qPCR Amplification Efficiency Calculator — Standard Curve Slope to E, Pfaffl Relative Quantification
Part 1: Standard Curve — Amplification Efficiency
Part 2: Pfaffl Relative Quantification (efficiency-corrected)
The 2 in 2^-ΔΔCt means products double every cycle — assuming amplification efficiency is exactly 100%. Real primers rarely hit exactly 100%. When target gene and reference gene efficiencies differ substantially, the fold-change will be systematically skewed, and the magnitude of the skew depends on ΔCt — it is not a constant that can be corrected post hoc.
To quantify the discrepancy, efficiency must be measured. Make a serial dilution of template, measure Ct at each concentration, and fit a line with log10(starting quantity) on the x-axis and Ct on the y-axis:
Ct = slope × log10(starting quantity) + intercept
E = 10^(−1/slope)
Efficiency (%) = (E − 1) × 100%
100% efficiency corresponds to E = 2, slope = −1/log10(2) = −3.3219.
Acceptance criteria (MIQE guidelines): efficiency 90–110% (slope −3.6 to −3.1), R² > 0.99. Primers outside this range should not be used directly for relative quantification.
When efficiency is out of spec, do not apply 2^-ΔΔCt — use the Pfaffl method instead, with each gene’s measured E as the base:
(E_target)^[Ct(control, target) − Ct(sample, target)]
ratio = ─────────────────────────────────────────────────────────────
(E_ref)^[Ct(control, ref) − Ct(sample, ref)]
When both efficiencies equal exactly 2, this equation reduces exactly to 2^-ΔΔCt — the Pfaffl method is a generalization of the latter, not a separate framework.
Common pitfalls:
- The dilution series must span the Ct range of your actual samples. Running the standard curve only at high concentrations and extrapolating to lower-concentration samples is unjustified.
- Efficiency above 110% usually does not mean true efficiency exceeds 100%; it indicates inhibitors, primer dimers, or pipetting errors in the serial dilution. Genuine amplification cannot produce more than one doubling per cycle.
- Efficiency is a property of the primer pair + reaction mix. Changing the master mix or instrument requires re-measurement.
- High R² only indicates good linearity, not that the efficiency value is accurate. The two metrics must be evaluated independently.
FAQ
My calculated efficiency is 105% — should I be concerned?
No. The MIQE-recommended acceptable range is 90–110%, and 105% falls within it. Efficiency above 100% does not mean more than one doubling per cycle is occurring; it reflects fitting uncertainty in the standard curve, dilution errors, or mild inhibition. What actually requires attention is efficiency outside the 90–110% window.
How much difference between target and reference efficiency is 'too much'?
There is no single cut-off, because the impact depends on ΔCt. Use the second calculator above: enter both measured efficiencies and your Ct values, then compare the Pfaffl ratio against 2^-ΔΔCt. If the discrepancy is within the effect size you care about, it is acceptable.
What units should I use for starting quantity in the standard curve?
ng, copy number, and relative dilution factor all work, as long as units are consistent within the column. The slope depends only on the ratio between points, not on the absolute units — changing units shifts only the intercept, not the slope or efficiency.
Does the Pfaffl method require a standard curve for every experiment?
Efficiency is a property of the primer pair plus reaction mix. Once measured for a given system it can be reused without repeating the standard curve on every plate. Re-measurement is needed after changing the master mix, instrument, or annealing temperature. The model itself does not require a calibration curve each run — this is one practical advantage over absolute quantification.
Why is efficiency written as E rather than a percentage?
E is the per-cycle amplification factor that goes directly into the exponent; the percentage is (E−1)×100. E = 2 means 100%, E = 1.9 means 90%. When filling in the form, do not enter 90 where E is expected.
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