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Pasteurisation F-Value Calculator

Pasteurisation F-Value Calculator

Time-temperature equivalence using Bigelow's z-value model

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Convert between time and temperature to find equivalent pasteurisation processes, and read the P* pasteurisation value, using Bigelow's z-value model. Useful for comparing processes, judging temperature deviations, and checking whether an equivalent time–temperature combination meets the standard.
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The Formula

The fundamental relationship for thermal equivalence is Bigelow's first-order log-linear inactivation model. For a given microorganism, the time required to achieve equivalent lethality at two different temperatures is:

t2 = t1 × 10(T1 − T2)/z t = exposure time at temperature T (s) · z = temperature change for 10× rate change (°C)

The z-value is the temperature change that alters the thermal death time by a factor of ten. Three different z-values appear in milk pasteurisation, and they answer different questions:

  • z = 8 °C — the P* pasteurisation index. The recognised basis for judging whether an alternative time–temperature combination is equivalent to the standard. A hold of 15 s at 72 °C is one unit (P* = 1); a compliant process must reach P* ≥ 1.
  • z ≈ 4.3–4.4 °C — Coxiella burnetii thermal death. This is why the two statutory anchors line up: 72 °C/15 s and 63 °C/30 min deliver the same C. burnetii lethality. It explains the historical calibration, but it is not the value used to assess compliance.
  • z ≈ 5 °C — alkaline phosphatase inactivation, the basis of the confirmatory phosphatase test.

Important: the law itself does not specify a z-value. Retained Regulation (EC) No 853/2004 defines pasteurisation as at least 72 °C for 15 s, at least 63 °C for 30 min, or any equivalent combination, such that the milk gives a negative alkaline phosphatase test immediately afterwards (for cows' milk, ≤ 350 mU/L by ISO 11816-1). The z-values above are engineering tools for comparing processes, not statutory constants.

Worked Example

Problem: A dairy operates HTST pasteurisation at 72°C for 15 seconds (the UK statutory minimum). For an audit, the QA manager needs to demonstrate this delivers equivalent lethality to a batch pasteuriser running at 63°C. How long must the batch process run?

Step 1. Apply Bigelow's formula with the C. burnetii z = 4.34 °C: t2 = 15 × 10(72−63)/4.34
Step 2. Calculate the exponent: (72-63)/4.34 = 9/4.34 = 2.074
Step 3. 102.074 = 118.5. So t2 = 15 × 118.5 = 1,777 seconds = 29.6 minutes.
Conclusion: 30 minutes at 63°C delivers equivalent C. burnetii lethality to 15 seconds at 72°C — which is why both appear in the regulations as accepted minimum processes. Note: this uses z = 4.34 °C (the C. burnetii basis). To test whether a different combination is compliant, use the P* index (z = 8 °C) in the calculator below — under P*, 63 °C/30 min is in fact far more severe than 72 °C/15 s (P* ≈ 9 vs 1).
Need help applying this calculation to your specific plant or process?

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Frequently Asked Questions

What is the z-value for milk pasteurisation?

There isn't a single one. The law (retained Regulation (EC) No 853/2004) does not specify a z-value at all — it defines pasteurisation by time and temperature (72 °C/15 s, 63 °C/30 min, or equivalent) plus a negative phosphatase test. In engineering practice three z-values are used: 8 °C for the P* equivalence index (the recognised basis for judging alternative processes), ~4.3 °C for Coxiella burnetii death (which explains why 72/15 and 63/30 match, after Enright et al., 1957), and ~5 °C for alkaline phosphatase.

Why is 72°C/15s equivalent to 63°C/30 min?

Because both were calibrated to kill Coxiella burnetii, the most heat-resistant non-spore-forming pathogen in milk. Using Bigelow's model with the C. burnetii z of about 4.3 °C, 15 seconds at 72 °C works out to roughly 30 minutes at 63 °C, and the regulations list both as accepted minimum processes. Note this equivalence is specific to that z; judged by the P* index (z = 8 °C), 63 °C/30 min is actually the more severe process.

What does UK law actually require for pasteurisation?

Retained Regulation (EC) No 853/2004 (Annex III, Section IX) requires milk to be pasteurised by at least 72 °C for 15 s, at least 63 °C for 30 min, or any equivalent combination, such that it gives a negative alkaline phosphatase test immediately afterwards — for cows' milk, an activity of ≤ 350 mU/L by ISO 11816-1. Cream and high-sugar or high-viscosity products need more than the milk minimum (cream at least 75 °C/15 s). Always confirm the current wording of the regulation that applies to you.

Can I use this for sterilisation (UHT) calculations?

The same model applies but with different z-values. For sterilisation targeting Clostridium botulinum spores, z is typically 10°C. F0 values for UHT are calculated at the reference 121.1°C. The principles are identical.

Need expert support on pasteurisation f-value? Watson Dairy Consulting provides independent support including process design, plant audit, and troubleshooting. Contact Watson Dairy Consulting.

References & Further Reading

  1. Bigelow, W. D. (1921). "The logarithmic nature of thermal death time curves." Journal of Infectious Diseases, 29(5), 528-536.
  2. Enright, J. B., Sadler, W. W., & Thomas, R. C. (1957). "Pasteurisation of milk containing the organism of Q fever." American Journal of Public Health, 47(6), 695-700.
  3. UK Statutory Instruments: The Food Safety and Hygiene (England) Regulations 2013, Schedule 6 Heat Treatments.
  4. Codex Alimentarius: CAC/RCP 57-2004 Code of Hygienic Practice for Milk and Milk Products.
  5. Lewis, M., & Heppell, N. (2000). Continuous Thermal Processing of Foods. Aspen.
  6. Regulation (EC) No 853/2004 (retained in UK law), Annex III, Section IX — pasteurisation time–temperature and alkaline phosphatase requirements.
  7. Tamime, A. Y. (ed.) (2018). Handbook of Dairy Technology — P* pasteurisation index (15 s at 72 °C = 1 unit, z = 8 °C).
  8. ISO 11816-1 / IDF 155-1 — determination of alkaline phosphatase activity in milk (reference method).

Further reading: John Watson publishes articles on dairy industry topics on LinkedIn. Browse all articles by John Watson on LinkedIn →

Disclaimer: This calculator and the calculations on this page are provided for educational and indicative purposes only. Real plant performance depends on many factors not captured by simple models. Always verify against your specific plant data, ingredient specifications, regulatory requirements and safety procedures. Watson Dairy Consulting accepts no liability for production, regulatory, safety or commercial decisions made on the basis of this calculator alone. For project-specific support, please contact Watson Dairy Consulting.

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