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ELISA Standard Curve Calculator (4PL)

Fit an ELISA standard curve with a four-parameter logistic model on a log scale, subtract the blank, and read sample concentrations with dilution factors and range flags.

Formula

OD=d+a−d1+(x/c)b\mathrm{OD} = d + \dfrac{a - d}{1 + (x/c)^{b}}
x=c(a−dOD−d−1)1/bx = c\left(\dfrac{a - d}{\mathrm{OD} - d} - 1\right)^{1/b}
coriginal=x×DFc_{\text{original}} = x \times \mathrm{DF}
a, da,\ d
the response at zero and at infinite concentration
cc
the concentration giving the mid-point response
bb
slope factor (steepness)

How it works

An immunoassay's response is sigmoidal against the logarithm of the concentration: flat at low amounts, steep in the middle and flat again near saturation. A straight line fits only the middle. The four-parameter logistic describes the whole curve, and is the usual model for ELISA standards.

Standards at zero concentration are taken as blanks and subtracted, because a zero cannot be plotted on a log axis. Each sample's blank-corrected OD is converted to a concentration by inverting the curve and multiplied by its dilution factor. A sample whose OD falls outside that of the standards is flagged, since the curve is flat there and the answer is unreliable.

Worked example

Seven standards from 15.6 to 1,000 pg/mL plus a blank (illustrative ODs), and three samples.

  1. After subtracting the blank (0.050), the fit gives a = 0.030, b = 1.26, c = 355 pg/mL and d = 3.05, R² = 0.9999.
  2. Serum 1 (OD 1.050, diluted 10×) reads 196.1 pg/mL in the well, so 1,961 pg/mL.
  3. Serum 3 (OD 2.80) lies above the highest standard and is flagged.

Serum 1 is about 1,960 pg/mL and serum 2 about 490 pg/mL; serum 3 must be diluted and re-run.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • Standards and samples are in the same matrix and were processed together.
  • A symmetric sigmoid on a log scale. An asymmetric curve calls for a five-parameter model.
  • The standards' ODs here are illustrative; use your own values.

Common mistakes

  • Fitting a straight line to a sigmoidal curve and reading samples outside the linear middle.
  • Reporting samples whose OD is above the top standard or near the blank.
  • Forgetting dilution factors, or using a curve from another plate.

Related tools

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Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.