When performing normalization of real time PCR results, I found two ways of doing it:

  1. In my lab they follow the next layout: $\text{Efficiency}^{-(CT\ _{\large\text{interest gene}} - CT _{\large\text{ housekeeping}})}$ each time controls with controls and treatments with treatments. Then they divide the all values (treated and controls) each with controls.

  2. On the other hand I found another way to normalize that follows this steps: $\text{Efficiency}^{(CT_{\large\text{control}} - CT_{\large\text{treated}})}$. Then you make the same for the normalizing gene and divide the first by the last.

The values obtained are similar but not exact. Also I noticed that first algorithm gives rather different values for most diluted when performing a standard curve. Which is correct?

  • 1
    $\begingroup$ For those who are not satisfied with $2^{\Delta(\Delta Ct)}$ and want to incorporate different efficiencies of the target and normalizer PCR reactions, would this formula work to calculate arbitrary values for relative expression: $$\frac{\mbox{Efficiency}_{target}^{-(Ct_{\text{target}})}}{\mbox{Efficiency}_{normalizer}^{-(Ct_{\text{normalizer}})}}$$ I have compared the results with that of the RTPCR instrument's own software using calibrators from a pool of tested samples, and they fit almost perfectly. But is the equation valid in a theoretical sense? $\endgroup$ Commented Apr 17, 2015 at 13:48

2 Answers 2


First step is the calculation of efficiency, denoted by lets say $E_{gene}$. See this post for calculation of primer efficiency.

So the fold change for that gene will be calculated by $E_{gene}^{-\Delta Ct_{gene}}$


$\Delta Ct = Ct^{treated} -Ct^{control}$

But these Ct values are not normalized. For normalization, you take some reference gene which need not be a housekeeping gene. Reference gene should chosen such that it is not affected by the treatment. In some cases usual housekeeping genes can also get affected for e.g. in treatments affecting cell cycle or differentiation. In such cases you should use a spike-in (an artificial RNA bearing low resemblance with any known gene).

You can either normalize the fold change (Case A) or find fold change of the normalized expression (Case B).

Means the same mathematically.

Case A:

$E_{gene}^{-\Delta Ct_{gene}} / E_{ref}^{-\Delta Ct_{ref}}$

Case B:

$\large\frac{[E_{gene}^{-Ct^{treated}_{gene}}]/[E_{ref}^{-Ct^{treated}_{ref}}]} {[E_{gene}^{-Ct^{control}_{gene}}]/[E_{ref}^{-Ct^{control}_{ref}}]}$

You can rearrange the numerator and denominator to get Case A from Case B. I'm not sure how you are ending up getting different values. Recheck once. It may be because of numerical approximation errors.

Case A looks much neater; so it is best to calculate that way :)

  • $\begingroup$ sorry for the trouble but mistook on the query, my point 1 is edited $\endgroup$
    – Katz
    Commented Mar 31, 2014 at 10:46
  • $\begingroup$ Answer still holds :) Case B is what your lab people follow (point 1) and Case A is the point 2 of your question $\endgroup$
    Commented Mar 31, 2014 at 10:47
  • $\begingroup$ Note: you cannot club the fractions in the numerator together to obtain the $point\ 1$ sort of form because the bases are not same ($E_{gene} \ vs \ \ E_{ref}$). It can only be done if the efficiencies are the same. $\endgroup$
    Commented Mar 31, 2014 at 10:58

This topic could probably have it's own StackExchange, there is so much info and trial and error done with rtPCR. Here's my 2 cents:

Your adjusted calculation does not normalize your data, it just subtracts the 'background' or control. For expression studies this is not good enough. Normalizing data for gene expression must involve setting it to a scale of another gene whose expression should be not only present but consistent between your treated and untreated samples. House keeping genes (you are probably using GAPDH) make good candidates for this because their expression rarely changes. If you don't normalize than you don't know if your your expression is actually changing, or if it's simply due to a larger input of mRNA. However it must be shown that the housekeeping gene's expression is also not changing, this is usually accomplished using a different sample set. Take if from me, I've done a lot of this and this step is one of the most important in your experiment. Any reviewer who knows what he's doing will reject a paper using rtPCR without the proper statistics.

I have had a lot of success using Applied Biosystems StepOne software to provide you with accurate Ct values. Generating the variable is complication, use software to do it right every time:


What method/system are you using?

  • $\begingroup$ There have been several instances in which GAPDH is not suitable as a reference gene. $\endgroup$
    Commented Mar 31, 2014 at 8:49
  • $\begingroup$ SYB GReen and roche, about normalizing no clue really $\endgroup$
    – Katz
    Commented Mar 31, 2014 at 10:19

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