How To Perform The Delta-Delta Ct Method

What is the delta-delta Ct method?

The delta-delta Ct method, also known as the 2∆∆Ct method, is a simple formula used in order to calculate the relative fold gene expression of samples when performing real-time polymerase chain reaction (also known as qPCR). The method was devised by Kenneth Livak and Thomas Schmittgen in 2001 and has been cited over 61,000 times.

The free Microsoft Excel template

We have created a FREE Excel template which contains all of the formula described in this article below. Use this to practise and get the hang of the calculations. Everything is done for you, all that is required is the Ct values!

If you would like to download this, simply click here.

Understanding the delta-delta Ct method formula

It is worthwhile understanding what the delta-delta Ct formula means before diving straight into the calculations.

The overall formula to calculate the relative fold gene expression level can be presented as:

2 delta delta Ct formulaThis looks like a scary mathematical formula when in actual fact, it isn’t. Let’s break the formula down into easier to understand chunks.

Firstly, Ct stands for the cycle threshold (Ct) of your sample. This is given after the qPCR reaction by the qPCR machine. Simply, it is the cycle number where the fluorescence generated by the PCR produce is distinguishable from the background noise.

The symbol refers to delta. Delta is a mathematical term used to describe the difference between two numbers. So it is useful to use when summarising long formulas.

So, let’s take a look to see what the ∆∆Ct part of the equation means:

∆∆Ct = ∆Ct (treated sample) – ∆Ct (untreated sample)

Essentially, ∆∆Ct is the difference between the ∆Ct values of the treated/experimental sample and the untreated/control sample. But what does ∆Ct refer to?

Let’s take a look:

∆Ct = Ct (gene of interest) – Ct (housekeeping gene)

Basically, ∆Ct is the difference in Ct values for your gene of interest and your housekeeping gene for a given sample. This is to essentially normalise the gene of interest to a gene which is not effected by your experiment, hence the housekeeping gene-term.

Using the delta-delta Ct formula to calculate gene expression

To use the delta-delta Ct method, you require Ct values for your gene of interest and your housekeeping gene for both the treated and untreated samples. If you have more than one housekeeping gene, it may be worth checking out the guide on analysing qPCR data with numerous reference genes.

Here is how to calculate the relative gene expression in 5 easy steps.

1. Average the Ct values for any technical replicates

The first step is to average the Ct values for the technical replicates of each sample. So, when performing the qPCR in duplicate or triplicate, for example, these values need to be averaged first. In the example below, each sample was run in duplicate (Ct1 and Ct2).

2. Calculate the delta Ct for each sample

The next step is to calculate delta Ct (∆Ct) for each sample by using the newly created average Ct values. The formula to calculate delta Ct is presented below.

∆Ct = Ct (gene of interest) – Ct (housekeeping gene)

For example, to calculate the ∆Ct for the ‘Control 1‘ sample:

∆Ct Control 1 = 30.55 – 17.18

 Calculate delta Ct

3. Select a calibrator/reference sample(s) to calculate delta delta Ct

The next step is to decide which sample, or group of samples, to use as a calibrator/reference when calculating the delta delta Ct (∆∆Ct) values for all the samples. This is the part which confuses a lot of people. Basically, this all depends on your experiment set-up.

A common way of doing this is to just match the experimental samples and determine the relative gene expression ratios separately. This is all well and true for experiments that have matched pairs, such as the case in cell culture experiments. However, this is difficult when the two experimental groups vary in n numbers and do not have matched pairs.

Another way to select a calibrator/reference sample is to pick the sample with the highest Ct value, so the sample with the lowest gene expression. This way, all the results will be relative to this sample. Or, you could simply select just one of the control samples to act as the reference sample.

I personally average the ‘Average Ct’ values of the biological replicates of the control group to create a ‘Control average’. By doing so would mean that the results are presented relative to the control average Ct values.

Whichever sample, or group of samples, you use as your calibrator/reference is fine so long as this is consistent throughout the analyses and is reported in the results so it is clear. Remember, the results produced at the end are relative gene expression values.

With this in mind, if we want to get ∆∆Ct values for every sample (including for each control sample), we first need to average the ∆Ct for the 3 control samples:

∆Ct Control average = (13.38 + 13.60 + 13.68)/3

4. Calculate delta delta Ct values for each sample

Now calculate the ∆∆Ct values for each sample. Remember, delta delta Ct values are relative to the untreated/control group in this example. The formula to calculate delta delta Ct is presented below.

∆∆Ct = ∆Ct (Sample) – ∆Ct (Control average)

For example, to calculate the ∆∆Ct for the Treated 1 sample:

∆∆Ct Treated 1 = 7.83 – 13.55

5. Calculate the fold gene expression values

Finally, to work out the fold gene expression we need to do 2 to the power of negative ∆∆Ct (i.e. the values which have just been created). The formula for this can be found below.

Fold gene expression = 2^-(∆∆Ct)

For example, to calculate the fold gene expression for the Treated 1 sample:

Fold gene expression = 2^-(-5.72)

Doing this would give a fold gene expression of 52.71 for the Treated 1 sample. Doing this for all of the samples will look like this:

And that is how you can use the delta-delta Ct method to work out the fold gene expression for your samples. You would then use the gene expression values (2^-(∆∆Ct)) to undertake some data analysis to determine if they are statistically different from one another.

18 COMMENTS

  1. Dear Sir

    Thank you for your video

    I have some of my genes cannot express in the treated group. If I use the Average from one sample the result some time not logical but I got express for the housekeeping gene.

    for example, housekeeping gene values cq 28, 27, 29 but my treated group I got only one value 37 but cq value for other sample or replicate

    Ashwaq

    • Hi Ashwaq,
      Thanks for your comment!
      So you got a Cq value of 37 for the housekeeping gene in your treated group? It sounds like your housekeeping gene is expressed at such a low level in your treated group, compared to your controls. This would suggest that the experiment is having a significant influence on the expression of this gene, therefore I would not recommend using it as a housekeeping gene. A suitable housekeeping gene should have the same or very similar values between your control and treated groups. It may be worth trying out a panel of different housekeeping genes to see which ones are the best.
      I hope that helps.
      Best wishes,
      Steven

  2. Dear Dr. Steven,

    Thank you for the video.
    Can you please tell me how to tell that there is Up or down-regulation of the gene by using the Fold change value.
    Thank you.
    Regards
    Houda

    • Hi Houda,
      Many thanks for your comment.
      To understand if there is an up- or down-regulation of your genes in a comparison between controls and treated groups, you simply compare the gene expression values between the two groups. So if the average gene expression of the controls was 1.2 and the treated group was 2.6 this would mean that there is an upregulation of the gene in the treated group. Conversely, if the values were 1.2 in the control and 0.8 in the treated group, this would mean that there is a downregulation in the treated group.
      I hope that makes sense?
      Best wishes,
      Steven

        • Hi Nina,
          Many thanks for your comment, and sorry about the slow reply.
          When I say “fold gene expression values”, I am referring to the final 2^-(∆∆Ct) values.
          I hope that clears it up.
          Best wishes,
          Steven

          • Hi Steven,

            I am wondering how you get “fold gene expression values” for your control samples, since the way you get those values for your experimental samples is by comparing it to the control samples. What are you using to get the delta delta CT for your control values?

            Thanks,
            Alaina

          • Hi Alaina
            Thanks for your comment.
            This way described, I still get fold gene expression values for all the control samples (refer to the 2^-(∆∆Ct) column in the above table).
            To get delta delta Ct values for the control samples, I use the average delta Ct value from the control group (see the Control average row in the above table) to compare against.
            I hope that makes sense.
            Best wishes,
            Steven

    • Hi Kurt,
      Many thanks for your comment and apologies for the slow reply.
      To handle multiple reference genes, it is best to take the geometric mean of the housekeeping gene Ct values. Then use this value to create the delta Ct’s.
      I will shortly create an article on how to do this with more detail.
      I hope that helps.
      Best wishes,
      Steven

  3. Hi Steven,
    Nice summary on delta delta Ct calculation.
    One question: Is one cell line treated in 3 different wells on the same day considered as n=3 for statistical analysis? Or do I have to treat the cells on 3 different days in order to add error bar?

    • Hi Jon,
      Many thanks for your comment!
      Ideally, it will be best to repeat the experiment on different days to be classed as true biological replicates. Since if you repeat it on the same day, obviously the variation will be lower, however, it is not an accurate representation of the amount of variation experienced.
      Refer to this recent paper in PLoS Biol by Lazic and colleagues which nicely sums this up (in the Cell Culture section).
      I hope that makes sense?
      Kind regards,
      Steven

  4. Why did you average the control? when you do this then you have a fold change different from 1. I have read that there should not be standard deviation from the control group as you are showing in this example…

    • Hi Irene,
      Many thanks for your comment.
      I used the average control delta Ct since this will enable the calculation of 2^-(∆∆Ct) for all the samples, including the individual control samples.
      Other people just match the experimental samples and determine the relative gene expression ratios separately. This is all well and true for experiments that have matched pairs, however, this is difficult when the two experimental groups vary in n numbers and do not have matched pairs. Another way to select a calibrator/reference sample is to pick the sample with the highest Ct value, so the sample with the lowest gene expression. This way, all the results will be relative to this sample.

      If you want to get an overall average fold change of 1 for the control group, you can normailse the results. To do this you would make a new column and divide all of the gene expression values (2^-DDCt) for all the samples by the control group average 2^-DDCt. Then average these values for the controls and the treated. The control average should now be set to ‘1’.
      I hope that makes sense?
      Thanks
      Steven

  5. Dear Steve
    I am really thankful for your explanation, I have understood perfectly (at least to do it in excel), but I would like to know if you have ever working with circulating microRNA expression? Because, I am going to work with that and I want to know if it applies the same method.

    Thank you so much for your time.
    Larissa.

    • Hi Larissa,
      Many thanks for your comment. I personally haven’t done qPCR on miRNAs. But it will depend on your experiment set-up. If you have control and treated samples, with at least one housekeeping gene then I am sure you can use the delta-delta Ct method as described for mRNA.
      Best wishes,
      Steven

  6. Thank you for great note!
    I wonder about the case that control group sample doesn’t have any GOI.
    For example, control group are wild type mouse and experimental group are knock-in mouse (EGFP).
    In this case, control group GOI was not detect any RT-qPCR result using EGFP primer.
    However, control group housekeeping gene was have Cq value such as 20.
    Then, how I can calculate delta Cq value of control? Was Cq of EGFP regarded zero?

    • Hi Lora
      In your case, you could give the samples with no signal on qPCR a Cq value of 40 (or the maximum cycle number from your qPCR run). That is, if you still want a value for your control group to do statistics? Obviously the difference is so strong anyway. But this will give you something at least to plot on a graph if you so wish?
      Thanks
      Steven

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