BioDeviceHub

qPCR Efficiency Calculator

Calculate qPCR amplification efficiency from the slope of a standard curve or directly from a dilution series, with R², range, residuals and a plot.

Formula

Ct=mlog⁡10(Q)+bC_t = m \log_{10}(Q) + b
E=10−1/m−1E = 10^{-1/m} - 1
m=−3.32 ⇒ E=100%m = -3.32\ \Rightarrow\ E = 100\%
mm
change in Ct per tenfold change in quantity; negative
EE
fractional increase of amplicon per cycle; 1 means the amount doubles

How it works

A serial dilution of a template is amplified, and Ct is plotted against the logarithm of the amount. If every cycle multiplies the product by (1 + E), a tenfold dilution shifts Ct by log₂(10) / log₂(1 + E) cycles, which is 3.32 when E is 100%. The efficiency follows from the slope of the fitted line.

An efficiency is only credible if the standard curve is good: enough points, spread over enough range, with small residuals. The tool refuses to fit fewer than three points, and warns when there are fewer than five, when the range is narrower than three orders of magnitude, or when R² is low. It also says plainly that a high R² alone does not show the assay is efficient, specific or accurate.

Worked example

Six tenfold dilutions from 10⁷ to 10² copies with Ct values 15.2, 18.6, 21.9, 25.3, 28.6 and 32.0.

  1. The fit gives a slope of −3.354 and an intercept of 38.69, with R² = 0.99998.
  2. E = 10^(−1 / −3.354) − 1 = 0.9867.

Efficiency is 98.7% over a 5-log range, inside the 90 to 110% range commonly quoted as acceptable.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • The dilutions were made accurately. Pipetting error in the series appears directly as error in the slope.
  • All points lie in the linear range, and none is at or near the detection limit.
  • Efficiency is the same throughout the range of the curve.

Common mistakes

  • Fitting with too few points or too narrow a range.
  • Including saturated or undetected points at the ends of the series, which flatten the slope.
  • Reading an efficiency above 100% as a real result. It is usually inhibition in the concentrated samples, or pipetting error.

Related tools

qPCR Absolute Quantification CalculatorCopy number of unknowns from a standard curveOpen calculatorqPCR Efficiency-Corrected Ratio (Pfaffl)Fold change when target and reference efficiencies differOpen calculatorqPCR ΔΔCt CalculatorRelative gene expression by the 2^−ΔΔCt methodOpen calculatorCalibration Curve Calculator (Standard Curve)Linear fit, residuals and an unknown with its uncertaintyOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.