An auditor at a fish cannery in Morocco is reading a heat penetration record for a large catering can of mackerel in tomato sauce. The cold spot never rose above 116 Β°C, yet the run is recorded as delivering an F0 above 7 minutes, the scheduled process asks for 6, and the botulinum cook is quoted as only 3. How can a can that never reached 121.1 Β°C be commercially sterile, and why are there three different numbers for one product? The answers come from the D value, z value and F value, three linked numbers every thermal processor should be able to calculate by hand.
In short
- The D value is the time at a stated temperature needed to reduce a microbial population by 90%, one log10 unit.
- The z value is the temperature change that changes D tenfold; z = 10 Β°C is the reference value for Clostridium botulinum spores.
- The F value converts any time-temperature history into equivalent minutes at a reference temperature; F0 uses 121.1 Β°C and z = 10 Β°C.
- The 12D botulinum cook needs F0 = 12 Γ 0.21 min β 2.5 min, rounded up to a minimum of about 3 min; most commercial processes deliver more to control spoilage spores.
- Lethality rises exponentially with temperature, so minutes near 121.1 Β°C count far more than minutes 10 to 20 Β°C below it.
What is a D value?
The D value, or decimal reduction time, is the time at a constant stated temperature needed to kill 90% of a population of a specific microorganism, a one-log10 reduction. It is always quoted with its temperature, as in D121.1 or D70, and holds only for the organism, strain and food in which it was measured.
At a fixed lethal temperature, many microbial populations die approximately log-linearly, with the same fraction dying in each equal time interval. Plot log10 survivors against time and D is the negative reciprocal of the slope.
t = D Γ (log N0 β log N)
N0 is the starting count and N the count after time t, both usually in CFU (colony-forming units, the viable cells that grow into colonies on a plate) per gram or millilitre. Spores are far more heat resistant than vegetative cells. Water activity (aw), a measure of how much water in a food is available to microorganisms, matters too: low aw and high fat protect cells, so literature D values are a starting point, not a substitute for data in your product.
Worked example
A laboratory heats a suspension of a spore-forming spoilage organism at 112 Β°C and counts survivors: 6.2, 5.0, 3.8 and 2.6 log10 CFU/mL at 0, 3, 6 and 9 min.
Slope = (2.6 β 6.2) Γ· 9 = β0.4 log per minute, so D112 = 1 Γ· 0.4 = 2.5 min.
A 5-log reduction at 112 Β°C would need 5 Γ 2.5 = 12.5 min at the slowest-heating point.
Real survivor curves often show a shoulder or a tail. Non-linear models such as the Weibull model then fit better, and extrapolating a straight line far beyond the measured data, as a 12D calculation does, calls for conservative assumptions.
What is a z value?
The z value is the number of degrees Celsius by which temperature must rise to reduce the D value tenfold. It measures how sensitive an organism, or a quality attribute, is to a change in temperature.
z = (T2 β T1) Γ· (log D1 β log D2)
Worked example
The same laboratory repeats the test at 118 Β°C and finds D118 = 0.63 min.
z = (118 β 112) Γ· (log 2.5 β log 0.63) = 6 Γ· (0.398 β (β0.201)) = 6 Γ· 0.599 β 10.0 Β°C.
Every 10 Β°C rise therefore makes this spore population die ten times faster.
| Target | Typical D | Typical z | Why it matters |
|---|---|---|---|
| Clostridium botulinum spores (proteolytic) | D121.1 β 0.21 min (reference value) | 10 Β°C | Basis of the botulinum cook for low-acid canned foods |
| Thermophilic spoilage spores, such as Geobacillus stearothermophilus | Several minutes at 121.1 Β°C | About 10 Β°C | Need much higher F0 where cans cool slowly or are stored hot |
| Listeria monocytogenes (vegetative cells) | D70 about 0.3 min (implied by 6 log in 2 min at 70 Β°C) | About 7.5 Β°C | Reference organism for cooked chilled foods |
| Colour, flavour, texture, vitamins | Not usually expressed as D | Often 25 to 50 Β°C | Explains why HTST and UHT processes protect quality |
The contrast in z values is the scientific basis of high-temperature short-time (HTST) processing. A 10 Β°C rise multiplies the kill rate of spores with z = 10 Β°C by 10, but speeds a quality reaction with z = 30 Β°C by only about 2.2 times, so hotter, shorter processes reach the same lethality with less cooking damage.
What is an F value, and how is F0 defined?
The F value is the total lethality of a heat process, expressed as the equivalent number of minutes at a reference temperature for a stated z value. F0 is the case used for low-acid canned foods: reference temperature 121.1 Β°C (250 Β°F) and z = 10 Β°C.
Each minute at temperature T is converted to equivalent minutes at the reference temperature by the lethal rate, L. With readings taken at equal intervals Ξt, F is the sum of the lethal rates multiplied by the interval:
L = 10^((T β Tref) Γ· z) and F = Ξt Γ Ξ£L
| Temperature (Β°C) | Lethal rate L (Tref 121.1 Β°C, z 10 Β°C) | Minutes needed to equal 1 min at 121.1 Β°C |
|---|---|---|
| 100 | 0.008 | 129 |
| 105 | 0.025 | 41 |
| 110 | 0.078 | 13 |
| 111.1 | 0.100 | 10 |
| 115 | 0.245 | 4.1 |
| 118 | 0.490 | 2.0 |
| 121.1 | 1.000 | 1.0 |
| 125 | 2.455 | 0.4 |
F values can be compared only when they share the same reference temperature and z. Pasteurisation uses lower references: for cooked chilled foods a common choice is 70 Β°C with z = 7.5 Β°C, aimed at Listeria monocytogenes.
How is the 12D botulinum cook calculated?
The 12D botulinum cook is a heat process that would reduce the most heat-resistant spores of proteolytic Clostridium botulinum by 12 log10 units. With the classic reference value D121.1 = 0.21 min, it needs F0 = 12 Γ 0.21 = 2.52 min, which is rounded up to a minimum F0 of about 3 min.
It applies to low-acid foods, those with pH above 4.6 and water activity above 0.85, packed in hermetically sealed containers and stored at ambient temperature. The assumptions are worth stating: log-linear death, z = 10 Β°C, a reference D value for the most resistant strains, and a notional starting load of one spore per container. Twelve log reductions from one spore leave a probability of one survivor in 10ΒΉΒ² containers. Acid foods with pH 4.6 or below do not need a botulinum cook, because the organism cannot grow and produce toxin in them.
The botulinum cook is a safety floor, not a typical process. Many scheduled processes deliver more to control spoilage spore-formers that are more heat resistant than C. botulinum. If a spoilage organism with D121.1 = 1.0 min must receive a 5-log reduction, F0 must be at least 5 Γ 1.0 = 5 min, and that larger requirement sets the process.
How do you calculate F0 from heat penetration data?
Convert each cold-spot temperature reading to a lethal rate, add them up and multiply by the logging interval. This numerical integration is called the general method, and it is the usual way to calculate the F0 that a run actually delivered. The cold spot is the slowest-heating point in the container, found by heat penetration tests with thermocouples.
| Time (min) | Cold-spot temperature (Β°C) | Lethal rate L |
|---|---|---|
| 0 | 40 | 0.000 |
| 5 | 68 | 0.000 |
| 10 | 90 | 0.001 |
| 15 | 102 | 0.012 |
| 20 | 109 | 0.062 |
| 25 | 113 | 0.155 |
| 30 | 115 | 0.245 |
| 35 | 116 | 0.309 |
| 40 | 116 | 0.309 |
| 45 | 116 | 0.309 |
| 50 | 108 | 0.049 |
| 55 | 95 | 0.002 |
| 60 | 72 | 0.000 |
Worked example
Sum of L = 1.453. F0 = Ξt Γ Ξ£L = 5 min Γ 1.453 β 7.3 min.
The can never reached 121.1 Β°C, yet it received lethality equivalent to 7.3 min at that temperature: well above the botulinum minimum of about 3 min and above the 6 min the scheduled process requires.
The first 20 minutes, with the cold spot below 110 Β°C, added less than 0.4 min. The three readings at 116 Β°C added about 4.6 min.
So the auditor’s three numbers do not conflict: 3 min is the safety floor, 6 min is the scheduled process for this product, and 7.3 min is what this run delivered. Real studies log at least every minute across several containers; five-minute steps keep this table short. A process is validated for one product, container, fill, headspace, initial temperature and retort load, and any change needs re-validation. Heat penetration study design and deviation handling are covered in Food Technology for Industry Professionals.
How are D, z and F values used in pasteurisation?
The same arithmetic sets pasteurisation and cooking processes, using a lower reference temperature and the z value of the target vegetative pathogen. A widely used benchmark for cooked chilled foods is 70 Β°C for 2 min at the slowest-heating point, which gives about a 6-log reduction of Listeria monocytogenes, with z = 7.5 Β°C.
t(T) = t(Tref) Γ 10^((Tref β T) Γ· z)
Worked example
Holding times equivalent to 70 Β°C for 2 min, with z = 7.5 Β°C:
At 72 Β°C: t = 2 Γ 10^(β2 Γ· 7.5) = 2 Γ 0.541 β 1.1 min (about 65 s).
At 75 Β°C: t = 2 Γ 10^(β5 Γ· 7.5) = 2 Γ 0.215 β 0.43 min (about 26 s).
At 65 Β°C: t = 2 Γ 10^(5 Γ· 7.5) = 2 Γ 4.64 β 9.3 min.
At 60 Β°C: t = 2 Γ 10^(10 Γ· 7.5) = 2 Γ 21.5 β 43 min.
These equivalences let a sous-vide producer cook lower and longer for texture, or a high-volume line cook hotter and faster, at the same lethality. Validation must still confirm the slowest-heating point and use a z value measured in a similar food, and critical limits usually sit above the calculated minimum to cover probe accuracy and product variation. The Food Science for Industry Professionals course practises these calculations on cooking and retort records alongside growth modelling and challenge tests.
Frequently asked questions
What is the difference between an F value and F0?
An F value is any lethality expressed as equivalent minutes at a stated reference temperature and z value. F0 is the particular F value used for low-acid canned foods, with a reference temperature of 121.1 Β°C and z = 10 Β°C, chosen to match Clostridium botulinum spores. Always quote the reference temperature and z with an F value, because values calculated on different bases cannot be compared.
Why is the reference temperature 121.1 Β°C?
Thermal process science grew up in the United States canning industry, which worked in degrees Fahrenheit and used 250 Β°F as its reference retort temperature. Converted to Celsius, 250 Β°F is 121.1 Β°C, and the value stayed when the rest of the world adopted the method. Nothing biological happens at exactly 121.1 Β°C; it is a fixed point that lets different processes be compared on one scale.
Is an F0 of 3 minutes enough for every canned food?
No. About 3 min is the minimum botulinum cook for low-acid foods (pH above 4.6, water activity above 0.85). Many products need more to control spoilage spore-formers, especially thermophiles where cans are cooled slowly or stored hot. Acid foods with pH 4.6 or below need much less, because C. botulinum cannot grow in them. Each scheduled process is set by a competent process authority and confirmed by heat penetration studies.
Can I use published D and z values to design my process?
Use them for screening and planning, not as the final basis. D values change with strain, food composition, pH, water activity, fat content and the history of the cells, and published figures may come from buffer or broth rather than your product. Design with conservative literature values, then validate in your own product and container with heat penetration studies and, where needed, inoculated pack or surrogate tests.
Why do z values differ so much between microbes and quality attributes?
Killing spores and vegetative cells depends far more steeply on temperature than most chemical reactions that change colour, flavour or vitamins. Spores typically have z values around 10 Β°C, while many quality attributes have z values of 25 to 50 Β°C. Raising temperature therefore speeds microbial death far more than quality loss, which is why UHT milk, heated to about 135 to 150 Β°C for a few seconds, tastes fresher than in-container sterilised milk.
Next step. Food Science for Industry Professionals teaches D, z and F calculations together with growth kinetics, predictive models, challenge tests and the difference between validation and verification, using calculation sets built on realistic retort and cooking records. It ends with a proctored final assessment and an ASC certificate. To compare levels and topics, see all eleven food science and technology courses.
Sources. Codex Alimentarius Commission, Code of Hygienic Practice for Low-Acid and Acidified Low-Acid Canned Foods, CXC 23-1979 (FAO/WHO); P. J. Fellows, Food Processing Technology: Principles and Practice, 5th edn (Woodhead Publishing, 2022); R. P. Singh and D. R. Heldman, Introduction to Food Engineering, 5th edn (Academic Press, 2014); M. P. Doyle, F. Diez-Gonzalez and C. Hill (eds), Food Microbiology: Fundamentals and Frontiers, 5th edn (ASM Press, 2019); ICMSF, Microorganisms in Foods 7: Microbiological Testing in Food Safety Management, 2nd edn (Springer, 2018).
This article is general guidance and is not a substitute for the applicable standard, your national legislation or the advice of a qualified thermal process specialist or food safety professional.