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qPCR Efficiency-Corrected Ratio (Pfaffl)

Calculate a target gene's expression in a sample against a control, normalised to a reference gene, with a separate amplification efficiency for each assay (Pfaffl).

Formula

R=(1+Etarget)ΔCttarget(1+Eref)ΔCtrefR = \dfrac{(1 + E_{\text{target}})^{\Delta C_t^{\text{target}}}}{(1 + E_{\text{ref}})^{\Delta C_t^{\text{ref}}}}
ΔCt=Ctcontrol−Ctsample(for each gene)\Delta C_t = C_t^{\text{control}} - C_t^{\text{sample}}\quad(\text{for each gene})
E=100% for both:R=2−ΔΔCtE = 100\%\ \text{for both:}\quad R = 2^{-\Delta\Delta C_t}
Etarget, EreferenceE_{\text{target}},\ E_{\text{reference}}
efficiency of each assay as a fraction, from its own standard curve
ΔCt\Delta C_t
the Ct of the control minus the Ct of the sample, for that gene

How it works

The Livak 2^−ΔΔCt method assumes every assay doubles the product each cycle. When the assays have measurably different efficiencies, that assumption biases the ratio, and the error grows with the size of the Ct differences. Pfaffl's model uses each assay's own efficiency, raised to the power of its own Ct shift.

The Livak value is shown for comparison so the effect of the efficiency correction is visible. The two agree exactly when both efficiencies are 100%.

Worked example

Target efficiency 95%, reference efficiency 98%. Control target Ct 26.4, sample target Ct 23.1; control reference Ct 20.2, sample reference Ct 20.0.

  1. Target: ΔCt = 26.4 − 23.1 = 3.30, so (1.95)^3.30 = 9.06.
  2. Reference: ΔCt = 20.2 − 20.0 = 0.20, so (1.98)^0.20 = 1.146.
  3. Ratio = 9.06 / 1.146 = 7.90.

The target is 7.9 times higher in the sample than in the control, against 8.6 by the Livak method.

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

Assumptions

  • Each efficiency was measured for that assay, in the same matrix and conditions.
  • The reference gene is stable between control and sample.
  • Ct values are means of replicates in the linear range of the assay.

Common mistakes

  • Taking efficiencies from a vendor sheet or another laboratory rather than measuring them.
  • Using an efficiency above 110% without finding out why.
  • Reporting a ratio without the efficiencies that produced it.

Related tools

qPCR ΔΔCt CalculatorRelative gene expression by the 2^−ΔΔCt methodOpen calculatorqPCR Efficiency CalculatorAmplification efficiency from a dilution series or a slopeOpen calculatorqPCR ΔCt CalculatorΔCt and relative expression to a reference geneOpen calculatorqPCR Replicate Ct CalculatorMean, SD and fold spread of replicate Ct values, with flagsOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.