Dynamic Viscosity Converter (Pa·s, poise, cP)

Understanding the dynamic viscosity converter — concept and principle

Dynamic (absolute) viscosity measures how strongly a fluid resists flowing. Lab reports, paint and adhesive datasheets, food science and lubrication tables quote it in pascal-seconds (Pa·s), millipascal-seconds (mPa·s), poise (P) or centipoise (cP). This converter moves a value between these units and lists them all, so you can compare a product sheet in cP with a textbook value in Pa·s.

How it is calculated

Every value is converted through centipoise: result = value × cP(from) ÷ cP(to).

• 1 P = 100 cP
• 1 Pa·s = 1,000 cP = 10 P
• 1 mPa·s = 1 cP exactly

The principle

Newton's law of viscosity states that the shear stress in a fluid is proportional to how fast neighbouring layers slide past each other: τ = μ × (du/dy). The constant μ is the dynamic viscosity. Stress is in pascals and the velocity gradient in 1/s, so μ has units of Pa·s in SI. The older CGS system measured stress in dyn/cm², giving the poise (1 P = 1 g/(cm·s) = 0.1 Pa·s), named after the physician Jean Léonard Marie Poiseuille, who studied blood flow in narrow tubes. A centipoise is one hundredth of a poise, which happens to equal exactly one mPa·s, and water at 20 °C is close to 1 cP, so cP is a convenient everyday unit.

Worked example

Default inputs: 1 centipoise to poise.

1. 1 P = 100 cP, so 1 cP = 1 ÷ 100 P.
2. 1 × 1 ÷ 100 = 0.01 P.
3. In SI: 1 cP = 0.001 Pa·s = 1 mPa·s.

How to read the result

Higher viscosity means a thicker, slower-flowing fluid. Rough values at room temperature: air about 0.018 cP, water about 1.0 cP (1.002 cP at 20 °C), and oils, syrups and honey from tens up to many thousands of cP. Viscosity of liquids falls sharply as temperature rises, so a value only makes sense with its temperature: water is about 1.8 cP at 0 °C but only about 0.3 cP near 100 °C.

Common mistakes

• Mixing dynamic viscosity (cP, Pa·s) with kinematic viscosity (cSt, mm²/s). Convert with kinematic = dynamic ÷ density: cSt = cP ÷ (g/cm³).
• Ignoring temperature when comparing datasheets.
• Writing Pa·s values as mPa·s, a 1,000-fold error.

Frequently asked questions

How many cP is 1 Pa·s?

1,000 cP.

Is cP the same as mPa·s?

Yes, exactly.

How do I convert cSt to cP?

Multiply by the density in g/cm³. For oil at 0.85 g/cm³, 100 cSt is 85 cP.

Sources: BIPM, The International System of Units (SI Brochure), 9th edition, 2019 · NIST Special Publication 811 (2008), Guide for the Use of the SI, Appendix B