qPCR efficiency calculator
Paste the Ct values of a dilution series. Get slope, R² and amplification efficiency.
Paste the Ct values of a dilution series. Get slope, R² and amplification efficiency.
In an ideal PCR every template molecule is copied once per cycle, so the amount of product doubles each cycle: an efficiency of 100%. Real reactions fall short because of primer quality, secondary structure, inhibitors or suboptimal conditions, and the shortfall changes how Ct relates to starting quantity. A standard curve measures the efficiency directly: a series of known dilutions is amplified, Ct is plotted against the logarithm of the quantity, and the slope of the line gives the efficiency. The number matters because every relative quantification method assumes something about it.
Worked example. Five 10-fold dilutions give Cts of 15.1, 18.4, 21.8, 25.1 and 28.5. The Ct rises by about 3.32 cycles per 10-fold dilution, so the slope is −3.32. Then 10^(1 ÷ 3.32) = 2.00, an amplification factor of exactly 2 per cycle, and E = 2.00 − 1 =1.00, or 100%. A slope of −3.6 gives 89.6%, a slope of −3.1 gives 110%. The calculator fits the line by least squares to all the points, averaging replicates first, and reports the fit quality as R².
The MIQE guidelines and instrument manufacturers agree on the same window: efficiency between90% and 110%, which is a slope between about −3.6 and −3.1, with R² ≥ 0.99 and a linear range of at least three orders of magnitude. Within this window the assay is quantitative and the Livak 2^−ΔΔCt method is valid. Outside it, either fix the assay or use an efficiency-corrected calculation.
The 2^−ΔΔCt method assumes the target and reference genes amplify with 100% efficiency, so one cycle equals one doubling for both. If both are within 90–110% and similar, the error is small. If they are not, the Pfaffl method corrects for it using the measured efficiencies of each assay, and this is where the numbers from this page go. TheΔΔCt calculator supports both.
Between 90% and 110%, which corresponds to a standard-curve slope between −3.6 and −3.1, with R² of 0.99 or better. This is the range the MIQE guidelines and most instrument manufacturers recommend. Efficiency near 100% means the amplicon doubles every cycle.
Plot Ct against the log10 of the template quantity for a dilution series and fit a straight line. Efficiency E = 10^(−1/slope) − 1. A slope of −3.32 gives E = 1.00, or 100%, because 10^(1/3.32) = 2, a doubling per cycle.
Efficiency cannot truly exceed 100%, so a value above it means something distorts the curve: PCR inhibitors carried over in the most concentrated dilutions delay their Ct, pipetting errors in the series, primer-dimers contributing signal at low template, or too few points. Check the R², re-make the dilution series and consider a wider dilution range.
At least five 10-fold dilutions covering the range of your samples, each in triplicate. Three points is the bare minimum for a line; fewer than three orders of magnitude gives an unreliable slope.
The Livak 2^−ΔΔCt method assumes both target and reference amplify at 100% efficiency, which is only valid if they are between about 90% and 110% and close to each other. If they differ, use the efficiency-corrected Pfaffl method, which takes the measured efficiencies as input.