Enter data
Example data table
| Temperature (C) | Viscosity (mPa·s) | Material note |
|---|---|---|
| 10 | 95 | High viscosity at low temperature |
| 20 | 60 | Rapid decrease with warming |
| 30 | 41 | Moderate change in mid-range |
| 40 | 30 | Approaching smoother flow regime |
| 50 | 23 | Lower viscosity at higher temperature |
Formula used
How to use this calculator
- Select your temperature and viscosity units.
- Paste temperature–viscosity pairs, one per line.
- Choose a fit model that suits your material.
- Enter a target temperature for prediction.
- Press Calculate Fit to view parameters.
- Download CSV or PDF for reports and sharing.
Viscosity–temperature fitting guide
This fitting workflow is useful when you need a compact relationship between measured viscosity and temperature for simulation, design, or quality control. Paste your dataset, choose a model, and review both parameters and residuals. A good fit should be physically reasonable, stable under small data edits, and consistent with what you know about the material.
1) Temperature dependence in real fluids
Dynamic viscosity describes resistance to flow and momentum diffusion. For many liquids it drops with rising temperature as thermal motion weakens intermolecular constraints. In melts and glass-forming systems it may change by orders of magnitude, so fitting helps compare materials and processing windows.
2) What the calculator is fitting
Your pairs are converted to kelvin and Pa·s, then the calculator fits either ln(η) or log10(η) against temperature terms. Log space is used because viscosity often varies exponentially. It outputs parameters, a target-temperature prediction, and R² plus SSE for quick screening.
3) Arrhenius-style behavior
Arrhenius fitting is linear in ln(η) versus 1/T. When points lie near a line, the slope corresponds to E/R and E indicates temperature sensitivity. Use it for simple liquids or limited ranges where no structural transitions occur.
4) When VFT tends to work better
If Arrhenius coordinates show curvature, VFT can capture stronger temperature dependence. It introduces a shift temperature C and fits A and B after searching for a stable C. This is common for supercooled liquids, polymers, and glass-forming melts.
5) Data quality and units
Use positive viscosities and cover the temperatures you care about. Keep units consistent across all lines; convert beforehand if needed. Repeated temperatures from replicate measurements are fine and can reduce noise, making residual patterns easier to interpret.
6) Reading residuals like an experimenter
Compare residual percentages, not only R². Random residuals around zero suggest an adequate model. Residuals that drift with temperature hint at curvature, regime changes, or experimental issues such as shear-rate effects, phase change, or calibration errors.
7) Prediction and extrapolation limits
Predictions are safest inside the measured range. Extrapolation can fail when mechanisms change, so add data closer to the target if possible. If two models disagree strongly at the target temperature, treat the prediction as uncertain.
8) Reporting results with traceability
For reports, record the chosen model, parameter values, units, and measurement range. Download CSV to archive the parameter table and point-by-point comparison. Use the PDF summary when you need a quick attachment for lab notes or collaborators.
FAQs
1) Which model should I choose?
Start with Arrhenius or Andrade for simple liquids and moderate ranges. If residuals curve or drift, try VFT. For narrow windows where physics-based models fail, the quadratic log model can interpolate smoothly.
2) Why does the tool use kelvin internally?
Most viscosity-temperature models are written in terms of absolute temperature. Converting to kelvin prevents errors near 0°C or 0°F and keeps the math consistent for log and reciprocal-temperature relationships.
3) What does R² mean here?
R² summarizes how much of the variation in the transformed viscosity data is explained by the fitted curve. It is useful for comparison, but you should also inspect residuals to spot systematic model mismatch.
4) What is SSE in this calculator?
SSE is the sum of squared errors between measured and fitted values in the model’s working space. For log models, SSE is computed in log space, which aligns with how the regression is performed.
5) Can I paste data with spaces or tabs?
Yes. Each line may use commas, semicolons, tabs, or spaces as separators. The first value is temperature and the second is viscosity. Extra columns are ignored after the first two entries.
6) Why are negative or zero viscosities rejected?
Log-based fitting requires positive values, and physically viscosity cannot be negative. If you have noisy near-zero readings, re-check units, instrument limits, and whether the sample was out of range for the method used.
7) How many data points are enough?
At minimum, use two points for a straight-line model and three for the quadratic model, but more is better. Aim for points spread across your operating range so the prediction is supported by nearby measurements.