# Help for lethal rate calculator

How does the calculator work? The calculator converts temperature readings to lethal rates, plots the lethal rates against time, and determines the F values for the overall heat-process. The area under the curve is determined using the Trapezoid rule and the calculator is capable of giving accurate F determinations for most thermal processes. In general the more values, and the smaller the time interval between the values, the more accurate the value for F will be.

Lethal rate is calculated using the formula, lethal rate= 10 ^{(T-Tr/Z)} where T is the temperature, in Celsius, at which the lethal rate is required and Tr is the reference temperature.

Tr will vary on whether Fo is being calculated or whether a pasteurisation process or other heat treatment is being assessed. A Tr of 121.1° C is used in the determination of Fo. If F_{70} or other F value is required then Tr must be set to 70° C or other temperature.

The Z-value, is measured in °C, and is the reciprocal of the slope of the thermal death curve for the target microorganism or spore; 10° C is the value frequently used in Fo calculations performed on low acid foods. **Note this calculator uses a default value of 10°C for Z.** The Z-value has a significant effect on the F value of a process. The effect of the Z-value can be seen in the free lethal rate tables that can be downloaded from here.

Tr can be varied by the user. If you need to use a different Z-value then try the other calculator.

## Using the calculator

Reference temperature should be set first. Next the data grid for entering data is produced.

The starting time e.g. 2 minutes from the beginning of heating and the final time e.g. 180 minutes from the start of heating should be set. The time interval between the temperature readings (∆t) must also be set e.g. 2 minutes. Once this information has been set, the user should press the “New data grid” button to create a data entry table. Temperature values are entered using the edit control.

The application can be tested using internal test data. This data when used with the set values should give a Fo value of 8.43. You may also change the Tr values once the data has been loaded and use the “Recalculate button” to investigate the effects of changing these variables on the F values generated by your dataset.

## Uploading a csv file

Instead of creating a new data grid to enter time and temperature data you can upload a text file containing your data and the application will determine the F value. If you want to use a different Tr value you should set the Tr-value after you have uploaded the data and then use the Recalculate button to determine the F value. The data must be submitted as a comma separated value (CSV) text file. Use a '.' and not a ‘,’ as the decimal separator. The file must have the extension “.csv”.

A csv file looks like:

Time, Temperature

2,90.2

4,100.9

6,112.45

8,115.9

9,101.6

10,95

16,93

and can be generated using a spreadsheet programme, if you do not want to prepare the data manually. While a csv file will enable users to use actual values, and will work with uneven time intervals, the use of uneven time (t) intervals is not recommended; keep the ∆t constant! Numerical integration (this is what we are actually doing) using the Trapezoid rule gives more accurate results when even time intervals are used.

Note. When a .csv file is imported the data in the table and on the chart will change to reflect the new values entered. Once this data has been entered you can vary the Tr and z-values and use the recalculate button to calculate a new F value.

The number of log cycles that a designated microbial population has been reduced can be calculated by dividing the F value by the D value at Tr. A 12 log cycle reduction is required for spores of *Clostridium botulinum* in 'commercially sterile' low acid canned foods.

Please post any queries in the forum.

You can also download Excel spreadsheets to calculate F values.

Return to lethal rate calculator

See survivor probability calculator

**How to cite this article**

Mullan, W.M.A. (2008).
[On-line]. Available from: __https://www.dairyscience.info/index.php/technology/276-lethal-rate-help.html .__ Accessed: 22 February, 2017.
Updated 2010, 2015.