Thermal processing calculator: D-value, z-value, F needed and F0 from a time-temperature profile (general method)

Fit a D-value to survivor counts and a z-value to D-values at several temperatures, work out the F needed for a log reduction, and add up lethal rates over a pasted time-temperature profile to get F0 or any F by the general method. For study. Nothing is uploaded.

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Counts
D and z
Profile
F value

Nothing is uploadedWorks offline once open

Reference

Reference temperature, T_ref (°C) z-value (°C)

F₀ is F with T_ref 121.1 °C and z 10 °C, the usual reference for low-acid canned food. Change them for other organisms or processes (for example pasteurisation).

D-value from survivor counts

Heating time (min) and survivors, one count per line

All counts at one temperature, in any unit (per g, per ml, per can). The D-value is the time for a tenfold (90 %) drop, from a straight line fitted to log₁₀(count) against time.

z-value from D-values

Temperature (°C) and D-value (min), one per line

The z-value is how many °C hotter it takes to make D ten times shorter, from a straight line fitted to log₁₀(D) against temperature.

F needed for a log reduction

D at T_ref (min) Starting count, N₀ Count wanted, N

F = D × (log₁₀ N₀ − log₁₀ N). A count below 1, such as 1e-9, means a chance of one survivor in a billion units. Write powers of ten as 1e-9.

F from a time-temperature profile

Time (min) and the temperature at the slowest-heating point (°C), one reading per line

Lethal rate L = 10^{(T − Tref)/z}: minutes at T_ref worth one minute at T. F adds up L over time with the trapezoid rule (the general method). Readings closer together give a better answer.

Download

For study and checking sums only, not a substitute for a process authority. A commercial heat process must be designed and validated by a qualified process authority and meet the rules where the food is sold; check the official source.

What it does

Heat kills microbes at a steady rate on a log scale: each minute at a fixed temperature removes the same fraction. This calculator does the standard sums of thermal process calculation, for coursework and for checking hand calculations:

D-value: the time for a tenfold (90 %) drop in survivors at one temperature. Paste heating times and survivor counts; the page fits a straight line to log₁₀(count) against time and shows it on a log chart.
z-value: the rise in temperature that makes D ten times shorter. Paste D-values measured at several temperatures; you also get D at the reference temperature.
F needed: the minutes at the reference temperature needed to go from a starting count N₀ to a target N: F = D × (log₁₀ N₀ − log₁₀ N).
F from a profile (general method): paste a time-temperature record from the slowest-heating point of the product. Each reading becomes a lethal rate, L = 10^((T − Tref)/z), and the page adds them up over time with the trapezoid rule. With Tref 121.1 °C and z 10 °C the result is F₀.

How to use it

Set the reference temperature and z at the top. They apply to the profile and to D at Tref.
Paste data in any of the boxes, two numbers per line, from a spreadsheet or a CSV, TXT or Excel file. A header row is fine.
Use this z and D copies the fitted z and the D at Tref into the boxes below, so the profile and the F needed use them.
Download the profile with its lethal rates as CSV, or the report as an image, PDF or Word file.

Worked example

Press Use the example (all values made up). The survivor counts fall from 1,000,000 to 2,000 per gram over 8 minutes: D = 2.96 min (R² 0.9999). The D-values of 20, 6.5, 2 and 0.62 minutes at 110 to 125 °C give z = 9.92 °C, and D at 121.1 °C of 1.55 min.

With D = 1.546 min, going from 1000 to 1e-9 per unit is 12 log reductions, so F = 18.6 min. The pasted heating curve peaks at 121.5 °C after 35 minutes and gives F = 27.4 min at 121.1 °C (z 10 °C), about 17.7 log reductions at that D.

Tips

Take temperatures often (every minute or less) where the product is hot; the trapezoid rule is only as good as the spacing.
Survivor curves with a shoulder or a tail do not follow one straight line; fit only the straight part.
F adds up lethality from heating and cooling, so record the whole cycle.

FAQ

Can I use this to set a canning process? No. It is for study, not a substitute for a process authority. Commercial heat processes must be designed and validated by a qualified process authority and follow the rules where the food is sold.

Why 121.1 °C? It is 250 °F, the traditional reference for sterilising low-acid food.

Is my data uploaded? No. Everything runs in your browser and works offline.

Where the numbers come from

General first-order microbial inactivation formulas: D from the slope of log10 N against time, z from the slope of log10 D against temperature, F = D·(log10 N0 − log10 N), lethal rate L = 10^((T − Tref)/z), and the general method (trapezoid rule). The reference of 121.1 °C and z = 10 °C for F0 is a general textbook convention.
Checked against numpy.polyfit (D, z and R²) and numpy.trapezoid / scipy cumulative_trapezoid (F0, F with other Tref and z, and F partway through) on the example data.
The survivor counts, D-values and heating profile in the example are made up for this tool, not from any study or organism.

Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.

Last updated 2026-11-09.