Viscosity Conversion: Centipoise, Stokes, and Poise Explained Viscosity is a fundamental property of fluids that describes resistance to flow. Engineers, scientists, and technicians often need to convert between different viscosity units—especially between dynamic viscosity units like poise (P) and centipoise (cP), and kinematic viscosity units like stokes (St) and centistokes (cSt). This article explains the key concepts, gives clear conversion formulas, walks through worked examples, and highlights practical applications and best practices so you can convert viscosities accurately and confidently. Introduction Viscosity appears in many fields: lubrication and tribology, chemical processing, food science, medical diagnostics (blood viscosity), coatings and inks, and fluid dynamics modeling. Two distinct types of viscosity are commonly measured: Dynamic (absolute) viscosity — resistance to shear stress (units: poise, Pa·s). Kinematic viscosity — dynamic viscosity divided by density; describes flow under gravity (units: stokes, m^2/s). A common source of confusion is that the numerical values of dynamic and kinematic viscosity differ and require the fluid density to convert between them. Moreover, many industries use cP and cSt because they are convenient for the magnitudes encountered. This article will make conversions clear, provide conversion tables, and present real worked examples. Key Concepts / Definitions Dynamic viscosity (μ): The shear stress required to produce a unit shear rate. Common units: poise (P): CGS unit, 1 P = 1 g·cm⁻¹·s⁻¹. centipoise (cP): 1 cP = 0.01 P (commonly used); equivalently 1 cP = 1 mPa·s = 0.001 Pa·s. SI unit: pascal-second (Pa·s). Kinematic viscosity (ν): Ratio of dynamic viscosity to density: ν = μ / ρ. Units: stokes (St) in CGS (1 St = 1 cm²/s) and centistokes (cSt) (1 cSt = 0.01 St). SI unit: square meter per second (m²/s). Note 1 St = 1e-4 m²/s, 1 cSt = 1e-6 m²/s. Density (ρ): Mass per unit volume, usually in g/cm³ for CGS conversions or kg/m³ for SI conversions. Conversion between systems: 1 g/cm³ = 1000 kg/m³. Important relation (the most-used formula for conversion between dynamic and kinematic viscosity): ν = μ / ρ (where μ and ρ are expressed in compatible units; e.g., μ in cP and ρ in g/cm³ gives ν in cSt) Why this is useful: because many catalogs list dynamic viscosity (cP) while hydraulic or flow calculations require kinematic viscosity (cSt or m²/s). Conversion Formulas Here are the essential conversion factors and formulas you will use regularly. Key conversion factors are bolded. Dynamic viscosity: 1 P = 0.1 Pa·s 1 cP = 0.01 P = 0.001 Pa·s = 1 mPa·s 1 Pa·s = 10 P = 1000 cP Kinematic viscosity: 1 St = 1 cm²/s = 1 × 10⁻⁴ m²/s 1 cSt = 0.01 St = 1 × 10⁻⁶ m²/s = 1 mm²/s 1 m²/s = 10⁴ St = 10⁶ cSt Dynamic ↔ Kinematic: ν (cSt) = μ (cP) / ρ (g/cm³) Because 1 cP = 1 mPa·s and 1 cSt = 1 mm²/s = 1e-6 m²/s, using μ in cP and ρ in g/cm³ gives ν in cSt. In SI units: ν (m²/s) = μ (Pa·s) / ρ (kg/m³) Examples of using these formulas are provided in the next section. Conversion Reference Table | Quantity | Unit | Symbol | Equivalent | |---|---:|---|---| | Dynamic viscosity | poise | P | 1 P = 0.1 Pa·s | | Dynamic viscosity | centipoise | cP | 1 cP = 0.01 P = 0.001 Pa·s = 1 mPa·s | | Dynamic viscosity | pascal-second | Pa·s | 1 Pa·s = 10 P = 1000 cP | | Kinematic viscosity | stokes | St | 1 St = 1 cm²/s = 1 × 10⁻⁴ m²/s | | Kinematic viscosity | centistoke | cSt | 1 cSt = 1 mm²/s = 1 × 10⁻⁶ m²/s | | Density | g/cm³ | — | 1 g/cm³ = 1000 kg/m³ | | Relation | — | — | ν = μ / ρ (ensure compatible units) | Practical Examples (with worked calculations) Below are step-by-step worked examples applying the above formulas and conversion factors. Each includes unit consistency checks. Example 1 — Convert 50 cP to Pa·s: Given: μ = 50 cP. Use: 1 cP = 0.001 Pa·s. Calculation: μ = 50 × 0.001 = 0.050 Pa·s. Result: 50 cP = 0.050 Pa·s. Example 2 — Convert 20 cSt to m²/s: Given: ν = 20 cSt. Use: 1 cSt = 1 × 10⁻⁶ m²/s. Calculation: ν = 20 × 1e-6 = 2.0 × 10⁻⁵ m²/s. Result: 20 cSt = 2.0 × 10⁻⁵ m²/s. Example 3 — Convert dynamic viscosity to kinematic viscosity (use density): Given: μ = 3.5 cP, density ρ = 0.80 g/cm³ (e.g., a light oil). Use: ν (cSt) = μ (cP) / ρ (g/cm³). Calculation: ν = 3.5 / 0.80 = 4.375 cSt. Convert to m²/s: 4.375 × 1e-6 = 4.375 × 10⁻⁶ m²/s. Result: μ = 3.5 cP and ρ = 0.80 g/cm³ ⇒ ν = 4.375 cSt = 4.375 × 10⁻⁶ m²/s. Example 4 — Convert 0.045 Pa·s to cP and P: Given: μ = 0.045 Pa·s. Use: 1 Pa·s = 1000 cP, 1 Pa·s = 10 P. Calculation: In cP: 0.045 × 1000 = 45 cP. In P: 0.045 × 10 = 0.45 P. Result: 0.045 Pa·s = 45 cP = 0.45 P. Example 5 — Water at ~20°C (illustrating near equality of cP and cSt): Typical values: μ ≈ 1.002 cP, ρ ≈ 0.9982 g/cm³. Use: ν = μ / ρ. Calculation: ν ≈ 1.002 / 0.9982 ≈ 1.0038 cSt. Interpretation: For water near 20°C, 1 cP ≈ 1 cSt because density ≈ 1 g/cm³. This is a useful rule of thumb but only valid when density is near 1 g/cm³. Example 6 — Convert kine