How to use (3 steps)
- Paste your data (t, y) or load a CSV. You can also use a preset example.
- Choose the model (auto compare/exponential/logistic) and display options (log axis, extrapolation).
- Click “Calculate” to view parameters, fitted curves, residuals, and model comparisons. Share the same settings with a share URL.
Recommended order
- First, fit the growth curve (this calculator)
- Then check doubling time (how fast?) → Go to doubling time
- If saturation exists, check logistic K (upper limit) → Go to K
Go deeper
- Linear regression & correlation
Understand “ln makes a line” for exponential growth
- Descriptive statistics
Check variability
Data input & options
Results (parameters, charts, residuals)
Results will appear here.
Fitted curves
Residual plot
Per-row output (yhat & residuals)
| line | t | y | yhat_exp | resid_exp | yhat_log | resid_log |
|---|
Model comparison (RMSE/AIC)
| model | k | RMSE | AIC | note |
|---|
Calculation steps (How it’s calculated)
Models (exponential & logistic) and assumptions
- Exponential growth uses ln(y), so y>0 is required.
- Logistic growth includes saturation (K) and can be unstable with few points.
Calculation overview
Doubling time
Time to double. For the exponential model it is ln(2)/r (r>0).
Logistic K (upper limit)
The upper limit (carrying capacity). Logistic is useful when saturation is visible in the data.
- Exponential: regress
ln(y)=ln(y0)+rtto estimaterandy0. Doubling time isln(2)/r. - Logistic: estimate
y=K/(1+exp(-r(t-t0)))via nonlinear least squares. - Compute predicted
yhatand residuals (y−yhat), and output charts and tables.
How to use this calculator effectively
This calculator is designed to make scenario checks fast. Use a repeatable workflow: baseline first, one variable change at a time, then compare output direction and magnitude.
How it works
Run your first scenario with defaults. Then, change exactly one assumption and observe which result changes most. That is the fastest way to identify sensitivity and explain what drives the outcome.
When to use
Use this page when you need practical planning support, side-by-side alternatives, or a clean baseline for further discussion.
Common mistakes to avoid
- Changing multiple assumptions simultaneously.
- Confusing percent and decimal inputs.
- Mixing unit systems across scenarios.
- Relying only on rounded display output for final conclusions.
Worked example
Prepare a base case and one alternative case, then compare outputs and validate the direction, scale, and interpretation with the same assumptions across both cases.
See also
FAQ
How should I choose between exponential and logistic?
Use exponential when there is no saturation and logistic when a clear upper limit appears. Compare residuals and RMSE/AIC as well.
How is doubling time calculated?
It is ln(2)/r from the exponential growth rate r (r>0).
What if y is zero or negative?
The exponential model (ln) cannot use those values, so those rows are excluded. Try logistic or apply background correction.
Is extrapolation OK?
Predictions outside the data range are uncertain, so they are shown as pale dashed lines for reference.
What if the data does not fit or errors appear?
- Check that you have two columns (t and y) including headers and separators.
- If there are invalid rows, turn on “Remove missing/non-numeric” or fix the data.
- If the logistic fit is unstable, set the initial K to manual and enter a rough value.
- Exponential requires y>0 (rows with y=0 or negative are excluded).
How many points do I need?
The calculation runs with as few as 2 points, but logistic fits can be unstable with small n. If possible, use multiple points (e.g., 6–10) and check residuals.
When should I use the log axis?
In exponential regions, plotting y on a log axis can look close to linear (requires y>0).
Does the share URL include the data?
It saves settings (model/view), not the data itself.
How to use Growth curve fitter (exponential & logistic) effectively
What this calculator does
This page is for estimating outcomes by changing inputs in one controlled workflow. The model keeps your focus on variables, not output shape. Start with stable assumptions, then test sensitivity by changing one key input at a time to observe directional impact.
Input meaning and unit policy
Each input has an expected unit and a typical range. For reliable interpretation, check whether you are using the same unit system, period, and base assumptions across all runs. Unit mismatch is the most common source of unexpected drift in numeric results.
Use-case sequence
A practical sequence is: first run with defaults, then create a baseline log, then run one alternative scenario, and finally compare only the changed output metric. This sequence reduces cognitive load and prevents false pattern recognition in early experiments.
Common mistakes to avoid
Avoid changing too many variables at once, mixing incompatible data sources, and interpreting a one-time output without checking robustness. A single contradictory input can flip conclusions, so keep each experiment minimal and document assumptions as part of your note.
Interpretation guidance
Review both magnitude and direction. Direction tells you whether a strategy moves outcomes in the desired direction, while magnitude helps you judge practicality. If both agree, you can proceed; if not, rebuild the baseline and verify constraints before deciding.
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References (notes)
For understanding formulas and concepts. In research/education, check primary sources as needed.
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