qPCR 2^−ΔΔCt Relative Quantification Online Calculator

2^−ΔΔCt method (Livak method) is the most widely used algorithm for qPCR relative quantification, in three steps:

ΔCt   = Ct(target gene) − Ct(reference gene)          within the same sample
ΔΔCt  = ΔCt(treatment sample) − ΔCt(control group mean)
Fold change = 2^(−ΔΔCt)

The 2 in the exponent reflects one doubling of product per cycle, i.e., exactly 100% amplification efficiency.

This assumption is the biggest weakness of the 2^−ΔΔCt method. If the amplification efficiencies of the target and reference genes differ substantially, results will be systematically biased. Standard practice is to run a standard curve first and confirm that both primer pairs fall within 90–110% efficiency and are close to each other; if they differ significantly, switch to the Pfaffl method, which uses each gene’s actual efficiency as the base. Efficiencies and Pfaffl ratios can be calculated directly with the amplification efficiency calculator.

Other key points:

• The reference gene must genuinely be stable under your experimental conditions. Hypoxia and proliferation changes can render GAPDH and ACTB unreliable; screen reference genes first using methods such as geNorm or NormFinder.
• Technical replicates assess pipetting error; biological replicates are required for statistical testing. Using technical replicates to compute p-values is invalid.
• Statistical tests should be performed at the ΔCt or ΔΔCt level (these quantities are approximately normally distributed), not after the 2^−ΔΔCt transformation, because the exponential transform skews the distribution.