numbers mean (e.g., SAE 5W-40)?

"5W" = Winter cold-performance grade: maximum cold cranking viscosity at −30°C ≤ 6,600 cP. "40" = Hot viscosity grade: kinematic viscosity at 100°C must be 12.5–16.3 cSt per SAE J300. The "W" does NOT stand for "weight" — it means Winter. A lower W-number means better cold-start pumpability; a higher second number means thicker oil at operating temperature.

What is the best motor oil viscosity for my car?

Always follow your manufacturer's specification. This is printed in your owner's manual and often on the oil filler cap. Modern passenger cars typically require SAE 5W-30 or 0W-20. European engines often specify 5W-40. Older or high-mileage engines may use 10W-40. Using the wrong grade can affect fuel economy, engine protection, and may void warranty.

How does temperature affect motor oil viscosity?

Oil viscosity decreases dramatically with temperature. A typical SAE 30: ~100 cP at 40°C → ~10 cP at 100°C (10× reduction over 60°C). The relationship follows Walther's equation: \(\log\log(\nu + 0.7) = A - B\log T\) (ASTM D341). This is why multi-grade oils with high viscosity index (VI) were developed — they deliver adequate protection across the full operating range.

What is viscosity index (VI) and why does it matter?

VI (ASTM D2270) measures how much an oil's viscosity changes between 40°C and 100°C: \(VI = (L-U)/(L-H) \times 100\). High VI (above 150 for modern synthetics) = minimal viscosity change with temperature. Low VI oil thins too much when hot (poor film protection) and is too thick when cold (poor pumpability). Viscosity index improvers (polymeric additives) raise VI in multi-grade oils.

Is cP the same as mPa·s?

Yes — exactly equal. \(1\,\text{cP} = 1\,\text{mPa·s} = 0.001\,\text{Pa·s}\) (exact mathematical identity). Many modern technical publications and standards prefer mPa·s because it is an SI-coherent unit, while industry traditionally uses cP for its convenience (water ≈ 1 at 20°C). The numbers are always identical.

What is the viscosity of glycerin (glycerol)?

Glycerin at 20°C: approximately 1,490 cP = 1.49 Pa·s — about 1,490 times more viscous than water. At 40°C: ~630 cP. At 60°C: ~150 cP. Glycerin viscosity is extremely temperature-sensitive due to its hydroxyl groups forming a hydrogen-bonded network. Used as a reference fluid in viscometer calibration and as a viscosity standard in food and pharmaceutical formulation.

Why can't water lubricate a car engine?

At engine operating temperatures (~90°C), water viscosity is only ~0.315 cP, while SAE 5W-30 at 100°C is ~10 cP — about 32× more viscous. Hydrodynamic lubrication requires a minimum film thickness determined by the Stribeck curve and \(\eta N/P\) parameter. Water's viscosity is too low to sustain the required oil film between metal surfaces, leading to direct metal-to-metal contact and rapid wear.

What is the difference between dynamic and kinematic viscosity for oils?

Dynamic (μ): shear resistance, Pa·s or cP. Direct measure of force needed to flow. Kinematic (ν = μ/ρ): m²/s or cSt. Used when gravity drives flow. For petroleum oils (density ≈ 0.85–0.90 g/cm³): \(\nu\,[\text{cSt}] = \mu\,[\text{cP}] / \rho\,[\text{g/cm}^3] \approx \mu \times 1.11\). SAE grades use kinematic viscosity at 100°C; ISO VG uses kinematic at 40°C; cold cranking uses dynamic in cP.

What is the viscosity of crude oil?

Crude oil viscosity varies enormously by type: Light crude (API > 40°): 1–10 cP at 20°C. Medium crude (API 20–40°): 10–200 cP. Heavy crude (API < 20°): 200–100,000 cP. Extra-heavy crude & bitumen: \(>10^5\) cP at 25°C, often requiring heating to 60–80°C for pipeline transport. Venezuela's Orinoco Belt heavy crude often exceeds 10,000 cP and must be blended with diluents.

How accurate is the Num8ers Oil & Water Viscosity Converter?

The unit converter uses exact or highest-precision conversion factors per NIST SP 811: 1 cP = 0.001 Pa·s (exact); 1 P = 0.1 Pa·s (exact); 1 lbf·s/ft² = 47.8803 Pa·s (from exact 1959 foot and standard gravity definitions). Fluid viscosity reference values are typical measured values from NIST WebBook, CRC Handbook, and published peer-reviewed data — actual fluid viscosity depends on composition, exact temperature, pressure, and shear rate.

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