Delta Delta Ct Calculator (qPCR Fold Change)
Calculate relative gene expression from qPCR Ct values with the Livak 2^−ΔΔCt method: ΔCt, ΔΔCt, fold change and log2 fold change, with an optional amplification efficiency.
How it works
ΔCt = Ct(target) − Ct(reference) · ΔΔCt = ΔCt(treated) − ΔCt(control) · fold change = 2^(−ΔΔCt), or (1 + E)^(−ΔΔCt) with efficiency E · log2 fold change = −ΔΔCt × log2(1 + E)
The comparative Ct method of Livak and Schmittgen (2001) turns raw quantitative PCR cycle thresholds into relative expression. Subtracting the reference (housekeeping) gene Ct from the target Ct normalises for how much cDNA went into each well; subtracting the control sample’s ΔCt from the treated sample’s ΔCt gives ΔΔCt. Because each cycle doubles the product, a ΔΔCt of −1 means twice as much target. The method assumes both genes amplify with similar efficiency close to 100%; use the average of technical replicates, and do statistics on ΔCt values, not on fold changes.
Worked example
Treated: target Ct 24.5, reference Ct 18.0, so ΔCt = 6.50. Control: target Ct 26.0, reference Ct 18.2, so ΔCt = 7.80. ΔΔCt = 6.50 − 7.80 = −1.30 and the fold change is 2^1.30 = 2.46 — the target is up-regulated about 2.5-fold (log2 fold change 1.30).
Sources: Livak KJ, Schmittgen TD. Analysis of relative gene expression data using real-time quantitative PCR and the 2^−ΔΔCT method. Methods 2001;25:402–8 · Pfaffl MW. A new mathematical model for relative quantification in real-time RT-PCR. Nucleic Acids Res 2001;29:e45
Frequently asked questions
What does a negative ΔΔCt mean?
The target appears earlier (lower Ct) in the treated sample after normalisation, so it is more abundant: ΔΔCt = −1 means 2-fold up, −2 means 4-fold up. A positive ΔΔCt means down-regulation: +1 gives a fold change of 0.5.
How do I report down-regulation?
A fold change of 0.25 is often reported as −4-fold (the negative reciprocal) or as a log2 fold change of −2. Log2 values are symmetric around zero and better for plots and statistics.
When can I not use the 2^−ΔΔCt method?
When the target and reference genes amplify with clearly different efficiencies (they should be within about 5–10% of each other), or when the reference gene itself changes with treatment. Then use the Pfaffl efficiency-corrected method or several validated reference genes.
Should I average Ct values or fold changes?
Average technical replicate Ct values first, then calculate ΔCt for each biological replicate. Run statistics on ΔCt (or ΔΔCt) values, which are normally distributed, and convert to fold change only for presentation.
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This calculator is for educational purposes. Double-check important results before acting on them.