The Widmark formula estimates blood alcohol concentration from four inputs: the grams of pure alcohol you drank, your body weight, a distribution factor based on biological sex, and the hours since your first drink. It gives you a rough number, not a laboratory measurement. Individual variation in metabolism, stomach contents, medications, and body composition can push your actual BAC 20% or more above or below the figure the equation produces, so no formula-based estimate should decide whether you are safe to drive.
The Equation and Its Inputs
Written out, the formula is:
BAC = (A ÷ (W × r)) × 100 − (β × t)
Each letter stands for a specific input.1National Library of Medicine (PMC). Alcohol Calculations and Their Uncertainty
- A is the total grams of pure alcohol you consumed.
- W is your body weight in grams.
- r is the Widmark distribution factor, which reflects how alcohol spreads through your body’s water. The standard values are 0.68 for biological males and 0.55 for biological females.
- β (beta) is the rate your liver clears alcohol from your bloodstream, expressed as a BAC reduction per hour. The commonly cited average is 0.015 per hour.
- t is the hours from your first drink to the moment you want the estimate for.
The first half of the equation calculates what your BAC would be if every gram of alcohol were absorbed instantly and nothing had been metabolized. The second half subtracts what your liver has processed since you started drinking. If the result is negative, the math is saying your body has, in theory, eliminated everything you consumed.
The distribution factor exists because alcohol dissolves in water and not fat. People with less body water relative to their weight reach a higher concentration from the same drink, which is why the male and female defaults differ. Those fixed values work well enough for most adults but drift at the extremes of body composition, and dehydration, malnutrition, and kidney issues can shift total body water enough to throw off the result.2Washington State Patrol. Widmark’s Equation
The elimination rate deserves similar caution. The 0.015 per hour average is convenient, but the forensic range runs from 0.010 to 0.025 g/dL per hour across the population.3Texas District and County Attorneys Association. ANSI/ASB Best Practice Recommendation 122 – Best Practice Recommendation for Performing Alcohol Calculations in Forensic Toxicology Chronic heavy drinkers tend to clear alcohol faster because their livers produce more of the enzyme that breaks it down; occasional drinkers tend to sit closer to the low end. Three hours of elimination at 0.010 looks very different from three hours at 0.025.
Converting Drinks to Grams of Alcohol
The equation needs A as a mass in grams, not a count of drinks. A standard drink in the United States contains about 14 grams of ethanol, which corresponds to 12 ounces of regular beer at 5% ABV, 5 ounces of wine at 12% ABV, or 1.5 ounces of 80-proof liquor at 40% ABV.4Centers for Disease Control and Prevention. Alcohol and Public Health – About Standard Drink Sizes Three standard drinks is 42 grams.
For anything that doesn’t match the standard template, calculate directly: multiply the volume in fluid ounces by the ABV expressed as a decimal, then multiply by 23.34. That constant combines the conversion from fluid ounces to milliliters with the density of ethanol, about 0.789 grams per milliliter.5PubChem. Ethanol – Chemical and Physical Properties A 9-ounce pour of wine at 14% ABV is 9 × 0.14 × 23.34 = 29.4 grams, more than double a standard drink. For cocktails, add up each spirit’s contribution separately.
A Worked Example
A 180-pound man drinks three 12-ounce beers at 5% ABV over three hours.
Grams of alcohol: 3 × 14 = 42 grams.
Body weight in grams: 180 × 453.6 = 81,648 grams.
Pre-metabolism BAC: (42 ÷ (81,648 × 0.68)) × 100 = (42 ÷ 55,521) × 100 = 0.0756.
Metabolism offset at the average rate: 0.015 × 3 = 0.045.
Estimated BAC: 0.0756 − 0.045 = 0.031%. Well below the 0.08% adult limit.
Now change one assumption. If this person’s actual elimination rate were 0.010 instead of 0.015, the estimate becomes 0.0756 − 0.030 = 0.046%. Same drinks, same time, half again as high. And if the drinks weren’t really standard beers, the whole picture shifts.
When Standard-Drink Assumptions Break Down
A huge share of what people actually drink falls outside the 12-ounce, 5% beer template. A typical craft IPA runs 7% ABV, and many double IPAs and imperial stouts sit between 9% and 10%. A 16-ounce pint of a 7% IPA holds roughly 26 grams of alcohol, nearly double the 14 in a standard beer.
Rerun the same example with three 16-ounce pints at 7% ABV. Total alcohol climbs from 42 grams to about 78. Pre-metabolism BAC: (78 ÷ 55,521) × 100 = 0.140. After three hours at the average elimination rate: 0.140 − 0.045 = 0.095%. The same 180-pound man, drinking what he still thinks of as “three beers” over three hours, is now over the legal limit.
Wine pours create the same problem. Restaurant and home pours routinely run past 5 ounces, and many red wines sit at 14% to 15% ABV rather than the 12% baked into the standard-drink definition. A 7-ounce glass at 15% carries about 24.5 grams of alcohol versus 20 grams at 12%, which is enough to move a Widmark estimate noticeably. When the ABV matters, check the label and measure the pour.
Why the Estimate Can Be Significantly Off
The formula treats absorption as instantaneous and complete, which is never actually true. Alcohol enters the bloodstream over anywhere from 20 minutes on an empty stomach to several hours after a large meal, because food holds alcohol in the stomach longer, where it absorbs more slowly than in the small intestine.6Alcoholism: Clinical and Experimental Research. Effect of Food on the Pharmacokinetics of Alcohol Absorption Someone still absorbing can have a rising BAC at the exact moment the equation says it should be dropping.
Medications and medical conditions extend the problem. GLP-1 receptor agonists like semaglutide (Ozempic, Wegovy) and tirzepatide (Mounjaro) delay stomach emptying enough to stretch alcohol absorption well past the two-hour window the formula implicitly assumes.7National Library of Medicine (PMC). Extended Absorption, Implications – Rethinking Alcohol Pharmacokinetics in Forensic Calculations Gastroparesis and gastroesophageal reflux can do the same. A drink finished three hours ago may still be moving into the bloodstream.
Body composition also matters past the basic r value. Two people of the same weight with different body fat percentages produce different BACs from the same drinks, and the default 0.68 or 0.55 doesn’t capture that without an individualized adjustment most people will never calculate. Dehydration from exercise or heat concentrates alcohol in a smaller volume of body water than the formula assumes. Forensic experts typically cite a margin of error of ±20% or more for any Widmark-based estimate, which is why the number is useful as a guide and not a verdict.
Legal BAC Thresholds the Estimate Is Measured Against
Federal law requires every state to treat 0.08% BAC or higher as a per se impaired-driving offense for adult drivers of personal vehicles, with federal highway funding on the line for states that don’t comply.8Office of the Law Revision Counsel. 23 USC 163 – Safety Incentives to Prevent Operation of Motor Vehicles by Intoxicated Persons Two lower thresholds catch people who think they are clear of the main limit.
- Commercial drivers face a 0.04% BAC threshold. A first offense disqualifies the holder from a commercial driver’s license for a year, and a second offense is a lifetime disqualification.9eCFR. 49 CFR 383.51 – Disqualification of Drivers
- Drivers under 21 face a zero-tolerance threshold of 0.02%, which federal law also conditions on highway funding and which every state and the District of Columbia enforces.10Office of the Law Revision Counsel. 23 USC 161 – Operation of Motor Vehicles by Intoxicated Minors
The 0.031% that the worked example produced is comfortably under 0.08% but well over the 0.02% zero-tolerance line for anyone under 21, and uncomfortably close to the 0.04% commercial limit once you account for the possibility that this person’s real elimination rate is slower than 0.015.
Impairment Below the Legal Limit
A number under 0.08% isn’t the same as safe to drive. The National Highway Traffic Safety Administration documents measurable effects well below the legal threshold:11National Highway Traffic Safety Administration. Drunk Driving – Statistics and Resources
- At 0.02%: some loss of judgment and a decline in the ability to track moving objects or divide attention.
- At 0.05%: reduced coordination, difficulty steering, and slower response to emergencies.
- At 0.08%: poor muscle coordination affecting balance, speech, and reaction time, with noticeable drops in concentration and short-term memory.
- At 0.10%: clear deterioration in reaction time and in the ability to hold a lane and brake appropriately.
- At 0.15%: substantial loss of vehicle control and of the ability to process visual and auditory information.
A Widmark estimate of 0.05% might look legally fine, but the research shows real impairment is already underway. The equation gives you a number. It doesn’t tell you whether you should be driving, and given the error margins baked into every one of its inputs, it was never built to.