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qPCR ΔCt Calculator

Calculate ΔCt, the target Ct minus the reference-gene Ct, for each sample, and the expression relative to the reference gene with your amplification efficiency.

Formula

ΔCt=Cttarget−Ctreference\Delta C_t = C_t^{\text{target}} - C_t^{\text{reference}}
relative expression=(1+E)−ΔCt\text{relative expression} = (1 + E)^{-\Delta C_t}
E=1 for 100% efficiency, so (1+E)=2E = 1\ \text{for 100\% efficiency, so } (1+E) = 2
CttargetC_t^{\text{target}}
mean Ct of the gene of interest in the sample
CtreferenceC_t^{\text{reference}}
mean Ct of the reference (housekeeping) gene in the same sample
EE
amplification efficiency as a fraction

How it works

Each cycle multiplies the amount of amplicon by (1 + E). If the target crosses the threshold later than the reference by ΔCt cycles, it started with (1 + E)^−ΔCt times as much. Subtracting the reference corrects for differences in how much cDNA went into each well.

This is an abundance ratio within one sample, not a fold change between samples. To compare a treated sample with a control, subtract the control's ΔCt from the treated sample's (ΔΔCt), which is the next step.

Worked example

Control: target Ct 26.4, reference Ct 20.2. Treated: target 23.1, reference 20.0. Efficiency 100%.

  1. Control ΔCt = 26.4 − 20.2 = 6.20, so 2^−6.2 = 0.0136.
  2. Treated ΔCt = 23.1 − 20.0 = 3.10, so 2^−3.1 = 0.1166.

In both samples the target is less abundant than the reference, but the treated sample has 8.6 times more relative to its reference (0.1166 / 0.0136).

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

Assumptions

  • The target and reference assays both amplify at the single efficiency entered.
  • The reference gene is expressed stably across the conditions compared.
  • Ct values are means of technical replicates within the linear range of the assays.

Common mistakes

  • Using a reference gene that changes with the treatment, which shifts every ΔCt.
  • Assuming 100% efficiency for an assay that has not been tested.
  • Reporting 2^−ΔCt as a fold change between groups.

Related tools

qPCR ΔΔCt CalculatorRelative gene expression by the 2^−ΔΔCt methodOpen calculatorqPCR Efficiency-Corrected Ratio (Pfaffl)Fold change when target and reference efficiencies differOpen calculatorqPCR Replicate Ct CalculatorMean, SD and fold spread of replicate Ct values, with flagsOpen calculatorqPCR Efficiency CalculatorAmplification efficiency from a dilution series or a slopeOpen calculator

Related equipment

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