ΔΔCt Calculator: qPCR Fold Change and Relative Expression

Turn qPCR Ct values into fold change, step by step, with replicates, statistics and a chart.

The ΔΔCt (delta delta Ct) method calculates relative gene expression from qPCR data in three subtractions: ΔCt = Ct(target gene) − Ct(reference gene), ΔΔCt = ΔCt(sample) − mean ΔCt(control group), and fold change = 2^(−ΔΔCt). A ΔΔCt of −2 means a 4-fold increase; a ΔΔCt of +1 means half the expression of the control. It assumes both genes amplify with close to 100% efficiency; when they do not, the Pfaffl method uses each gene's measured efficiency instead of 2.

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How to use it

1. Paste your Ct table (Sample, Gene, Ct, optional Group), or type the values into the table. Put technical replicates in one cell, separated by commas.
2. Pick the reference (housekeeping) gene or genes.
3. Put biological replicates in the same group and choose the control group.
4. Choose 2^-ΔΔCt, or the Pfaffl method if your primer efficiencies differ from 100%.
5. Read the fold change, 95% confidence interval and p-value for each gene and group, check the quality notes, and download the CSV.

What you enter

• Ct values for at least one target and one reference gene
• Two or more groups, one of them the control
• Optional: amplification efficiency for each gene (Pfaffl)

What you get

• Fold change and log2 fold change for each target in each group
• 95% confidence interval and Welch p-value (raw and Holm-adjusted) when groups have 2 or more biological replicates
• Per-sample ΔCt and ΔΔCt and per-well replicate statistics
• Flags for outlying replicates, high replicate SD, late Ct and unstable reference genes
• Bar chart and a CSV of every value

Formula

ΔCt = Ct(target) − Ct(reference) | ΔΔCt = ΔCt(sample) − mean ΔCt(control) | Fold change = 2^(−ΔΔCt) | Pfaffl ratio = E_target^ΔCt_target(control − sample) ÷ E_ref^ΔCt_ref(control − sample)

Every calculation is done on the log2 scale, where qPCR data are close to normally distributed. With several reference genes, their Ct values are averaged (a geometric mean of quantities). Biological replicates are averaged as log2 values, so the group fold change is a geometric mean, and the Welch t-test is run on those log2 values, never on raw fold changes. The Pfaffl option weights each Ct by log2 of that gene's amplification factor E (E = 1 + efficiency); with E = 2 for every gene it gives exactly the 2^-ΔΔCt result.

Worked example: IL6 after LPS stimulation, normalized to GAPDH

Input: Three control and three LPS-treated samples, each in triplicate. Mean ΔCt (IL6 − GAPDH): control 9.76, 9.82, 9.67; LPS 6.09, 6.23, 6.04 (one outlying LPS replicate excluded).

Result: Mean control ΔCt 9.75, mean LPS ΔCt 6.12, ΔΔCt −3.63, fold change 2^3.63 = 12.4 (95% CI 10.7 to 14.2), Welch p < 0.001

IL6 is about 12-fold higher after LPS. The confidence interval comes from the three biological replicates per group; technical replicates only make each sample's Ct more precise.

Questions

How do you calculate fold change from delta delta Ct?

Fold change = 2^(−ΔΔCt). First subtract the reference gene Ct from the target Ct in every sample (ΔCt), then subtract the control group's mean ΔCt (ΔΔCt). A ΔΔCt of −3 gives 2^3 = 8-fold higher expression; a ΔΔCt of +1 gives 0.5, half the control level.

What is the difference between ΔCt and ΔΔCt?

ΔCt normalizes one sample: target Ct minus reference gene Ct, which corrects for how much RNA was loaded. ΔΔCt compares two conditions: the ΔCt of a sample minus the ΔCt of the control (calibrator). Only ΔΔCt gives a fold change relative to the control.

When should I use the Pfaffl method instead of 2^-ΔΔCt?

When the amplification efficiencies of your target and reference genes are not both close to 100% and close to each other. The Pfaffl method uses each gene's measured efficiency, usually from a standard-curve slope (efficiency = 10^(−1/slope) − 1).

Should I average Ct values or fold changes across biological replicates?

Average on the log scale: average the ΔCt (or ΔΔCt) values, then convert to fold change. Averaging raw fold changes overweights high values; averaging log values gives the geometric mean, and statistics should be run on ΔCt or log2 fold change.

Which statistical test should I use for qPCR data?

Test ΔCt or log2 fold change values, not fold changes. For two groups, a Welch t-test on ΔCt across biological replicates is standard; with several groups or genes, adjust for multiple comparisons (this calculator reports Holm-adjusted p-values) or use ANOVA.

What does a negative ΔΔCt mean?

A negative ΔΔCt means the target reached threshold earlier in the sample than in the control after normalization, so it is more highly expressed: ΔΔCt = −1 is a 2-fold increase and −2 a 4-fold increase.

Limitations

• The 2^-ΔΔCt method assumes near-100% and similar efficiencies for target and reference genes. A 5% efficiency difference already distorts fold changes over many cycles; use the Pfaffl option with measured efficiencies when in doubt.
• Results are only as good as the reference gene. If its Ct shifts with treatment, fold changes are biased; MIQE recommends validated reference genes, ideally two or more.
• Technical replicates measure pipetting precision, not biological variation. p-values need at least two (better three or more) biological replicates per group.
• Ct values above about 35 are close to the detection limit, where replicate scatter grows and fold changes are unreliable.

References

• Livak KJ, Schmittgen TD (2001) Methods 25:402-408.
• Pfaffl MW (2001) Nucleic Acids Research 29:e45.
• Schmittgen TD, Livak KJ (2008) Nature Protocols 3:1101-1108.
• Bustin SA et al. (2009) Clinical Chemistry 55:611-622.
• Vandesompele J et al. (2002) Genome Biology 3:research0034.
• Hellemans J et al. (2007) Genome Biology 8:R19.
• Yuan JS, Reed A, Chen F, Stewart CN (2006) BMC Bioinformatics 7:85.

More Molecular Biology

• Codon Table (Interactive Genetic Code)
• Amino Acid Chart
• qPCR Efficiency & Standard Curve Calculator (Copy Number)
• Ligation Insert-to-Vector Mass Calculator

All free tools · By Dr. Zubair Khalid, DVM, MS, PhD.