Standard Curve Calculator

Results

How to Use the Standard Curve Calculator

1. 1. Choose the curve. A straight line suits assays that respond linearly over the range you use, such as a BCA or Bradford protein assay on a narrow range. Use the four-parameter logistic fit for ELISA and other immunoassays, whose standard curves are S-shaped.
2. 2. Enter the standards. One concentration and response per line. Put replicates on separate lines, and include the zero standard.
3. 3. Enter the unknowns. One reading per line, optionally with a name before it. Set the dilution factor if you diluted the samples before the assay, and a blank to subtract if your protocol calls for it.
4. 4. Check the fit before you trust the numbers. Look at the plot, at R², and at the recovery of the back-calculated standards. Readings above the top standard or below the lowest one are flagged.

Straight-Line and Four-Parameter Logistic Fits

A standard curve turns a response such as absorbance into a concentration. You measure standards of known concentration, fit a curve to them, then read each unknown through the curve in reverse.

In the 4PL, a is the response at zero concentration, d the response at infinite concentration, c the concentration at the midpoint (often called the EC50 or inflection point), and b the slope factor, which controls how steeply the curve rises. It describes the flat bottom, the steep middle and the flat top that a sandwich ELISA gives, and it is the fit most ELISA software uses. The same equation fits a falling curve, as in a competitive assay, when a is the larger response. The calculator fits it by iterative least squares from several starting slopes and keeps the best result.

Which Assay Needs Which Fit?

Working ranges depend on the kit and protocol: Thermo Fisher gives 100–1,500 µg/mL for its standard-tube Coomassie Bradford protocol and 1–25 µg/mL for the micro protocol, so check your kit's instructions. Always run the standards on the same plate as the unknowns, read at the wavelength the kit specifies (a different wavelength lowers the slope), and keep unknowns inside the range of the standards.

Worked Example 1: An ELISA With a 4PL Fit

The calculator opens with illustrative duplicate standards from 0 to 1,000 pg/mL (2-fold dilutions, read at 450 nm) and four serum samples diluted 1 in 2. The fit is y = 2.7 + (0.06086 − 2.7) ÷ (1 + (x ÷ 319.9)^1.249), with R² = 0.9995. Reading the unknowns through the curve:

• Serum 1, OD 0.412: 71.36 pg/mL, which is 142.7 pg/mL once the dilution factor of 2 is applied.
• Serum 2, OD 0.905: 174.9 pg/mL, so 349.8 pg/mL in the original sample.
• Serum 3, OD 1.87: 597 pg/mL, so 1,194 pg/mL.
• Serum 4, OD 2.95: higher than the top plateau of the curve (d = 2.7), so no concentration can be read. The sample needs diluting and repeating.

Worked Example 2: A Straight Line for a Protein Assay

Five BSA standards at 0, 0.25, 0.5, 0.75 and 1 mg/mL read 0.02, 0.14, 0.27, 0.37 and 0.50 (illustrative values). The line is y = 0.476x + 0.022 with R² = 0.9987. A lysate that reads 0.300 after a 1 in 5 dilution is (0.300 − 0.022) ÷ 0.476 = 0.584 mg/mL in the tube, and 0.584 × 5 = 2.92 mg/mL in the lysate.

Judging Whether the Fit Is Good

• Do not rely on R² alone. A curve can have R² above 0.99 and still misread the low end. The back-calculated standards table shows how accurately the fit reproduces each standard; many assays accept recoveries of 80–120%, a convention from kit makers rather than a formal standard.
• Enough standards. A four-parameter fit has four unknowns, so four standards reproduce it exactly with no check on the fit. Use at least six, ideally in duplicate.
• Stay inside the standards. The curve is only trustworthy between the lowest and highest standard. Dilute high samples and rerun.
• The blank. Subtract it consistently from standards and unknowns, or use a zero standard in the fit, but not both.
• Dilution. Enter the factor so that the answer is the concentration in the original sample, not in the tube.

Frequently Asked Questions

How do you calculate concentration from a standard curve?

Fit a curve to the responses of the standards, then solve the fitted equation for concentration at the response of the unknown. For a straight line that is (response − intercept) ÷ slope. Multiply by the dilution factor to get the concentration of the original sample.

What is a 4PL standard curve?

A four-parameter logistic curve is an S-shaped function with a lower asymptote, an upper asymptote, a midpoint and a slope factor. It describes the response of most immunoassays, which are flat at very low and very high concentrations, and it is the usual fit for ELISA data.

How many standards do I need for a standard curve?

At least three for a straight line, and at least six for a four-parameter fit, preferably in duplicate or triplicate across the whole range. With only as many standards as parameters the curve passes through every point, so R² is 1 and says nothing about quality.

What is a good R² for a standard curve?

Protein assays often aim for R² above 0.99, and ELISA 4PL fits are typically above 0.99 as well. Read it together with the recovery of the back-calculated standards and a look at the plot, because R² can look excellent when the curve is badly fitted at the low end.

Why can't the calculator give a concentration for some readings?

In a 4PL fit, a reading above the top plateau or below the bottom one has no matching concentration, because the curve never reaches that response. The reading is outside the assay's range. Dilute the sample and run it again, or concentrate it if it is below the lowest standard.

Should I subtract the blank before fitting?

Either subtract it from every reading, or include a zero standard in the fit, but do not do both. Subtracting the blank from the standards and the unknowns before the fit removes the reagent's background so the curve passes close to the origin.