How to use it
- 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.
- To fold biological replicates together, paste a group name as a fourth column. Without it each sample is its own group.
- 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.
- Pick the control group. Every fold change is measured with that group set to 1.
- Enter amplification efficiencies if you know them. If you do not, leave them — 100 % is the assumption 2^−ΔΔCt makes.
- 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
If you did not measure efficiencies, report 2^−ΔΔCt and state the assumption. If you have a standard curve, Pfaffl is the number that actually uses that measurement. A large gap between the two columns is itself a reason to go and check your efficiencies.
By the geometric mean of the quantities. Because quantity goes as E^−Ct, that geometric mean is exactly the arithmetic mean of the Ct values when the efficiencies match — so the plain average you see on screen is the geometric mean, not an approximation of it.
Each sample becomes its own group. Everything still calculates, but there are no biological replicates, so the error bars come from technical ones only and the table says so.
They are not treated as numbers and are left out of the means; the count is shown under the input box. They are not filled in with 40 or any other stand-in — that number would be chosen rather than measured, and it would move the result quietly.
They are standard errors, so “mean ± SEM” is accurate. They are not confidence intervals and not a significance test. If you need a test, take the group fold changes into a statistics tool.