What does the Widmark formula assume?
It assumes the subject is post-absorptive, that ethanol distributes instantaneously and uniformly through body water, that elimination is a straight line, and that a single distribution factor describes the individual. None of those hold exactly, which is why forensic guidance requires the result to be reported as a range.
The Formula, And What Each Term Hides
Widmark relates blood alcohol concentration to the mass of ethanol consumed, body mass, and a distribution factor commonly written as r, with elimination subtracted over elapsed time. Written out it looks like a closed calculation. In practice each term carries an assumption that has to be stated before the number means anything.
- Ethanol dose: derived from beverage volume and alcohol concentration. It depends on what was actually poured, not on what a menu says a serving contains.
- Volume of distribution (r): not a measured property of the subject. It is a population value standing in for body composition, and it varies substantially between individuals of the same weight and sex.
- Elimination rate: treated as linear, when elimination is a saturable enzymatic process that only approximates a straight line across the middle of the range.
- Elapsed time: only meaningful if the subject was post-absorptive throughout. If absorption was still under way, the model is being applied outside its stated conditions.
Why A Single r Value Is Indefensible On Cross Examination
A point estimate presents a population average as though it were a measurement of the individual. It is not, and the witness cannot say it is. Asked how the value was determined for this subject, there is no answer available other than that it was taken from a table.
ANSI/ASB Best Practice Recommendation 122 addresses this directly by specifying ranges rather than single values: fixed volume of distribution by sex, a sex independent range, and individualized approaches based on total body water. A calculation that reports one number has discarded the variance the standard exists to preserve, and it has done so silently.
The same reasoning applies to elimination. ASB 122 sets a minimum elimination range of 0.010 to 0.025 g/dL per hour, and it specifically addresses the practice of deriving a rate from two test results and substituting it for that range. See the ASB 122 conformance mapping for the clause-level detail.
Where The Formula Fails Outright
- During absorption: the model describes a post-absorptive subject. Applied to a rising concentration it does not merely lose precision, it answers a different question.
- At low concentrations: the linear elimination assumption degrades as concentration approaches the saturable region of the curve.
- Across long extrapolation intervals: uncertainty in the elimination rate compounds with elapsed time, so a wide interval produces a range too broad to support a conclusion.
- On converted specimens: serum or plasma results require conversion before the formula applies at all, and the conversion is itself a range.
What To Do Instead
Run the calculation across the ranges the standard specifies and report the interval, not a value. Where the interval is too wide to support the conclusion being asked for, that width is the finding. DUI Professional models the calculation this way by default and carries the assumption set into the report, so the basis for each bound is visible without the analyst reconstructing it from memory.
For a simplified interactive version of the arithmetic itself, see the Widmark equation calculator. For the wider timeline treatment, see absorption and elimination and retrograde extrapolation.
DUI Professional does not determine guilt, impairment, admissibility, or the legal sufficiency of evidence. It provides structured blood alcohol calculation and report support for qualified professional review.
Frequently Asked Questions
Is the Widmark formula still accepted in forensic work?
Yes, as a calculation method. What has changed is the reporting requirement: current forensic guidance expects the inputs to be applied as ranges and the result to be reported as an interval rather than a single value.
What is the r value in the Widmark formula?
It is the volume of distribution, a factor describing how ethanol distributes through body water. It is a population-derived value rather than a measurement of the individual, which is why it is specified as a range.
Can the Widmark formula be used during absorption?
No. The model assumes a post-absorptive subject. ASB 122 prohibits retrograde extrapolation from an absorptive phase concentration, and a forward estimate made during absorption carries the same defect.
What is the difference between the Widmark formula and the calculator page?
This page covers the assumptions, ranges, and failure modes. The calculator page provides a simplified interactive estimate for illustration.
Report the range, not the number
Use DUI Professional to run Widmark across the ASB 122 ranges and produce a report that documents every assumption behind each bound.
Sources
These references support the scientific and forensic context discussed on this page.
- ANSI/ASB Best Practice Recommendation 122, First Edition 2024 Current forensic alcohol calculation guidance for assumption-based alcohol calculations, reporting, specimen considerations, and limitations.
- NIST OSAC Standards Library entry for ANSI/ASB BPR 122-24 Registry context for ANSI/ASB Best Practice Recommendation 122-24.
- UKIAFT Alcohol Calculation Guidelines v4.4 Alcohol calculation guidance for total body water, elimination ranges, low-BAC caution, and clear reporting of assumptions.
- Jones, A.W., Evidence-based survey of ethanol elimination rates, 2010 Forensic context for ethanol elimination-rate variation and retrograde extrapolation review.
- Watson, Watson, and Batt, Total body water volumes, 1980 Anthropometric equations for estimating total body water from age, height, weight, and sex-specific calculation basis.
- Maskell et al., Total body water in forensic blood-alcohol calculations, 2020 Forensic comparison of total-body-water approaches and volume-of-distribution approaches for blood-alcohol calculations.
