Log Reduction to Percent Kill

Three-log is 99.9 percent. Four-log is 99.99 percent. They are the same statement said two ways, and this page exists because people mix them up constantly — in reports, in tender documents, in conversations with regulators, and occasionally in the same sentence.

The arithmetic is one line. A log reduction of $\mathrm{LR}$ leaves a surviving fraction of $10^{-\mathrm{LR}}$, so the fraction killed is $P = 1 - 10^{-\mathrm{LR}}$, and running it backwards, $\mathrm{LR} = -\log_{10}(1-P)$. One log leaves a tenth and kills 90%. Two logs leave a hundredth and kill 99%. Six logs leave a millionth and kill 99.9999%.

The percent form hides everything interesting in its last decimal places. Moving a claim from 99.9% to 99.99% looks like a typographical refinement and is a whole extra log — a tenfold cut in survivors, which in treatment terms is often another barrier, another vessel, another capital project. That asymmetry is exactly why every disinfection rule in the world is written in logs, and why a percent kill quoted to several decimals should always be converted before it is believed.

The confusion that costs money is double-counting. I have read reports that say a process achieves "3-log inactivation, that is 99.9% removal", and then add a further "99.9% removal" from a second barrier, and conclude something enormous. Those are two barriers of three logs, which is six logs total — 99.9999% — and the correct way to get there is to add the logs. Percentages cannot be added or multiplied intuitively, which is the practical case for never working in them at all.

One hundred percent is not a number this equation accepts. Its log form is infinite, and no disinfection process delivers it — 100% is always a rounding, or a non-detect being reported as an absence. If a supplier's literature says 100%, ask what the detection limit was and what the starting count was, and convert those two into the minimum log reduction the data actually supports. That number is usually respectable and always defensible; the 100% is neither.

Worth keeping the survivor form in your head as well as the percentage. A log reduction of $\mathrm{LR}$ means one organism in $10^{\mathrm{LR}}$ survives: 3-log is one in a thousand, 6-log is one in a million. Said that way, the difference between 99.9% and 99.9999% stops being three extra nines and becomes what it is — a thousandfold difference in what reaches the tap.