Quick answer
Kinematic viscosity is ν (cSt) = μ (cP) ÷ ρ (g/cm³). Water at 1.002 cP with a density of 998.2 kg/m³ has ν = 1.0038 cSt, and 0.001002 Pa·s.
Choose a conversion and enter the viscosity and density. The calculator returns the kinematic or dynamic viscosity.
Related tools: Water Viscosity Calculator: Dynamic viscosity of liquid water at a temperature. Pressure Calculator: Pressure from force and area, with unit conversions. Reynolds Number Calculator: Reynolds number and flow regime in a pipe.
How to use the Viscosity Calculator
- Choose convert: Dynamic (cP) → kinematic (cSt) and Kinematic (cSt) → dynamic (cP).
- Enter viscosity (above 0).
- Enter fluid density (kg/m³) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Convert | Choose one: Dynamic (cP) → kinematic (cSt); Kinematic (cSt) → dynamic (cP) | Starts at Dynamic (cP) → kinematic (cSt) |
| Viscosity | A number | > 0 |
| Fluid density | A number, in kg/m³ | > 0 |
Formula and method
Formula
ν (cSt) = μ (cP) ÷ ρ (g/cm³)
IEEE-754 double precision; shown to the decimals indicated.
1 cP = 1 mPa·s and 1 cSt = 1 mm²/s.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Convert = Dynamic (cP) → kinematic (cSt); Viscosity = 1.002; Fluid density = 998.2.
| Result | Value |
|---|---|
| Kinematic viscosity | 1.0038 cSt |
| In Pa·s | 0.001002 |
Example 2
Inputs: Convert = Kinematic (cSt) → dynamic (cP); Viscosity = 32; Fluid density = 870.
| Result | Value |
|---|---|
| Dynamic viscosity | 27.84 cP |
| In Pa·s | 0.02784 |
Example 3
Inputs: Convert = Dynamic (cP) → kinematic (cSt); Viscosity = 100; Fluid density = 900.
| Result | Value |
|---|---|
| Kinematic viscosity | 111.1111 cSt |
| In Pa·s | 0.1 |
The first line is the headline result (kinematic viscosity). Below it the viscosity Calculator lists in Pa·s, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Dynamic versus kinematic
Dynamic viscosity (μ) is the resistance to shear, in Pa·s or centipoise (1 cP = 0.001 Pa·s). Kinematic viscosity divides by density and is in m²/s or centistokes (1 cSt = 10⁻⁶ m²/s).
Temperature
Viscosity falls sharply as liquids warm, so use the density at the same temperature. Motor oils are graded in cSt at 40 °C and 100 °C. Water at 20 °C is about 1 cP.
How the result changes with viscosity
Holding every other input at the first worked example, this table changes only viscosity. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Viscosity | Kinematic viscosity | In Pa·s |
|---|---|---|
| 0.501 | 0.5019 cSt | 0.000501 |
| 1.002 | 1.0038 cSt | 0.001002 |
| 2.004 | 2.0076 cSt | 0.002004 |
| 4.008 | 4.0152 cSt | 0.004008 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Viscosity: entering "0" shows "Viscosity must be greater than 0." beside that field and no result.
- Fluid density: entering "0" shows "Fluid density must be greater than 0." beside that field and no result.
Choosing between the Viscosity Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Water Viscosity Calculator](/science/water-viscosity/) | temperature | Dynamic viscosity |
| [Pressure Calculator](/science/pressure-calculator/) | force and area | Pressure |
| [Reynolds Number Calculator](/science/reynolds-number-calculator/) | fluid density, flow velocity and pipe diameter | Reynolds number |
| [Flow Rate Calculator](/science/flow-rate-calculator/) | use | Flow rate |
| [Specific Gravity Calculator](/science/specific-gravity/) | density | Specific gravity |
Background: fluid flow
Volumetric flow rate is Q = A × v (cross-sectional area times average velocity). Bernoulli's equation, P + ½ρv² + ρgh = constant, holds along a streamline for steady, incompressible, frictionless flow, so real pipes need friction corrections. The Reynolds number Re = ρvL/μ compares inertia with viscosity.
Laminar flow in a pipe is usually quoted below Re of about 2,100 to 2,300 and fully turbulent above about 4,000, with an uncertain transition between; treat the thresholds as approximate.
Assumptions and limitations
- Use the density at the same temperature
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for viscosity and fluid density to confirm this.
Frequently asked questions
What is 1 Pa·s in cP?
1 Pa·s equals 1,000 cP, so water's 0.001002 Pa·s is 1.002 cP.
What is the viscosity of honey?
About 2,000 to 10,000 cP.
What is a stoke?
A CGS unit of kinematic viscosity.
What does the Viscosity Calculator calculate?
Convert between dynamic viscosity (cP) and kinematic viscosity (cSt). It returns Kinematic viscosity and In Pa·s.
What formula does the Viscosity Calculator use?
ν (cSt) = μ (cP) ÷ ρ (g/cm³). 1 cP = 1 mPa·s and 1 cSt = 1 mm²/s.
What do I need to enter in the viscosity Calculator?
You enter Convert, Viscosity and Fluid density (kg/m³).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Use the density at the same temperature.
What does the “Convert” option change?
It sets how the viscosity is worked out. The choices are Dynamic (cP) → kinematic (cSt) and Kinematic (cSt) → dynamic (cP).
What is an example of a viscosity result?
With convert Dynamic (cP) → kinematic (cSt), viscosity 1.002 and fluid density 998.2, the kinematic viscosity is 1.0038 cSt.
Where does the method come from?
The method follows: NIST Special Publication 811, Guide for the Use of the International System of Units (SI), Appendix B (poise, stokes, pascal second and square metre per second).
Related calculators
- Water Viscosity Calculator — Dynamic viscosity of liquid water at a temperature.
- Pressure Calculator — Pressure from force and area, with unit conversions.
- Reynolds Number Calculator — Reynolds number and flow regime in a pipe.
- Flow Rate Calculator — Volumetric flow rate from area and velocity, or volume and time.
- Specific Gravity Calculator — Specific gravity from density, relative to water at 1,000 kg/m³.
- Water Velocity Calculator — Water velocity in a pipe from flow and inside diameter.
Sources
- NIST Special Publication 811, Guide for the Use of the International System of Units (SI), Appendix B (poise, stokes, pascal second and square metre per second)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.