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ΔΔCt calculator

Paste Ct values, choose the reference gene and the control sample. Livak 2^−ΔΔCt or Pfaffl.

Fold change

What the ΔΔCt method calculates

Quantitative PCR reports a Ct, the cycle at which fluorescence crosses a threshold. A lower Ct means more starting template. To turn Cts into a change in expression you need two corrections: normalise to a reference gene to cancel differences in how much RNA went into each reaction, and compare to a control sample so the result is a ratio. Those two subtractions are ΔCt and ΔΔCt, and because the product doubles each cycle, a difference of ΔΔCt cycles corresponds to a 2^−ΔΔCt fold change. This is the Livak method (Livak and Schmittgen 2001), the standard way to report relative gene expression.

The formulas, with a worked example

ΔCt = Ct(target) − Ct(reference)
ΔΔCt = ΔCt(sample) − ΔCt(control)
Fold change = 2^−ΔΔCt  ·  log2 fold change = −ΔΔCt

A treated sample gives MYC Ct 22.1 and GAPDH Ct 18.4, so ΔCt = 3.7. The control gives MYC 24.5 and GAPDH 18.2, ΔCt = 6.3. ΔΔCt = 3.7 − 6.3 = −2.6, and 2^2.6 = 6.1-fold more MYC in the treated sample, or a log2 fold change of +2.6. Each cycle of ΔΔCt is a factor of two.

Livak or Pfaffl: when efficiency matters

The Livak method assumes both assays amplify with 100% efficiency, doubling every cycle. Real assays run at 90 to 110%, and if the target and reference differ, the error compounds over the cycles between them. The Pfaffl method (Pfaffl 2001) replaces the 2 with the measured amplification factor of each assay:

Ratio = E(target)^ΔCt(target) ÷ E(reference)^ΔCt(reference)

where ΔCt here is control minus sample and E is 1 plus the efficiency, so 95% gives 1.95. Get efficiencies from a dilution series with the qPCR efficiency calculator. When both are 100% the Pfaffl ratio equals 2^−ΔΔCt exactly. Use Pfaffl whenever the two efficiencies differ by more than a few percent, or whenever ΔCt values are large.

Choosing the reference gene and control

The reference gene must be expressed at a stable level across every condition in the experiment; a reference that itself responds to the treatment silently distorts every fold change. Commonly used genes such as GAPDH, ACTB, B2M, HPRT1 and TBP are stable in some tissues and not others, so check with geNorm or NormFinder, and use the mean of two or three references for important results, which this page allows by averaging their Cts before pasting. The control sample is whatever you are comparing against: untreated, vehicle, time zero, wild type. Its fold change is 1 by definition.

Replicates, error and what the ranges mean

Technical replicates of the same reaction should agree within about 0.3 cycles; the page flags any triplicate whose SD exceeds 0.5. The SD of each ΔCt is the two replicate SDs combined in quadrature, the ΔΔCt SD combines the sample and control ΔCt SDs, and the fold-change range is 2 to the power of ΔΔCt plus and minus that SD. Because the transform is exponential the range is asymmetric, which is why log2 fold change, with its symmetric error, is preferred for plots and statistics. These ranges describe technical variability only; conclusions need biological replicates, each analysed separately.

Common mistakes

  • Averaging Cts across biological replicates before calculating. Compute ΔΔCt per replicate, then average the log2 fold changes.
  • Cts above 35. They sit near the detection limit where single-molecule noise dominates; the page marks them. Increase input or accept the result as qualitative.
  • Comparing Cts from different runs without an inter-run calibrator; thresholds and baselines shift between plates.
  • Reporting fold change without the direction of ΔΔCt. A ΔΔCt of +2 is a 4-fold decrease, not increase; the sign is easy to flip by hand.
  • Subtracting in the wrong order for Pfaffl, where ΔCt is control minus sample rather than target minus reference.

Frequently asked questions

What does 2^−ΔΔCt mean?

It is the fold change in expression of a target gene in a sample relative to a control, after normalising both to a reference gene. ΔCt removes differences in input amount, ΔΔCt compares sample to control, and raising 2 to the negative power converts a difference in cycles into a ratio of starting copies, since each PCR cycle doubles the product.

Which gene should be the reference?

A gene whose expression does not change between your conditions: GAPDH, ACTB, B2M, HPRT1, TBP, PPIA and 18S rRNA are common choices, but none is stable in every tissue and treatment. Validate the reference with a tool such as geNorm or NormFinder, and average two or three references when the conclusion matters.

When should I use the Pfaffl method instead of Livak?

When the amplification efficiencies of the target and reference assays differ from 100% or from each other. The Livak method assumes both double every cycle; the Pfaffl method uses the measured efficiencies from a standard curve. With efficiencies near 100% the two give the same answer.

How do I report the result: fold change or log2?

Fold change reads naturally for increases (a 4-fold increase) but compresses decreases into 0 to 1. Log2 fold change is symmetric: +2 is a 4-fold increase, −2 a 4-fold decrease. Use log2 for plots and statistics, and quote fold change in text, with the range from replicate variability.

How many replicates do I need?

Three technical replicates per reaction catch pipetting errors, and their SD should be below about 0.3 cycles. Biological replicates, separate samples of the condition, are what statistics need: at least three, and the fold change should be computed per biological replicate then summarised.