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qPCR ΔΔCt Calculator

Calculate relative gene expression from qPCR Ct values with the Livak 2^−ΔΔCt method: ΔCt for each sample, ΔΔCt, and the fold change against a control.

Formula

ΔCt=Ctgene of interest−Ctreference\Delta C_t = C_t^{\text{gene of interest}} - C_t^{\text{reference}}
ΔΔCt=ΔCttreated−ΔCtcontrol\Delta\Delta C_t = \Delta C_t^{\text{treated}} - \Delta C_t^{\text{control}}
fold change=2−ΔΔCt\text{fold change} = 2^{-\Delta\Delta C_t}
CtC_t
cycle at which fluorescence crosses the threshold; a lower Ct means more starting template
reference gene\text{reference gene}
a gene whose expression is stable across the conditions compared

How it works

Each Ct for the gene of interest is first normalised to a reference gene measured in the same sample, which corrects for differences in the amount of input. The normalised value of the treated sample is then compared with that of the control.

Because product doubles each cycle at perfect efficiency, a difference of one cycle is a two-fold difference in starting amount. A fold change above 1 means higher expression in the treated sample; below 1, lower.

Worked example

Treated: gene of interest Ct 22.4, reference 17.9. Control: gene of interest Ct 25.1, reference 18.0.

  1. ΔCt treated = 22.4 − 17.9 = 4.5; ΔCt control = 25.1 − 18.0 = 7.1.
  2. ΔΔCt = 4.5 − 7.1 = −2.6.
  3. Fold change = 2^2.6 = 6.06.

The gene is expressed about 6-fold higher in the treated sample than in the control.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • Both assays amplify at close to 100% efficiency and at similar efficiency to each other.
  • The reference gene is unaffected by the treatment.
  • Ct values are means of technical replicates.

Common mistakes

  • Skipping the efficiency check. If the two assays differ in efficiency, use an efficiency-corrected model such as Pfaffl's instead.
  • Choosing a reference gene that changes with the treatment.
  • Averaging fold changes across biological replicates instead of averaging ΔCt values and converting at the end.

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