Hong Life CalculatorsUnderstanding the qPCR efficiency calculator — concept and principle
Amplification efficiency tells you what fraction of template molecules is copied in each PCR cycle. It is estimated from a standard curve: a serial dilution of known template is run, Ct is plotted against log₁₀ of the input amount, and a straight line is fitted. This calculator converts the slope of that line into efficiency and the per-cycle amplification factor, which you need to validate an assay or to correct relative quantification.
How it is calculated
- Amplification factor = 10^(−1/slope).
- Efficiency E = (10^(−1/slope) − 1) × 100%.
The slope is negative because more template gives a lower Ct. A slope of about −3.32 corresponds to 100% efficiency.
The principle
If every molecule is copied each cycle, the amount doubles per cycle, so a ten-fold increase in starting template reaches the threshold log₂10 ≈ 3.32 cycles earlier. In general, with amplification factor (1 + E) per cycle, a ten-fold change shifts Ct by 1 ÷ log₁₀(1 + E) cycles, which is the magnitude of the slope. Rearranging gives 1 + E = 10^(−1/slope). Steeper slopes (for example −3.6) mean that each ten-fold step takes more cycles, so the reaction is less efficient; shallower slopes (−3.1) mean apparently higher efficiency.
Worked example
- Input: slope = −3.32.
- −1 ÷ (−3.32) = 0.30120.
- Amplification factor = 10^0.30120 = 2.0008.
- Efficiency = (2.0008 − 1) × 100 = 100.08%.
| Standard curve slope | Efficiency |
|---|---|
| -0.83 | 1,502.58% |
| -1.66 | 300.32% |
| -2.49 | 152.12% |
| -3.32 | 100.08% |
| -4.15 | 74.17% |
| -4.98 | 58.78% |
| -6.64 | 41.45% |
How to read the result
A common acceptance range is about 90–110%, which corresponds to slopes of roughly −3.58 to −3.10. Efficiency below 90% often points to poor primer design, secondary structure or suboptimal reaction conditions. Values above 110% usually do not mean better amplification; they are typically caused by inhibitors in the concentrated standards, pipetting errors in the dilution series or primer-dimer signal in dye-based assays. Check that the fit is good (R² is often expected to be about 0.98 or higher) and that the dilutions span several orders of magnitude.
Common mistakes
- Plotting Ct against the amount itself rather than log₁₀ of the amount.
- Using a slope fitted to only two or three points.
- Entering a positive slope, which gives a meaningless result.
- Including the most dilute points where Ct is noisy or the template is near single copies.
Frequently asked questions
What slope means 90% efficiency?
About −3.58, since 10^(1/3.58) − 1 ≈ 0.90.
How is efficiency used in ΔΔCt?
Enter it so the calculator uses (1 + E) instead of 2 as the base of the fold change, or use separate efficiencies in the Pfaffl model.
Why can efficiency exceed 100%?
True copying cannot exceed doubling, so values above 100% reflect artefacts such as inhibition in concentrated samples that compresses the curve.
Sources: Bustin, S. A. et al. (2009), Clinical Chemistry 55, 611–622 (MIQE guidelines) · Pfaffl, M. W. (2001), Nucleic Acids Research 29, e45