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qPCR Replicate Ct Calculator

Summarise technical replicate Ct values for any number of samples: mean, standard deviation, range and fold spread, with samples above your SD limit flagged.

Formula

Ct‾=∑Ctn\overline{C_t} = \dfrac{\sum C_t}{n}
s=∑(Ct−Ct‾)2n−1s = \sqrt{\dfrac{\sum (C_t - \overline{C_t})^2}{n-1}}
fold spread=2 s\text{fold spread} = 2^{\,s}
SEM=sn\mathrm{SEM} = \dfrac{s}{\sqrt{n}}
nn
number of replicate wells with a Ct
2s2^{s}
factor by which one SD of Ct changes the quantity, at 100% efficiency

How it works

Technical replicates are repeated wells of the same sample. Their spread measures pipetting and instrument precision, and the mean Ct is what goes forward into ΔCt and ΔΔCt calculations. Wells with no amplification, marked Undetermined or N/A, are counted separately and kept out of the mean.

Ct is proportional to the logarithm of the starting amount, so the statistics are taken on Ct itself. A spread of 0.3 cycles corresponds to about a 1.23-fold difference in starting quantity. Laboratories set their own limit for acceptable replicate spread; the tool flags any sample above the limit you enter and names the well farthest from the median.

Worked example

Three samples in triplicate, plus a no-reverse-transcriptase control that did not amplify, with an SD limit of 0.3 cycles.

  1. Control A: 24.1, 24.3, 24.2 gives a mean of 24.20 and an SD of 0.10.
  2. Treated A: 22.0, 22.1, 22.6 gives a mean of 22.23 and an SD of 0.32, above the limit; 22.60 is farthest from the median.
  3. Treated B: 21.8, 21.9, 21.9 gives a mean of 21.87 and an SD of 0.06.

One of four samples is above the limit, and the no-RT control shows no amplification, as it should.

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

Assumptions

  • The values are technical replicates of one sample, not biological replicates.
  • Undetermined means no amplification below the cycle limit, not a Ct of the maximum cycle number.
  • The SD limit is a convention chosen by the user.

Common mistakes

  • Averaging quantities instead of Ct values, or reporting a coefficient of variation of Ct, which has no meaning on a log scale.
  • Dropping the well that looks different without looking for the reason. A single outlier may be a pipetting error, but it may also signal a problem with the assay.
  • Treating two replicates as a reliable SD. With two wells, the range is more honest.

Related tools

qPCR ΔCt CalculatorΔCt and relative expression to a reference geneOpen calculatorqPCR ΔΔCt CalculatorRelative gene expression by the 2^−ΔΔCt methodOpen calculatorqPCR Efficiency CalculatorAmplification efficiency from a dilution series or a slopeOpen calculatorReplicate Measurement Statistics (SD, %RSD, SE, CI)Mean, SD, %RSD, standard error and 95% CI of replicatesOpen calculator

Related equipment

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