Lab-Tacular

qPCR Relative Quantification Calculator

Calculates fold changes against a control group from qPCR Ct values.Paste your Ct table, then pick the reference genes and the control group.

One well per line: sample ⇥ gene ⇥ Ct ⇥ group (optional). Copying the sample, target and Cq columns straight out of your instrument's export works.

Repeated lines with the same sample and gene are technical replicates and get averaged. A group name in the fourth cell makes the different samples inside that group biological replicates. The two levels are kept apart all the way through.

How to use it

  1. Copy the sample name, target name and Cq columns out of your instrument's results table and paste them in. Header rows are skipped for you.
  2. To fold biological replicates together, paste a group name as a fourth column. Without it each sample is its own group.
  3. Pick the reference genes. Two or more are combined by geometric mean, which on the Ct scale is the same arithmetic as a plain average.
  4. Pick the control group. Every fold change is measured with that group set to 1.
  5. Enter amplification efficiencies if you know them. If you do not, leave them — 100 % is the assumption 2^−ΔΔCt makes.
  6. The group table is what goes into a figure; the sample table is where you see how far the biological replicates spread.

The formulas, and what to watch for

Two methods are reported side by side. One is the familiar one and carries an assumption; the other does not.

1. Average the technical replicates

Wells from the same sample and the same gene are averaged. The uncertainty of that average is its standard error — the standard deviation over the square root of the number of wells.

Mean Ct
Ct = ΣCtᵢ / n
Standard error
u = s / √n

2. Combine the reference genes

Several reference genes are combined by the geometric mean of the quantities. Quantity goes as E^−Ct, so that geometric mean is exactly an arithmetic mean of the Ct values — which is why the two methods below cannot drift apart.

Reference Ct
Ct_ref = ΣCt_i / m

3. Subtract twice

Reference off target (ΔCt), then the control group's ΔCt off that (ΔΔCt). Uncertainty follows by the usual propagation through a difference of independent means.

ΔCt
ΔCt = Ct_target − Ct_ref
ΔΔCt
ΔΔCt = ΔCt_sample − ΔCt_control
Fold change
2^−ΔΔCt
Propagation
u(A − B) = √(u(A)² + u(B)²)

4. Correct for efficiency (Pfaffl)

Pfaffl's equation does not assume an efficiency of 2. Leave every efficiency at 100 % and it becomes the equation above.

Ratio
R = E_target^ΔCP_target / E_ref^ΔCP_ref
ΔCP
control Ct − sample Ct
Efficiency to base
E = 1 + efficiency(%) / 100

What to watch for

  • 2^−ΔΔCt assumes the target and the reference both amplify at exactly 2. Pfaffl states that assumption in his paper and calls the method usable only for a quick estimate. Showing both columns is how the size of the assumption becomes visible.
  • Three reference genes are the recommended starting point (Vandesompele et al., 2002). With one, a reference that responds to the treatment tilts the whole result and nothing on the page can tell you it happened.
  • Technical and biological replicates measure different things. Three wells from one dish tell you about pipetting; three dishes tell you about biology. This tool keeps them apart to the end and writes on the table which level an error bar came from.
  • The error is a propagated standard error, not a confidence interval, and it is not a significance test.
  • The control group's fold change is 1 by construction rather than by measurement, so no bar is drawn on it. Its own ΔCt spread is shown separately instead.
  • A well that never amplified is not a zero. Entering it as zero makes that sample look like the highest expresser in the run, so those lines are left out of the means and counted for you.

Frequently asked questions

References

Where the equations in this tool come from. Every entry was checked against its Crossref record.

  1. Pfaffl MW. (2001) A new mathematical model for relative quantification in real-time RT-PCR. Nucleic Acids Res 29(9):e45.doi:10.1093/nar/29.9.e45The efficiency-corrected ratio (the Pfaffl method), and the statement that the comparative Ct method (2^−ΔΔCt) presumes target and reference efficiencies of 2
  2. Vandesompele J, De Preter K, Pattyn F, Poppe B, Van Roy N, De Paepe A, Speleman F. (2002) Accurate normalization of real-time quantitative RT-PCR data by geometric averaging of multiple internal control genes. Genome Biol 3(7):research0034.doi:10.1186/gb-2002-3-7-research0034Why several reference genes are combined by their geometric mean rather than their arithmetic mean

Livak & Schmittgen (2001) and Applied Biosystems User Bulletin No. 2 could not be opened and are not cited; 2^−ΔΔCt is cited in the form the Pfaffl paper states it.

Often used together

Open →

qPCR Amplification Efficiency Calculator

Calculates qPCR amplification efficiency (%) from a standard curve slope.

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Error Bar Chart Maker

Draws an error bar chart from grouped data, with the summary statistics.

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Statistical Test Chooser

Picks the statistical test that fits your data, and runs it.