Standard Curve Calculator: Unknown Concentration

How to use the standard curve calculator

Copy the concentration and absorbance columns for your standards from Excel, Google Sheets or your plate reader export, and paste them into the first box. They split into the two boxes automatically.
Paste the readings of your unknown samples, one per line, with an optional name in front.
Enter the dilution factor if you diluted the samples, and the concentration unit.
Click Calculate concentrations.
Check R² and the back-calculated standards, then read each sample's concentration from the table. Samples outside the range of your standards are flagged.

Standard curve formula

The calculator fits a straight line to the standards by least squares, with the signal (y) against concentration (x):

y = mx + b , m = S_xyS_xx , b = y − mx

Then it solves the line for x to turn each unknown's reading into a concentration:

concentration = y − bm × dilution factor

y: The signal: absorbance, fluorescence, luminescence or peak area
x: The concentration of the standard
m: The slope: the change in signal per unit of concentration (the assay's sensitivity)
b: The intercept: the signal at zero concentration, often the reagent background
S_xy: The sum of cross-products of the deviations of x and y from their means
S_xx: The sum of squared deviations of the concentrations from their mean
R²: How closely the standards follow the line; 0.99 or higher is the usual target

Worked example

Four protein standards of 0, 10, 20 and 30 µg/mL give absorbances of 0.01, 0.21, 0.40 and 0.62. An unknown sample reads 0.35. What is its concentration?

Find the means
x = 15, y = 0.31
Sum the cross-products and the squared deviations of x
S_xy = (−15)(−0.30) + (−5)(−0.10) + 5(0.09) + 15(0.31) = 10.1

S_xx = 225 + 25 + 25 + 225 = 500
Slope and intercept
m = 10.1500 = 0.0202, b = 0.31 − 0.0202 × 15 = 0.007
Solve for the unknown's concentration
x = 0.35 − 0.0070.0202 = 16.98 µg/mL

What it means: the standards fit the line very closely (R² = 0.9991), and the unknown's reading of 0.35 falls between the 10 and 20 µg/mL standards, so its concentration of about 17.0 µg/mL is reliable. If the sample had been diluted 1 in 5 before measuring, the original concentration would be 5 × 16.98 = 84.9 µg/mL.

How to check your standard curve

R² should usually be 0.99 or higher. Lower values point to a pipetting error, a bad standard or a curve that isn't straight.
Back-calculated standards: run each standard's own reading back through the line. Each should land within about 10–15% of its nominal concentration (the results table shows this as % of nominal).
The shape: many assays, including Bradford and ELISA, flatten out at high concentrations. If the top standards curve away from the line, leave them out and use only the linear range.
Unknowns in range: only trust concentrations whose readings fall between your lowest and highest standards. Dilute and re-run samples that read above the top standard.
Replicates: run standards and samples in duplicate or triplicate. You can paste every replicate as its own row; the line uses them all.

The line itself is ordinary least-squares regression. For slope tests, confidence intervals and predictions in other settings, use the linear regression calculator.

Frequently asked questions

What is a standard curve?

A standard curve (or calibration curve) is a graph of the signal your instrument gives, such as absorbance, fluorescence or peak area, against known concentrations of a standard. Once you fit a line to it, you can turn the signal of an unknown sample into a concentration. It’s the basis of protein assays like Bradford and BCA, ELISA, colorimetric assays and HPLC quantification.

What R² is acceptable for a standard curve?

Most labs look for R² of 0.99 or higher for a linear standard curve, and 0.98 is often the minimum. A lower value usually means a pipetting error in one standard, a standard outside the linear range, or a curve that isn’t really straight. Check the back-calculated concentration of each standard: values within about 10–15% of the nominal concentration are a common acceptance rule.

Should I force the standard curve through zero?

Usually not. Fitting a normal intercept lets the line absorb a constant background signal, such as the color of the reagent itself. Force the line through zero only if you have subtracted the blank from every reading and your method says the curve should pass through the origin. With a forced zero, R² is calculated differently (as in Excel), so it often looks higher than it really is.

What if my unknown is outside the range of the standards?

Don’t trust the number. Outside the standards you are extrapolating, and many assays stop being linear at high concentrations (the curve flattens out). Dilute a concentrated sample so it falls inside the range, run it again, and multiply the result by the dilution factor. For a very low reading, concentrate the sample or use a more sensitive assay.

How do I use a dilution factor?

If you diluted the sample before measuring it, the curve gives the concentration in the diluted solution. Multiply by the dilution factor to get the original concentration. For example, 10 µL of sample in 90 µL of buffer is a 1 in 10 dilution, so a factor of 10: a reading of 12.5 µg/mL means 125 µg/mL in the original sample.

How do I make a standard curve in Excel or Google Sheets?

Put concentrations in column A and absorbance in column B. Use =SLOPE(B2:B7, A2:A7), =INTERCEPT(B2:B7, A2:A7) and =RSQ(B2:B7, A2:A7) for the line and R². Then for each unknown absorbance in D2, the concentration is =(D2 - intercept) / slope. To see it, insert a scatter chart and add a linear trendline with the equation and R² displayed.