Dynamic Viscosity Converter
Convert dynamic viscosity between Pa·s, mPa·s, centipoise (cP), poise (P), and lb/(ft·s). Fundamental to fluid flow, lubrication, and process engineering calculations.
Dynamic Viscosity in Fluid Mechanics
Dynamic viscosity (also called absolute viscosity) measures a fluid's resistance to shear deformation — essentially, how 'thick' or 'sticky' it is. The SI unit is the pascal-second (Pa·s). Water at 20 °C has a dynamic viscosity of 0.001002 Pa·s = 1.002 mPa·s = 1.002 cP (centipoise). Honey has a viscosity about 10,000 times higher; air about 50 times lower. These enormous differences have profound consequences for fluid flow, heat transfer, and mass transfer calculations.
Dynamic viscosity governs pressure drop in pipes and ducts (Hagen-Poiseuille equation), settling rates of particles in suspension (Stokes' law), lubrication film thickness in bearings, and mixing power in stirred vessels. Engineers in the US commonly work in centipoise (cP) or lb/(ft·s); EU and UK engineers use mPa·s or Pa·s. Since 1 cP = 1 mPa·s exactly, this is the most convenient equivalence in all of fluid mechanics.
Units: Pa·s, mPa·s, and cP
The pascal-second (Pa·s) is the SI unit of dynamic viscosity, defined as the force needed to move a 1 m² layer at 1 m/s relative velocity when 1 m apart. The centipoise (cP) is the CGS unit widely used in industry because of its convenient scale: water at 20 °C is exactly 1.002 cP — essentially 1 cP. This 'water = 1 cP' benchmark makes centipoise intuitive for comparing fluid viscosities. Since 1 Pa·s = 1,000 mPa·s and 1 cP = 1 mPa·s, the conversion between cP and mPa·s is trivial.
The poise (P), the CGS base unit, equals 0.1 Pa·s or 100 cP. It is named after Jean Léonard Marie Poiseuille, whose 1840s experiments on flow in capillary tubes laid the foundation of viscous flow theory. The poise is rarely used in modern engineering except in historical texts and some US chemical engineering references. Motor oil viscosities are sometimes published in poise in older ASTM data sheets.
Practical Viscosity Values
Understanding the viscosity range across common fluids is essential for engineering design. Air at 20 °C has a dynamic viscosity of about 0.018 mPa·s (0.018 cP). Water at 20 °C is 1.002 mPa·s. Whole blood is approximately 3–4 mPa·s — relevant for blood pump and artificial heart valve design. Motor oil (SAE 10W-40) has a viscosity of approximately 90–110 mPa·s at 40 °C, falling to 15–20 mPa·s at 100 °C.
Very viscous fluids present significant engineering challenges. Heavy fuel oil (HFO) used in ship engines has a viscosity of 380–700 mPa·s at 50 °C, requiring heating to reduce viscosity for pumping. Polymer melts processed in injection moulding machines reach viscosities of 100–100,000 Pa·s. Asphalt/bitumen used in road paving has viscosities of 10,000–1,000,000 Pa·s at ambient temperature, which is why it flows so slowly under gravity.
US and UK Engineering Applications
The American Society for Testing and Materials (ASTM) publishes viscosity test methods (ASTM D445, D7042) for petroleum products, with results in mPa·s (= cP). SAE International viscosity grades for engine oils (SAE 5W-30, 10W-40) specify kinematic viscosity limits in mm²/s (cSt), which requires density data to convert to dynamic viscosity. US chemical engineers typically work in cP for process calculations.
UK lubrication and fluid power engineering follows ISO viscosity grades (ISO VG 32, 46, 68, 100) defined in mm²/s at 40 °C. Hydraulic fluid specifications in BS EN ISO 6743-4 use kinematic viscosity (cSt/mm²/s) and must be combined with density to give dynamic viscosity in mPa·s. UK pharmaceutical manufacturing specifications for injectable drug solutions typically require viscosity measurements in mPa·s using pharmacopoeial methods (BP/USP capillary viscometer tests).
Core Conversion Formulas
The underlying mathematics used by our converter engine.
| Conversion | Exact Mathematical Formula |
|---|---|
| Pa·s → mPa·s | mPa·s = Pa·s × 1000 |
| cP → Pa·s | Pa·s = cP × 0.001 |
| cP → mPa·s | mPa·s = cP × 1 (exact — cP ≡ mPa·s) |
| P → Pa·s | Pa·s = P × 0.1 |
| lb/(ft·s) → Pa·s | Pa·s = lb/(ft·s) × 1.48816 |
Frequently Asked Questions
What is the viscosity of water?
Water at 20 °C has a dynamic viscosity of 1.002 mPa·s (1.002 cP). It decreases significantly with temperature: at 60 °C it is 0.467 mPa·s; at 100 °C it is 0.282 mPa·s. This temperature dependence is why hot water flows more easily through pipes and why cooling water velocity must account for seasonal temperature variation.
What is the difference between dynamic and kinematic viscosity?
Dynamic viscosity (μ, Pa·s or cP) measures absolute resistance to shear. Kinematic viscosity (ν, m²/s or cSt) is dynamic viscosity divided by density: ν = μ/ρ. Kinematic viscosity appears in flow equations where gravity or inertia drives the fluid (pipe flow Reynolds number, Navier-Stokes equations). For water at 20 °C: μ = 1.002 mPa·s, ρ = 998 kg/m³, ν = 1.004 mm²/s = 1.004 cSt.
Is centipoise the same as mPa·s?
Yes, exactly. 1 cP = 1 mPa·s. This is one of the most convenient unit equivalences in engineering. Water at 20 °C ≈ 1 cP = 1 mPa·s. You can use centipoise and millipascal-second interchangeably in all calculations.
What viscosity is motor oil?
SAE 10W-40 motor oil has a dynamic viscosity of approximately 90–110 mPa·s at 40 °C and 14–18 mPa·s at 100 °C. The W (winter) rating relates to cold-start viscosity; the hot viscosity determines oil film thickness at operating temperature. Lower numbers mean thinner oil; modern engines typically use 5W-30 or 0W-20 for better fuel efficiency.
How is viscosity important in pipeline design?
Pipe pressure drop is proportional to dynamic viscosity (Hagen-Poiseuille: ΔP = 128·μ·L·Q/(π·d⁴) for laminar flow). Pumping viscous fluids like heavy oil requires much larger pressure heads than water. A pipeline designed for water (1 mPa·s) pumping heavy crude oil (500 mPa·s) would require 500 times the pressure drop — necessitating complete redesign of the pump, pipe diameter, or heating of the oil.
Real-World Benchmarks
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Air at 20 °C
Standard atmosphere
0.0182 mPa·s
0.0182 cP
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Water at 20 °C
Reference standard
1.002 mPa·s
1.002 cP
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Whole blood
Human at 37 °C
3–4 mPa·s
3–4 cP
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SAE 10W-40 oil
At 40 °C
~100 mPa·s
~100 cP
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Honey (liquid)
At 25 °C
~2,000–10,000 mPa·s
~2,000–10,000 cP