How to Fit a 4PL ELISA Standard Curve in Excel (and a Faster Free Alternative)
Step-by-step: fit a 4PL ELISA standard curve in Excel with Solver, interpolate sample concentrations, and see why a free browser tool does the same in two minutes.
Excel does not have a built-in 4PL fit. Its trendline options (linear, polynomial, logarithmic, power) cannot describe a sigmoidal ELISA curve. You can still do it with Solver, and this guide shows exactly how. At the end we show how to get the same result, plus quality checks Excel will not give you, in a couple of minutes.
What you need
- Blank-corrected mean OD for each standard
- Nominal concentration of each standard (non-zero only)
- Sample ODs
- Excel with the Solver add-in enabled (File → Options → Add-ins → Manage Excel Add-ins → Solver Add-in)
Step 1: Lay out the data
| A | B | C | |
|---|---|---|---|
| 1 | Concentration | Mean OD | Predicted OD |
| 2 | 1000 | 2.41 | |
| 3 | 500 | 1.62 | |
| 4 | ... | ... |
Leave out the zero standard. It defines the background, but log(0) is undefined, so it cannot sit on the 4PL curve.
Step 2: Create the four parameters
Put starting guesses in separate cells:
F2 A (bottom) = lowest standard OD
F3 B (slope) = 1
F4 C (EC50) = a middle standard concentration
F5 D (top) = highest standard OD
Good starting values matter. Solver can stop at a poor solution if they are far off.
Step 3: Write the 4PL formula
The 4PL model:
OD = D + (A - D) / (1 + (conc / C)^B)
In C2, then fill down:
=$F$5 + ($F$2 - $F$5) / (1 + (A2 / $F$4)^$F$3)
Step 4: Calculate the error to minimize
In D2, the squared residual, then fill down:
=(B2 - C2)^2
In F7, the sum of squared residuals:
=SUM(D2:D8)
Step 5: Run Solver
Data → Solver:
- Set Objective: F7
- To: Min
- By Changing Variable Cells: F2:F5
- Solving Method: GRG Nonlinear
- Untick "Make unconstrained variables non-negative" if your slope can be negative
Click Solve. Check that the predicted OD column now follows the measured OD closely.
Step 6: Interpolate the samples
Invert the model to get concentration from a sample OD in cell H2:
=$F$4 * (($F$2 - $F$5) / (H2 - $F$5) - 1)^(1 / $F$3)
Multiply by the dilution factor afterwards. If a sample OD is outside the OD range of the standards, the result is extrapolated. Flag it, and do not report it as a number.
Where the spreadsheet approach breaks down
The Excel method works, but each plate leaves you with things you have to build or check by hand:
- No confidence intervals. Solver returns parameter values without standard errors, so you cannot tell whether EC50 is well defined.
- No weighting by default. ELISA variance usually grows with signal. Weighted fits (1/Y or 1/Y²) need extra columns.
- No back-calculation of standards. You have to add recovery columns yourself to check the 80–120% criterion.
- No LLOQ/ULOQ flags. Out-of-range samples are not marked automatically.
- No 5PL comparison. Asymmetric curves need a fifth parameter and a second fit.
- Fragile. One wrong absolute reference ($) or a poor starting guess gives a curve that looks fine but is wrong, and nobody notices.
- Repeated for every plate. The template drifts as it is copied between people and projects.
The same analysis in Labreador
Labreador's ELISA module is free, needs no account, and runs entirely in your browser. Your data is never uploaded.
- Paste or upload the plate-reader grid (A–H by 1–12).
- Mark wells on the plate map as blank, standard or sample by clicking and dragging.
- Enter the top standard and dilution factor. The standard concentrations are filled in for you.
- Read the results: 4PL or 5PL fit with parameter confidence intervals, interpolated sample concentrations, LLOQ/ULOQ flags, replicate %CV, back-calculated standard recovery, and Method Health warnings (low dynamic range, EC50 outside the standard range, very wide confidence intervals).
- Export a PDF report or CSV for your lab notebook.
No Solver set-up, no starting guesses, no formulas to copy. If you want to check it against your spreadsheet, run the same plate through both. The parameters should agree closely when Solver has converged.
If you use Labreador in a publication, please cite:
Helczman, M. (2026). Labreador - Bioassay Analysis Platform (Version 1.6.0) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.21676846
