How to use it
- Paste the standard series into the first box — known concentration in the first column, reading in the second. Keep the zero standard: it is the blank, and the fit uses it as the lower plateau.
- Paste the samples into the second box — name, reading, and the fold dilution if the sample was diluted before the well. Separate the columns with a tab, comma or two spaces.
- Read the concentrations off the table. A dilution is already multiplied in, with the concentration in the well shown underneath it.
- Check the curve below the table. The standards should sit on the line at both ends; where they do not, that plateau is guesswork and every concentration near it inherits the guess.
- Rows saying the reading fell off the curve got no number on purpose. Dilute those samples and read them again.
💡 The units are yours. Whatever the standards are given in, the samples come out in.
Formula & notes
An immunoassay does not answer in a straight line. It is flat at the bottom where there is nothing to detect, steep through the middle, and flat again at the top where the antibody is saturated — an S, and fitting a line to it is wrong everywhere except in the middle.
The four-parameter logistic is that S, written down. A is the reading at zero concentration, D the reading where the assay saturates, C the concentration half way between them, and B how steeply the curve climbs through C.
- Standard curve
- y = D + (A − D) / (1 + (x / C)^B)
Reading a sample is the same equation rearranged. It is exact — there is no search and no approximation.
- Concentration from a reading
- x = C × ( (A − y) / (y − D) )^(1/B)
The bracket has to be positive, and that is the whole safety story: it is positive exactly when the reading lies strictly between A and D. A reading outside them has no concentration — not a large one, not a small one, none — and the arithmetic refuses rather than rounding to the nearest plateau.
The reported concentration is what was in the original sample, so a dilution multiplies back in.
- With a dilution
- concentration = x × dilution factor
⚠️ The 4PL is symmetric about its inflection. Assays whose upper and lower halves have genuinely different shapes are fitted with a five-parameter logistic instead, which this tool does not offer — a fifth parameter that nobody knows when to turn on does more harm than a limitation stated plainly.
Practical notes
- Run the standards on the same plate as the samples. A curve carried over from yesterday carries yesterday's coating, substrate and incubation with it.
- Keep the blank in as the zero standard rather than subtracting it first. The lower plateau is the blank, estimated from the whole series instead of from one well; subtracting it and then fitting one counts it twice.
- Replicate wells go in as separate rows. A fit told about both wells is better informed than a fit told about their mean, and two rows that disagree are worth seeing.
- A reading beyond a plateau has no concentration at all — not a large one. Dilute the sample and read it again; the dilution column puts the answer back on the original scale.
- Extrapolated is not the same as impossible. A concentration below the lowest standard or above the highest does exist on the curve, but no calibrator was ever measured there, so the number is the curve's opinion.
- A high R² says the curve passes near the points. It says nothing about whether the plateaus were reached, and the plateaus are what the back-calculation divides by.
FAQs
Often used together
Standard Curve Regression Calculator
Fits a linear regression for slope, intercept, and R², then back-calculates unknown concentrations.
Serial Dilution Prep Calculator
Calculates per-step concentration plus stock and diluent volumes.
IC50 / EC50 Calculator
Fits a sigmoid to dose–response data and returns the half-maximal concentration and the Hill slope.