F0, D-Value and Z-Value: The Arithmetic Behind a Validated Sterilization Cycle

Quick facts

• A D-value is the time, under stated conditions, required to inactivate 90 % of a population of the test microorganisms (ISO 17665:2024, 3.15).
• An Fo value expresses how much lethality a moist heat process actually delivered, stated as the equivalent number of minutes at 121,1 °C with reference to organisms with a z value of 10 °C (ISO 17665:2024, 3.22).
• FBIO describes the indicator (the log to base 10 of its initial population multiplied by its D-value); FBIOLOGICAL describes the process (what the cycle actually killed) — two different quantities that are often used interchangeably (ISO 17665:2024, 3.23 and 3.24).
• Sterility is expressed as a probability, not as a property that can be measured on a single item; that is stated in the introduction to ISO 17665:2024 itself.
• ISO 17665:2024 deliberately does not set a sterility assurance level: designating a device "sterile" is left to national or regional requirements such as EN 556-1 or ANSI/AAMI ST67 (clause 1.2.3).
• In Ontario a biological indicator must be used to test the sterilizer on each day it is used and for each type of cycle used. The weekly cadence familiar from United States material is the CDC and ANSI/AAMI ST79 baseline and is not the Ontario requirement.

Sterility assurance arithmetic is the layer most clinic staff never see. A biological indicator certificate lists a population and a D-value; a sterilizer printout lists time and temperature; a validation report states that a 10⁻⁶ sterility assurance level was demonstrated. Those three things are connected by four short formulas, and understanding them changes how a manager reads a failing result. This article sets out the arithmetic, names the clause each term comes from, and explains why a positive biological indicator is not the same thing as a sterilizer that failed to sterilize.

What does a D-value actually measure?

ISO 17665:2024 defines the D value as the "time or dose required under stated conditions to achieve inactivation of 90 % of a population of the test microorganisms" (3.15). Two notes in that definition matter more than the sentence itself. First, a D-value always refers to the exposure period, not to the total cycle time. Second, the definition assumes that a plot of the log to base 10 of the population against exposure time is a straight line, within accepted tolerances (3.15, Notes 1 and 2).

That straight line is the whole basis of the arithmetic. If a population falls by 90 % for each equal increment of exposure, then the surviving population after an exposure F is:

N = N₀ × 10^(−F / D)

where N₀ is the starting population, D is the D-value, and F is the delivered exposure in the same units. Rearranged, this is the survivorship curve that ISO 11138-1:2017 describes in its normative Annex C, "D value determination by survivor curve method", and it is why the same standard carries a second normative method, Annex D, "D value determination by fraction negative method", for the cases where a countable survivor curve cannot be produced.

Quantity	Symbol	What it belongs to	Where it is defined
Population of test organisms	N₀	The indicator	ISO 11138-1:2017, clause 6.3
D-value	D	The indicator, at a stated temperature	ISO 17665:2024, 3.15
z-value	z	The indicator's temperature sensitivity	ISO 11138-3:2017, Annex B (calculation)
Delivered exposure	F	The process	ISO 17665:2024, clause 8 (process definition)
Fo value	F₀	The process, normalised to 121,1 °C	ISO 17665:2024, 3.22
FBIO value	F_BIO	The indicator's resistance	ISO 17665:2024, 3.23
FBIOLOGICAL value	F_BIOLOGICAL	The process, expressed as observed kill	ISO 17665:2024, 3.24

The z-value is the second half of the arithmetic. In moist heat work it is the change in temperature that multiplies or divides the D-value by ten, and for steam sterilisation the working convention is 10 °C. ISO 11138-3:2017, the part of the indicator series that covers moist heat, carries it as a normative annex named "Calculation of z value and coefficient of determination, r²" — in other words, a z-value purchased off a certificate is itself the output of a regression on measured D-values, and the coefficient of determination is reported alongside it precisely because a fitted line is only as good as its fit.

Once a z-value is fixed, temperature can be converted into equivalent time. A process run at temperature T can be restated as an equivalent number of minutes at 121,1 °C by multiplying each minute by 10^((T − 121,1) / z). That conversion is exactly what the Fo value in ISO 17665:2024, 3.22 formalises: a "measure of microbiological lethality delivered by a moist heat sterilization process expressed in terms of the equivalent time, in minutes, at a temperature of 121,1 °C with reference to microorganisms with a z value of 10 °C".

Temperature	Multiplier per minute (z = 10 °C)	Equivalent minutes at 121,1 °C
115,0 °C	0,25	1 minute = 0,25
118,0 °C	0,49	1 minute = 0,49
121,1 °C	1,00	1 minute = 1,00
124,0 °C	1,95	1 minute = 1,95
127,0 °C	3,89	1 minute = 3,89
130,0 °C	7,76	1 minute = 7,76
134,0 °C	19,50	1 minute = 19,50

The table is arithmetic, not a cycle specification. It shows why the same lethality can be reached by very different combinations of time and temperature, and why a validation report can legitimately quote a single number — the Fo value — for a process that ran at several temperatures. The multipliers are computed from the z-value convention, not taken from any sterilizer manual; the cycle a facility actually runs is the one the sterilizer manufacturer validated.

What is the difference between F0, FBIO and FBIOLOGICAL?

These three symbols are the most frequently confused part of the vocabulary, and ISO 17665:2024 separates them cleanly. The Fo value is a property of the process. The FBIO value is a property of the indicator: "expression of the resistance of a biological indicator calculated as the product of the logarithm to base 10 of the initial population of microorganisms and the D value" (3.23). The FBIOLOGICAL value is the delivered lethality actually observed, "measured in terms of actual kill of microorganisms on or in a biological indicator challenge system" (3.24). The note to 3.24 gives the method: multiply the D-value at 121 °C by the difference between the log to base ten of the starting population and the log to base ten of the population enumerated after processing.

Symbol	Kind of quantity	Formula	Illustration (D₁₂₁ = 2,0 min, N₀ = 1 × 10⁶)
F_BIO	Indicator resistance	F_BIO = log₁₀(N₀) × D	6,0 × 2,0 = 12,0 min
F₀	Process lethality, normalised	F₀ = Σ Δt × 10^((T − 121,1)/10)	a 4,0 min exposure at 133,0 °C ≈ 6,2 min at 121,1 °C
F_BIOLOGICAL	Observed kill	F_BIOLOGICAL = D₁₂₁ × (log₁₀ N_start − log₁₀ N_after)	if the count falls 4 logs, 2,0 × 4 = 8,0 min
Survivors after a given exposure	Predicted survivors	N = N₀ × 10^(−F/D)	F = 12,0 min at D = 2,0 min leaves N₀ × 10⁻⁶

The illustration values are deliberately round: they are chosen so the arithmetic is visible, and they are not a statement about any particular indicator on the market. Different indicator designs carry different populations and different D-values, and the certificate of analysis that ships with a lot is the document that states them. What matters for practice is the direction of the comparison: if the process delivers less lethality than the indicator's F_BIO, the indicator can survive even though the cycle ran its full time — and that gap, not the colour of a chemical indicator, is what a positive biological indicator result is announcing.

How is a 10⁻⁶ sterility assurance level derived from biological indicator data?

The starting point is uncomfortable but explicit. The introduction to ISO 17665:2024 describes inactivation kinetics as an exponential relationship between the number of microorganisms surviving and the extent of treatment, and then draws the conclusion: "inevitably this means that there is always a finite probability that a microorganism can survive regardless of the extent of treatment applied." It continues: "It follows that the sterility of any one product in a population subjected to sterilization processing cannot be ensured and the expression of sterility of a processed population is defined in terms of the probability of there being a viable microorganism present on a product item."

That sentence is the reason a sterility assurance level is a probability and not an assurance of anything about a single instrument. The same standard then deliberately steps back from choosing the number: clause 1.2.3 states that the document "does not detail a specified requirement for designating a medical device as 'sterile'", with a note pointing to EN 556-1 and ANSI/AAMI ST67. Those are the documents in which a 10⁻⁶ level becomes a designation requirement. The practical translation is that a 10⁻⁶ SAL is a design target for a validated process applied to a defined bioburden, not a measurement that a clinic performs on a tray.

The arithmetic that connects a target to a process is short. To reduce a starting population N₀ to a target population N, the required exposure is F = D × (log₁₀ N₀ − log₁₀ N). Substituting the familiar numbers — a bioburden of 10⁶ and a target of 10⁻⁶ — gives a required exposure of 12 D, that is, twelve log reductions. The biological indicator enters the calculation in one of two directions: either it is the surrogate that stands in for the bioburden, in which case the process is established from its survival and kill responses, or the physical parameters of the process are measured and the lethality is calculated from them. ISO 17665:2024 splits those routes into two informative annexes with names that say exactly what they are: Annex B, "Establishment and evaluation of a sterilization process primarily based on microbiological inactivation", and Annex C, "Establishment and evaluation of a sterilization process primarily based on the measurement of physical parameters".

Step	Question answered	The arithmetic
1	How resistant is the challenge organism?	D-value at the reference temperature, from a survivor curve (ISO 11138-1:2017, Annex C) or a fraction-negative series (Annex D)
2	How much resistance does the indicator present?	F_BIO = log₁₀(N₀) × D (ISO 17665:2024, 3.23)
3	How many log reductions are required?	log₁₀(N₀) − log₁₀(target), e.g. 6 − (−6) = 12
4	What exposure does that require?	F = D × (log₁₀ N₀ − log₁₀ N), added to the equilibration and safety margins
5	Did the cycle deliver it?	F₀ from the recorded time–temperature profile, or F_BIOLOGICAL from the observed kill

Step 5 is the only one carried out routinely in a health care facility, and even that is carried out by recording physical parameters and incubating indicators, not by re-deriving the D-value. This arithmetic is validation mathematics. It belongs to the sterilizer manufacturer, the indicator manufacturer and the microbiology laboratory that performed the original qualification; a clinic that tried to establish its own SAL from scratch would be re-validating a device it does not own. What a clinic does own is the monitoring record, and the record is what an assessment asks for.

Why does a positive biological indicator not automatically mean the sterilizer failed?

Because the indicator and the machine are two different hypotheses, and the arithmetic does not distinguish between them. A positive result tells you that the delivered lethality, as experienced by that indicator in that load, was below the indicator's F_BIO. There are several ways to arrive at that number without a mechanical fault: an overloaded chamber, packages too close together, a package too large for steam penetration, the indicator placed where air removal was incomplete, an incubation error, or a control indicator that was mishandled. The College's own guidance is explicit about which explanation is statistically the more likely one, and it is not the machine.

The Royal College of Dental Surgeons of Ontario's guidance on the causes of a positive biological indicator states that "in the event of a positive BI, it must be assumed that the cycle load was not sterilized, and that the sterilizer has malfunctioned, until a full investigation has proven otherwise", and then adds that "the most common cause of a positive BI is operator error". The standard of practice sets out a five-step response: remove the sterilizer from service; review the records of physical and chemical indicators since the last negative biological indicator, looking for operator error such as overloading, insufficient spacing between packages, or oversized packaging; where the cause is identified as operator error, re-test using the same cycle while the sterilizer remains out of service; return the sterilizer to service when the repeat is negative and the physical and chemical indicators are adequate; and, where the repeat is positive or the cause is not identified, keep the sterilizer out of service until it has been serviced and successfully re-challenged with biological indicators in three consecutive cycles.

That sequence is an investigation protocol, not a re-validation. It reconciles cleanly with the arithmetic: a single positive result shifts the probability estimate and triggers quarantine of the affected load, while a pattern of positives — or a positive that survives a controlled repeat — is evidence that the process itself, and not the handling of it, is delivering less than the indicator demands. The United States baseline reaches the same conclusion from the other side: CDC's healthcare disinfection guideline notes that a single positive biological indicator for a non-implant load does not by itself mean the sterilizer is defective, and directs immediate retesting in three consecutive cycles before broader recall. For implant loads, both the Ontario standard and the United States practice require quarantine until the result is known, which removes the judgement call entirely.

Result	What the arithmetic says	What the Ontario standard requires
Negative control, negative test	Delivered lethality exceeded the indicator's F_BIO	Release on the recorded cycle
Positive test, identified operator error	Load was not exposed to the assumed conditions	Sterilizer stays out of service; repeat the same cycle
Positive test, cause not identified	Either the process or the challenge is out of specification	Service the unit; three consecutive negative challenges before return to service
Implant load, result pending	Probability applies to a population, not to one item	Quarantine the load until the result is known

Where do these numbers sit in Canadian dental practice?

Two different things are being regulated, and mixing them is the most common source of confusion in clinic training. Process validation and process monitoring are separate obligations with separate owners.

Question	Ontario	United States comparison
Who establishes the sterilisation process?	The sterilizer manufacturer, against ISO 17665:2024 or the equivalent; the facility follows the validated instructions	Same split; the facility follows the manufacturer's validated cycle
Routine biological monitoring cadence	A BI in a process challenge device on each day the sterilizer is used and for each type of cycle used (RCDSO)	At least weekly, preferably every day in use (CDC; ANSI/AAMI ST79)
Where the two differ	The Ontario cadence is daily. A weekly schedule is not the Ontario requirement; it is the United States comparison baseline	—
Air removal test	At the beginning of each day the dynamic air removal sterilizer is used	Daily, before the first load
Records	Log book retained at least 10 years from the date of the last entry	Retention set by facility policy and local requirements

The reason the cadence is stricter than the arithmetic requires is statistical, not mathematical. A 10⁻⁶ design target protects a population of items; it says nothing about the day a door gasket starts leaking. Frequent monitoring buys detection speed, and ISO 17665:2024 treats that as a separate control — clause 10 covers routine monitoring and control, including process verification (10.3) and record retention (10.6), while clause 12 covers maintaining process effectiveness, including recalibration (12.3), equipment maintenance (12.4), requalification (12.5) and assessment of change (12.6). None of those clauses restates a numerical cadence, because cadence is a jurisdictional decision.

What should a manager check when a certificate of analysis arrives?

Four fields carry the arithmetic, and a certificate that omits any of them cannot be checked against a failed result.

Field on the lot documentation	Why it matters	Where it originates
Population of test organisms	Feeds log₁₀(N₀) in both F_BIO and the required log reduction	ISO 11138-1:2017, clause 6.3
D-value with its stated temperature	The exponent in N = N₀ × 10^(−F/D)	ISO 17665:2024, 3.15
z-value with the coefficient of determination	Converts a temperature deviation into a change in lethality	ISO 11138-3:2017, Annex B
Test organism identity	Determines whether the indicator matches the process	ISO 11138-3:2017, clause 5

ISO 11138-3:2017 requires the test organisms used for moist heat to be spores of Geobacillus stearothermophilus or strains of demonstrated equivalent performance (clause 5.1), and notes that Bacillus stearothermophilus has been reclassified under the Geobacillus genus. The same standard states in its introduction that moist heat is defined for its purposes as dry saturated steam — a definition worth remembering when a facility also runs a low-temperature process, because the indicator that monitors steam and the indicator that monitors a chemical process are not interchangeable, and their certificates are not comparable.

It is also worth knowing what a certificate cannot tell you. It describes an indicator lot manufactured under ISO 11138-1:2017, a third edition that cancels and replaces the 2006 edition. That standard makes the resistance characteristics explicit: indicators "provide resistance characteristics expressed as D values and, where relevant, z values", and it points readers to ISO 14161 for advice on selection, use and interpretation of results. Interpreting a result is therefore a documented discipline in its own right, and the person who signs the deviation should be working from the same definitions the certificate was produced under.

What does an assessor actually ask for?

Rarely the arithmetic. The audit trail is built from the conclusions the arithmetic produces, recorded at the time. In practice the questions reduce to four.

1. Which cycles were run, and what did the physical record show — time, temperature, pressure, and the equilibration between the reference probe and the load?
2. Which biological indicator lot was used, from which certificate, and what was its result?
3. Which chemical indicator class was checked in the load, and does the release decision follow the rule the standard sets out?
4. Where a result was positive, what was the investigation, what was the disposition of the load, and what evidence returned the sterilizer to service?

Each of those answers is a record field rather than a calculation, which is why the arithmetic matters mainly for the person writing the policy. A manager who knows that F_BIO is a property of the indicator and F₀ is a property of the process will not accept a supplier's claim that a cycle "failed" because a single indicator turned positive, and will not accept the opposite claim that a passing indicator proves the load sterile. Both statements are wrong for the same reason: they treat a probability as a certainty.

If the terminology in this article is new to the staff member who reads cycle results, the more useful starting point is a documented monitoring routine rather than a formula. The sterilization monitoring guides on this site cover the indicator classes, the record fields and the frequency rules as they apply in Canadian practice; the arithmetic sits underneath all of them.

Indicators, incubators and readers are consumed by the monitoring routine that sits above this arithmetic: a 24-hour self-contained steam indicator, 25-pack carries its population and resistance data on the lot documentation, and a 4-well fluorescence biological indicator reader takes the visual judgement out of the readout. Facilities that want to see the lot paperwork before committing to a routine can start with a five-pack indicator trial, and multi-chair practices can compare case quantities through the sterilization monitoring range.

Records and templates. The compliance log centre holds the printable records a daily monitoring routine depends on, including a biological indicator log, a cycle record layout and an audit checklist that can be printed and kept with the unit. Download the sterilization log templates.

Check your own cadence. The same centre carries the frequency calendar and the self-check used to confirm that daily monitoring is happening for every sterilizer and every type of cycle, rather than only for the cycle that happens to be printed most often. Run the monitoring self-check.

Have a question about your own facility? Send it in and you will get a written answer specific to your setup, with the regulation or standard it is based on cited. Ask your compliance question.

Reselling or buying for a facility? become a distributor for wholesale and multi-site ordering.

Related reading

• Sterility assurance level 10⁻⁶, log reduction and D-value: what the numbers mean
• The ISO 11138 series, part by part
• ISO 17665:2024 read clause by clause for Canadian clinic practice

Frequently Asked Questions

Is a D-value a fixed property of an organism?

No. A D-value is always stated under stated conditions, which is why certificates pair the figure with a temperature and a medium. ISO 17665:2024 defines it as the time or dose required under stated conditions to achieve inactivation of 90 % of a population of the test microorganisms, and its second note records the assumption that a plot of log to base 10 of population against exposure time is linear within accepted tolerances. Change the temperature and the D-value changes by a factor set by the z-value.

Why is the z-value usually 10 °C for steam?

Because the convention is built into how the reference values are defined. ISO 17665:2024 defines the Fo value as the equivalent time in minutes at a temperature of 121,1 °C with reference to microorganisms with a z value of 10 °C. The convention is what makes lethality comparable between facilities running different time and temperature combinations, and it is why a single F0 figure can describe a cycle that was not held at one steady temperature.

Can a clinic calculate its own sterility assurance level?

The arithmetic is reproducible, but the inputs are not ones a clinic generates. A defensible SAL arithmetic needs a measured bioburden, a D-value determined by survivor curve or fraction negative methods, and a validated process, which is the manufacturer and microbiology laboratory side of the work. What a clinic generates is the monitoring record, and ISO 17665:2024 keeps that separate in clause 10, which covers routine monitoring, process verification and record retention.

Does a passing biological indicator mean a load is sterile?

No. A negative result means the delivered lethality exceeded the resistance of that indicator in that position in that load. Because sterility for a population is expressed as a probability rather than as a property of a single item, a passing test supports a release decision but does not convert a probability into a certainty for any one instrument on the tray.

What is the difference between a weekly and a daily monitoring cadence in Canada?

They belong to different jurisdictions. In Ontario the standard of practice requires a biological indicator in a process challenge device on each day the sterilizer is used and for each type of cycle used. The at least weekly cadence, preferably every day in use, is the United States baseline carried by CDC guidance and ANSI/AAMI ST79, and it is not the Ontario requirement.

Where does the arithmetic appear in a routine audit?

Almost never as a calculation. An assessment asks for the cycle records, the indicator lot and its certificate, the chemical indicator check, the release decision and, where a result was positive, the investigation and the evidence that returned the sterilizer to service. The arithmetic is what makes those records interpretable, which is why it appears in the policy rather than in the daily paperwork.

Do these definitions apply to low-temperature sterilisation as well?

The symbol set does not transfer unmodified. Fo value, holding time and equilibration time in ISO 17665:2024 are moist heat constructs, and the standard states that moist heat means steam processes, including saturated steam and contained product cycles. Low-temperature processes are governed by their own parts of the standards family, and their indicators are qualified against those processes rather than against the steam reference conditions.

Sources

1. ISO 17665:2024, Sterilization of health care products — Moist heat — Requirements for the development, validation and routine control of a sterilization process for medical devices, preview (PDF)
2. ISO 11138-1:2017, Biological indicators — Part 1: General requirements, preview (PDF)
3. ANSI/AAMI/ISO 11138-3:2017, Biological indicators for moist heat sterilization processes, preview (PDF)
4. ISO 14937:2009, General requirements for characterization of a sterilizing agent and the development, validation and routine control of a sterilization process, preview (PDF)
5. RCDSO, Standard of Practice: Infection Prevention and Control in the Dental Office, v3 (PDF)
6. RCDSO, Potential Causes of a Positive Biological Indicator, v3 (PDF)
7. Public Health Ontario, provincial guidance for cleaning, disinfection and sterilization in all health care settings (PDF)
8. CDC, Guideline for Disinfection and Sterilization in Healthcare Facilities, 2008
9. ANSI/AAMI ST79, comprehensive guide to steam sterilization and sterility assurance in health care facilities
10. CSA Group, CAN/CSA-Z314, medical device reprocessing in all health care settings
11. ISO, ISO 17665 catalogue record showing the edition and superseded parts
12. ISO, ISO 11138-3 catalogue record
13. CliniEco Medical, sterilization compliance hub

CliniEco Medical distributes sterilization monitoring consumables for Canadian dental, laboratory and care settings under MDEL #35334.