Viscosity Unit Converter (Pa·s ↔ Poise ↔ cP ↔ Stokes)
**Viscosity measures internal friction in a fluid** — two *distinct* physical quantities: **dynamic (absolute) viscosity µ** (SI unit pascal-second, Pa·s = N·s/m² = kg/(m·s)), the ratio of shear stress to shear rate between fluid layers, and **kinematic viscosity ν** (SI unit m²/s), defined as ν = µ / ρ and incorporating density. **Water at room temperature ≈ 1 cP (= 1 mPa·s)**, which is why centipoise and centistokes are the everyday units. This tool converts instantly across the common units (Pa·s, mPa·s, poise, centipoise, lbf·s/ft², reyn, kgf·s/m², m²/s, stokes, centistokes, ft²/s, in²/s) and also crosses between µ and ν via fluid density — useful for ISO VG oil grades, rheology data and SAE motor-oil specifications.
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Live value in every unit
Note: viscosity is strongly temperature-dependent (hotter → less viscous). The conversions here are exact unit identities and ignore rheological effects.
Cross-conversion (via density ρ)
Identity: ν = µ ÷ ρ. Enter the fluid density and the tool also shows the equivalent in the other family.
- cP Water at room temperature ≈ 1 cP; blood 3–4 cP; olive oil ≈ 84 cP; honey 2 000–10 000 cP.
- cSt ISO VG oil grade equals the cSt value at 40 °C — ISO VG 46 = 46 cSt.
- Pa·s Polymer melts, asphalt and glass paste can reach 1–1e9 Pa·s.
- reyn The reyn is the US tribology unit; 1 reyn ≈ 6 895 Pa·s.
- P The poise (Poise) is the CGS unit named after Poiseuille; 1 P = 0.1 Pa·s.
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Formula
Dynamic viscosity (µ): 1 Pa·s = 1 N·s/m² = 1 kg/(m·s) 1 mPa·s ≡ 1 cP (centipoise) = 0.001 Pa·s 1 Poise (P) = 0.1 Pa·s (CGS) 1 lbf·s/ft² = 47.880 258 980 33 Pa·s 1 reyn = 1 lbf·s/in² = 6 894.757 293 168 Pa·s 1 kgf·s/m² = 9.806 65 Pa·s (1 kgf = 9.80665 N) Kinematic viscosity (ν): 1 m²/s = SI base unit 1 St (Stokes) = 1 cm²/s = 1×10⁻⁴ m²/s 1 cSt = 1 mm²/s = 1×10⁻⁶ m²/s 1 ft²/s = 0.092 903 04 m²/s Cross-family: ν = µ / ρ (µ in Pa·s; ρ in kg/m³; ν in m²/s)
- · **Dynamic viscosity (µ) vs kinematic viscosity (ν) — the fundamental distinction.** µ describes the internal viscous force (shear stress / shear rate), units Pa·s; ν = µ / ρ describes the viscous diffusivity once divided by inertia, units m²/s. **Which to use?** (a) **chemistry / rheology** — µ (intrinsic material property, density-free, easier cross-fluid comparison); (b) **petroleum / lubricants industry (ISO VG, SAE)** — ν (a U-tube viscometer measures cSt directly); (c) **fluid mechanics / Reynolds number** — Re = ρVL/µ = VL/ν, either works.
- · **ISO VG oil grades equal the cSt value at 40 °C** — e.g. **ISO VG 32** means 28.8 ≤ ν ≤ 35.2 cSt at 40 °C (ISO 3448-1992). SAE motor-oil grades (5W-30, 10W-40 etc.) are *not* ISO VG: **5W-30** uses the 5W cold-pump rating plus the 100 °C cSt band 30 (9.3 ≤ ν₁₀₀ < 12.5 cSt, SAE J300). This tool will not interpolate multi-grade oils between temperatures — that requires Vogel-Fulcher or Walther equations — it only converts units.
- · **Misleading "equality" of centipoise and centistokes** — for water (ρ ≈ 1 g/cm³ = 1000 kg/m³) the numerical values of µ in cP and ν in cSt agree within about 0.2 %. **For other fluids — e.g. glycerin (ρ ≈ 1261 kg/m³) — they do not match.** Room-temperature glycerin has µ ≈ 1410 cP and ν = µ/ρ ≈ 1119 cSt. The cross-family block uses the density you enter to handle this correctly.
- · **reyn and lbf·s/ft² mostly appear in US lubrication engineering and fluid-mechanics textbooks** — 1 reyn = 1 lbf·s/in² ≈ 6 895 Pa·s (seven orders of magnitude larger than water at µ ≈ 0.001 Pa·s); reyn shows up in journal-bearing oil-film calculations (Sommerfeld number S = (μN/P)(R/c)²). **1 lbf·s/ft² = 1 slug/(ft·s)** (the slug is the Imperial mass unit), so this unit can also be written slug-per-foot-second.
- · **Viscosity is strongly temperature-dependent** — water at 0 °C has µ ≈ 1.79 cP; 20 °C ≈ 1.00 cP; 80 °C ≈ 0.355 cP (a 5× drop relative to 0 °C). Motor oil can swing 100–300× between 0 and 100 °C. This tool does pure unit conversion and **does not apply temperature corrections** — use ASTM D341 (the Walther equation) or a vendor data-sheet curve for that.
- · **References**: (1) NIST SP 811 (2008), *Guide for the Use of the International System of Units*, Appendix B; (2) ISO 80000-4 (2019), *Quantities and units — Part 4: Mechanics*; (3) CRC Handbook of Chemistry and Physics, 97th ed. (2016); (4) ASTM D2161-21, *Conversion of Kinematic Viscosity to Saybolt Universal / Furol Viscosity*; (5) SAE J300 (2021), *Engine Oil Viscosity Classification*; (6) ISO 3448-1992, *Industrial liquid lubricants — ISO viscosity classification*.
Frequently asked
The oil drum says "ISO VG 46" — what does that translate to in mPa·s (cP)?
**Short answer**: **ISO VG 46 = ν ≈ 46 cSt at 40 °C** (ISO 3448 mid-point with the band 41.4 – 50.6 cSt); to convert to µ in mPa·s (cP) you need the *oil's* density at 40 °C. **For a typical mineral oil at 40 °C, ρ ≈ 870 kg/m³**, giving µ ≈ ν × ρ = 46 × 10⁻⁶ m²/s × 870 kg/m³ ≈ **0.040 Pa·s = 40 mPa·s = 40 cP**. **Watch-outs**: (a) base oils (synthetic, PAO, ester) span 820–920 kg/m³ which moves the result by about ±5 %; (b) data sheets quote "Kinematic Viscosity @ 40 °C" (cSt) and "Density @ 15 °C" (kg/m³ or SG) — correct 15 °C density to 40 °C (roughly −0.007 g/cm³ per +10 °C); (c) in this tool: pick "kinematic viscosity" → start from cSt → enter ρ = 870 in the cross-family block → read cP instantly.
For water, centipoise (cP) and centistokes (cSt) are "equal" — when is each one correct?
**They *look* equal only because water has ρ ≈ 1 g/cm³ = 1000 kg/m³** — numerically µ(cP) = ν(cSt) × ρ(g/cm³), so the equality holds whenever density equals 1 in CGS units. **For other fluids it breaks**: (a) **glycerin at 20 °C**: µ ≈ 1410 cP, ρ ≈ 1.261 g/cm³ → ν = µ/ρ ≈ **1119 cSt** — a 25 % gap; (b) **air at 20 °C**: µ ≈ 0.0181 cP, ρ ≈ 0.001 204 g/cm³ → ν ≈ **15.0 cSt** (= 1.5×10⁻⁵ m²/s) — a 800× difference. **Which one to use?** (1) The instrument decides: a U-tube viscometer measures *time*, which scales to cSt (kinematic); a rotational / cone-and-plate viscometer measures *torque*, which scales to cP (dynamic). (2) The equation decides: Reynolds number Re = VL/ν uses cSt; shear stress τ = µ × dV/dy uses cP. (3) In this tool either family is one click away, with density-based cross-conversion built in.
Both reyn and lbf·s/ft² are pound-force × second / area — what is the difference?
**The unit area differs**: (a) **reyn = lbf·s/in²** (per square inch) — large numerical value because the area is small; 1 reyn ≈ 6 894.757 Pa·s. (b) **lbf·s/ft² = lbf·s/(12 in)² = reyn / 144** ≈ 47.880 Pa·s. **Usage**: (1) **reyn** is the standard unit in lubrication engineering (journal-bearing oil films, Sommerfeld number); (2) **lbf·s/ft²** is the standard unit in classical fluid-mechanics textbooks (e.g. White, *Fluid Mechanics*) and equals the Imperial slug/(ft·s) since 1 slug = 1 lbf·s²/ft → slug/(ft·s) = lbf·s/ft². **Modern trend**: Europe, chemistry and academia use Pa·s (SI); US lubrication still uses reyn. **Mnemonic**: 1 reyn = 6 894.757 Pa·s; 1 Pa·s ≈ 1.45×10⁻⁴ reyn.
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