qPCR Efficiency Calculator
A slope of -3.32 is exactly 100 percent, because log base 2 of 10 is 3.32.
The formula
E = 10^(-1/slope) - 1 ; a slope of -3.32 is 100 percent
Why -3.32 is the target
A perfect reaction doubles every cycle, so a tenfold change in starting material shifts the threshold cycle by log₂10, which is 3.32 cycles. The standard curve therefore has a slope of −3.32, and any slope shallower or steeper than that means the reaction is not doubling. It is one of the few numbers in molecular biology that is a mathematical consequence rather than a convention.
The acceptable window
Efficiencies between about 90 and 110 % are normally accepted, corresponding to slopes from −3.6 to −3.1. Below that, something is inhibiting the reaction; above 110 % usually means primer dimers or a pipetting error in the dilution series rather than a reaction that has beaten thermodynamics.
Efficiency compounds
The difference between 90 and 100 % efficiency looks small and is not: over 30 cycles it is a 4.7-fold difference in final product, and by 40 cycles nearly eightfold. This is why comparing two genes assayed at different efficiencies without correcting for it produces confidently wrong quantification.
Ratios are expectations, not promises
Every genetic ratio on these pages is a probability distribution, not a guarantee. A 3:1 cross does not produce three dominant offspring for every recessive one in a litter of four — it produces each offspring independently with a three-quarters chance. Small families depart from the expected ratio routinely, and that is the reason Mendel needed thousands of pea plants rather than dozens.