What blood alcohol concentration actually measures
Blood alcohol concentration is a mass-per-volume figure: grams of ethanol in every 100 millilitres of blood. A BAC of 0.08% means 0.08 g of ethanol per 100 mL, which is 80 mg/dL — the unit a hospital laboratory reports. Europe and most of the Commonwealth quote the same quantity as 0.8 g/L. All three describe one number.
Two facts about ethanol make the arithmetic tractable. First, ethanol is completely miscible with water and effectively insoluble in fat, so it distributes only into the body's water. Second, above a very low threshold the liver clears it at a constant rate rather than a constant fraction — the enzyme alcohol dehydrogenase is saturated, so you burn off roughly the same number of grams per hour whether your BAC is 0.05% or 0.20%. That is why sobering up is a straight line on a graph and not a decay curve, and why nothing you do speeds it up.
Those two facts are the whole of Widmark's model. Divide the dose by the space it dissolves into, then subtract a fixed amount per hour.
How the Widmark equation is built
Erik Widmark published the equation in 1932 after measuring ethanol distribution in human volunteers. It has three parts.
The dose, A. You never drink grams of ethanol; you drink millilitres of a beverage at a stated strength. Multiply the liquid volume by the ABV fraction to get millilitres of pure ethanol, then by 0.789 g/mL — ethanol's density at room temperature — to get grams. A 12 fl oz (354.9 mL) beer at 5% carries 354.9 × 0.05 × 0.789 = 14.0 g. That is not a coincidence: the US standard drink is defined as 14 g of pure ethanol, and a 12 oz 5% beer, a 5 oz 12% wine and a 1.5 oz 40% spirit each land on it.
The distribution space, m·r. Ethanol dissolves in body water, so the concentration depends on how much water you carry, not how much you weigh. The factor r converts total body mass into an equivalent alcohol-distribution mass. Widmark's original figures were 0.68 for men and 0.55 for women — the difference reflects average body-composition differences, since fat holds almost no water. A leaner person of the same weight has a higher effective r and therefore a lower BAC from the same drinks.
The burn-off, β·t. Multiply the hourly elimination rate by hours elapsed and subtract. The forensic default of 0.015 %/h corresponds to clearing roughly one standard drink per hour for a person of average size. Reported individual rates run from about 0.010 to 0.025 %/h, with habitual heavy drinkers at the fast end because of enzyme induction.
Note what the equation contains no term for: how fast you drank, whether you ate, what you drank, your age, or your tolerance. Widmark deliberately produced the simplest model that fit his data, and the price of that simplicity is that it front-loads the entire dose at time zero.
Worked example: four beers, 180 lb, two hours
A 180 lb man drinks four 12 fl oz beers at 5% ABV. Two hours have passed since the first one.
- Convert the drink volume. 12 fl oz × 29.5735 mL/fl oz = 354.88 mL.
- Find the ethanol in one drink. 354.88 × 0.05 = 17.74 mL of pure ethanol. × 0.789 g/mL = 14.00 g.
- Total the dose. A = 4 × 14.00 = 56.00 g, which is 56 ÷ 14 = 4.00 US standard drinks.
- Convert body mass to grams. 180 lb × 0.45359237 = 81.647 kg = 81,647 g.
- Find the distribution space. m·r = 81,647 × 0.68 = 55,520 g.
- Divide and scale to percent. C₀ = (56.00 × 100) ÷ 55,520 = 0.1009%. That is the modelled peak.
- Subtract the burn-off. β·t = 0.015 × 2 = 0.030. BAC = 0.1009 − 0.030 = 0.0709%.
Two follow-on numbers fall straight out. Time from the first drink until the model crosses 0.08%: (0.1009 − 0.08) ÷ 0.015 = 1.39 hours, so about 1 h 23 min. Time from now to zero: 0.0709 ÷ 0.015 = 4.73 hours. Four beers on a weekday evening put this man over the US limit for roughly the first hour and a half, and leave measurable alcohol in his blood until nearly 3 a.m.
How to read the number you get
Treat the output as the centre of a wide distribution, not as a reading. Validation studies of Widmark-type estimates routinely find individual errors of a few hundredths of a percent in both directions — which matters enormously when the threshold that ends a driving licence is itself 0.08.
The legal thresholds are what most people are looking for. In every US state the per se limit for drivers aged 21 and over is 0.08% BAC, except Utah, which moved to 0.05% in 2018. Commercial drivers are held to 0.04% federally, and every state operates a zero-tolerance rule for drivers under 21, typically 0.00% or 0.02%. Most of continental Europe uses 0.05%, and several countries use 0.02% for new drivers. Set the limit field to whichever applies to you.
The physiological landmarks are broader. Impairment of divided attention and reaction time is measurable well below 0.05%. By 0.15% most people show clear ataxia and vomiting risk. Above roughly 0.30% the picture is stupor with a real risk of losing airway protection, and the range above 0.40% overlaps the concentrations reported in fatal poisonings. These bands are population descriptions; a tolerant drinker can look composed at a concentration that would render a naïve drinker unconscious, which is a tolerance of behaviour, not of respiratory depression.
The one figure to distrust most is time to zero. It assumes your elimination rate equals the value in the β field for the whole night. If your true rate is 0.012 rather than 0.015, a predicted 5-hour clearance actually takes 6 hours 15 minutes. Morning-after arrests happen in exactly that gap.
Estimated peak BAC by body weight and number of standard drinks
| Body weight | 1 drink | 2 drinks | 3 drinks | 4 drinks | 5 drinks |
|---|---|---|---|---|---|
| 120 lb (54.4 kg) | 0.038 | 0.076 | 0.113 | 0.151 | 0.189 |
| 140 lb (63.5 kg) | 0.032 | 0.065 | 0.097 | 0.130 | 0.162 |
| 160 lb (72.6 kg) | 0.028 | 0.057 | 0.085 | 0.113 | 0.142 |
| 180 lb (81.6 kg) | 0.025 | 0.050 | 0.076 | 0.101 | 0.126 |
| 200 lb (90.7 kg) | 0.023 | 0.045 | 0.068 | 0.091 | 0.113 |
| 220 lb (99.8 kg) | 0.021 | 0.041 | 0.062 | 0.082 | 0.103 |
| 240 lb (108.9 kg) | 0.019 | 0.038 | 0.057 | 0.076 | 0.095 |
Every cell is 4.539 × drinks ÷ weight in pounds, which is the Widmark equation with A = 14n grams and r = 0.68 rewritten in imperial units.
This calculator cannot tell you it is safe to drive
The Widmark equation was built to reconstruct a past BAC from a measured one in forensic casework, not to forecast a future BAC from a description of a night out. It has no term for absorption rate, food, carbonation, drinking pace, medication, illness or measurement error, and each of those can move a real result by more than the gap between 0.05% and 0.08%.
Impairment also begins below every legal limit. A number under 0.08% is not a finding that you are unimpaired; it is an estimate that you might not be arrested. If you have been drinking, do not drive.
Where Widmark estimates go wrong
- Assuming instant absorption. The model puts every gram in your blood at time zero. In reality peak BAC arrives some time after the last drink, so the model overstates BAC early in a session and can understate it just after the last round.
- Ignoring food. A meal slows gastric emptying, flattens the absorption curve and lowers the true peak substantially. Widmark has no term for it.
- Using total body weight for someone with high or low body fat. The r factor is a population average. Fat holds almost no water, so at the same weight a more muscular person has a larger distribution space and a lower BAC.
- Guessing the pour. A home-poured spirit is frequently well over the nominal 1.5 fl oz, and craft beers at 7–9% ABV carry half again as much ethanol as a 5% lager of the same size.
- Extrapolating time to zero. Elimination rate is the single most variable parameter in the model. Treat the hours-to-zero figure as a lower bound and add a safety margin.
- Applying it to someone with liver disease or on interacting drugs. Elimination can be markedly slower, and the linear model no longer describes the tail at very low concentrations, where kinetics turn first-order.
Refinements, alternatives and related calculations
Several later models replace Widmark's fixed r with an estimate of total body water. Watson's equations predict body water from height, weight, age and sex; Forrest and Seidl published population distributions for r itself. These reduce the scatter in forensic back-calculation but need more inputs and do not change the structure of the equation — dose divided by space, minus burn-off. If you want to reason about body composition first, work through the lean body mass calculator, since lean mass is where nearly all your body water lives.
For counting what you actually drank rather than modelling what it did, the standard drink and alcohol units calculator converts any container size and ABV into US standard drinks or UK units. For the other common bar-and-kitchen pharmacokinetics question, the caffeine half-life calculator uses first-order decay, which is the shape ethanol would follow if the liver were not saturated.
In a clinical setting, ethanol shows up indirectly: it is an osmotically active small molecule, so a raised osmolal gap is a classic clue to alcohol ingestion, and the serum osmolality calculator includes an ethanol term. In acute intoxication the numbers that actually drive management are haemodynamic and respiratory rather than the BAC itself — see the mean arterial pressure calculator for the perfusion target used at the bedside.
Finally, remember what a breathalyser measures. Evidential breath instruments report breath alcohol concentration and convert it to a blood equivalent using an assumed blood:breath partition ratio, generally 2100:1 in the United States. That assumed ratio is itself a population average, and it is the single most litigated number in drink-driving defence work.
Key terms
- BAC
- Blood alcohol concentration, grams of ethanol per 100 mL of blood, written as a percentage. 0.08% = 80 mg/dL = 0.8 g/L.
- Widmark factor r
- The fraction of body mass that behaves as alcohol-distribution space. Classically 0.68 for men and 0.55 for women.
- Zero-order elimination
- Clearance at a constant amount per unit time rather than a constant fraction. Above roughly 0.02% BAC, ethanol metabolism is zero-order because alcohol dehydrogenase is saturated.
- US standard drink
- 14 grams of pure ethanol — about 12 fl oz of 5% beer, 5 fl oz of 12% wine, or 1.5 fl oz of 40% spirit.
- Per se limit
- A BAC above which driving is an offence regardless of observed impairment. 0.08% in most US states.
- Blood:breath ratio
- The assumed factor, usually 2100:1 in the US, by which a breath instrument converts measured breath alcohol into a reported blood concentration.