# Log Reduction Calculator

By Przemek Trzepiński
Last updated: Sep 20, 2021

Log reduction calculator provides a simple method to calculate the efficacy of disinfectants such as alcohol or bleach. This tool works by comparing the number of microorganisms in a sample before and after the treatment. The collected results are then expressed as a percentage and as on the logarithmic scale. Higher result mean that the given agent has a higher efficacy. For example, a 1 log reduction is equivalent to a 90% bacterial reduction, whereas a 5 log reduction equals a reduction of 99.999%.

## What is log reduction?

Due to the nature of science, researchers often deal with extremely large or small values. Problems can occur when working with very long numbers as they are hard to read and make evaluations more confusing. To keep numbers manageable and facilitate the correct interpretation of results, scientific notation was created. This method expresses values as a simple decimal number multiplied by ten raised to an exponent, typically written as `n x 10ᵐ`, where `n` is the decimal number and `m` is the exponent.

Similarly, when determining a change in such large numbers, it is often useful to apply the logarithmic scale. Unlike the linear one, this scaling system uses the logarithmic change from one number to another to represent increment or decrement. Typically, base ten logarithm is used to transform numbers multiplied by ten raised to an exponent into simple 1-2 digits values.

Therefore this log reduction calculator measures how the number of bacteria in a sample has changed due to the impact of a given factor and expresses the result in a logarithmic scale. The result is referred to as an X log reduction, typically in the range of a 1 log reduction to a 5 log reduction.

## How to calculate log reduction in microbiology

Calculating log reduction for disinfectant validation is a four-step process:

1. Collect samples according to the fixed or standardized protocol.
2. Incubate the some of the samples with sanitizer as well as create some control samples.
3. Calculate the number of microorganisms in the control and treated sample to determine how many cells have been killed by the agent.
4. Calculate log reduction according to the formula, which is given in the section below. The expected result should be in the range of a 1 to 5 log reduction.

However, using microscopes or other direct cell quantity counting systems is usually too expensive or time-consuming for routine work. Therefore, microbiologists often apply indirect methods, some of which utilize sample dilution and culturing it on a petri dish with an appropriate, typically semi-solid, medium. During incubation in specific conditions, microbial colonies should grow, and the amount of growth depends on the starting amount of cells. If you're interested in estimating incubation time, feel free to take a look at our cell doubling time calculator.

However, it is not guaranteed that a single colony grows from a single cell. Thus, for practical reasons, the amount of microbes is expressed in colony forming units (CFU), defined as a single propagule that can produce an isolated colony. Thus, to answer the question "How to calculate log reduction in microbiology?", one should count the average number of CFU visible after the incubation of both the control and the treated samples. Please note, that control samples are considered to contain a number of microorganisms before disinfectant is used.

## Log Reduction Formula

This log reduction calculator uses the following formula to determine log reduction:

`log reduction = log10(initial CFU/final CFU)`

To translate calculated log reductions to percentage values, we utilised this equation:

`percentage reduction = 100 * (initial CFU - final CFU)/initial CFU`

These values are directly connected with each other as they basically express same thing on a different scale. Table below shows how the subsequent log reduction values corresponds with percentages and absolute numbers:

Percentage reduction CFU
0 log reduction 0% 1 x 106
1 log reduction 90% 1 x 105
2 log reduction 99% 1 x 104
3 log reduction 99.9% 1 x 103
4 log reduction 99.99% 1 x 102
5 log reduction 99.999% 10

Once you have collect your results the usage of this log reduction calculator is simple. Provide the number of `Initial CFU` - it is multiplied by 107 by default but feel free to change this multiplier. Then input your `Final CFU` (pay attention this value is often in a different order of magnitude. 105 is set as the default as typically there is a significantly fewer number of CFU after treatment - of course you can change it to fit your needs). When you inputs your values into the calculator the log reduction and percentage values will appear in the appropriate fields.

By the way, this works bi-directionally and you can simply fill log reduction and either of initial or final CFU to calculate the other values!

Przemek Trzepiński
Initial CFU amount
x10⁷
CFU
Final CFU amount
x10⁵
CFU
Log reduction
Perecentage reduction
%
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