Viscosity Calculator
Use this calculator to find dynamic viscosity or kinematic viscosity using common fluid mechanics formulas.
For Newtonian fluids, viscosity remains constant at a given temperature.
Kinematic viscosity measures momentum diffusion independent of fluid mass density.
To convert ν to centistokes (cSt), multiply m²/s by 1,000,000.
What is viscosity?
Viscosity describes a fluid’s internal resistance to flow. A high-viscosity fluid (like honey) resists deformation and flows slowly, while a low-viscosity fluid (like water) flows more easily. In engineering, viscosity is essential in pipe design, lubrication, process control, pumping systems, and Reynolds number analysis.
Dynamic vs kinematic viscosity
Dynamic viscosity (μ)
Dynamic viscosity links shear stress to shear rate in a fluid. For Newtonian fluids:
- μ = τ / γ̇
- Units: Pa·s (pascal-seconds)
- Common practical unit: cP (centipoise), where 1 Pa·s = 1000 cP
Kinematic viscosity (ν)
Kinematic viscosity is dynamic viscosity divided by fluid density:
- ν = μ / ρ
- Units: m²/s
- Common practical unit: cSt (centistokes), where 1 m²/s = 1,000,000 cSt
How to use this calculator
- Select the calculation type from the dropdown.
- Enter the required values in SI units.
- Click Calculate.
- Read the result in both base and practical units (where relevant).
Unit reminders
- Shear stress: Pa
- Shear rate: s⁻¹
- Density: kg/m³
- Dynamic viscosity: Pa·s and cP
- Kinematic viscosity: m²/s and cSt
Worked examples
Example 1: μ from shear stress and shear rate
If τ = 15 Pa and γ̇ = 30 s⁻¹, then:
μ = 15 / 30 = 0.5 Pa·s = 500 cP
Example 2: ν from μ and ρ
If μ = 0.001 Pa·s and ρ = 998 kg/m³ (water near room temperature):
ν ≈ 1.002 × 10⁻⁶ m²/s ≈ 1.002 cSt
Typical viscosity values (approximate)
| Fluid | Dynamic Viscosity (Pa·s) | Dynamic Viscosity (cP) |
|---|---|---|
| Air (20°C) | 1.8 × 10⁻⁵ | 0.018 |
| Water (20°C) | 1.0 × 10⁻³ | 1.0 |
| Olive oil (20°C) | ~0.08 | ~80 |
| Glycerin (20°C) | ~1.5 | ~1500 |
Why viscosity matters in real applications
- Pumps and pipelines: Pressure drop increases with viscosity.
- Lubrication: Correct viscosity prevents metal-to-metal contact.
- Heat transfer: Viscosity impacts flow regime and convection.
- Chemical processing: Mixing power and mass transfer depend on viscosity.
- Automotive and aerospace: Fuel and lubricant behavior changes with temperature.
Common mistakes to avoid
- Mixing SI and non-SI units without conversion.
- Ignoring temperature effects (viscosity is highly temperature-dependent).
- Applying Newtonian formulas to non-Newtonian fluids without care.
- Using density values that do not match the operating temperature.
Final note
This calculator is ideal for quick engineering estimates and educational use. For critical designs, validate with measured data at operating conditions, especially for non-Newtonian fluids such as paints, slurries, blood analogs, and polymer solutions.