The Widmark Blood Alcohol Estimate, Explained
After reading this you will understand how a Widmark blood alcohol estimate is built from drinks, body weight and time, why the number carries a wide error bar, and why it can never tell you that you are safe to drive.
What the estimate does
The Widmark equation turns a count of drinks into an estimated blood alcohol concentration (BAC), expressed as a percentage by mass. A BAC of 0.05% means roughly 0.5 grams of alcohol per litre of blood.
Here is the shape of the problem. A 75 kg man drinks three standard drinks of 10 grams each. Two hours later, the estimate puts his BAC near 0.03%. Change the person to a 60 kg woman with the same three drinks and the estimate jumps to about 0.055%. Same alcohol, very different number, because body water differs.
The estimate answers two questions: what is your BAC now, and how many hours until it falls below a given limit. Both answers are approximations built on population averages.
When it is useful, and when it is not
Use this to build intuition. It shows you how quickly BAC rises with each extra drink, how much slower a heavier person's number climbs, and how flat the decline is once drinking stops. Those relationships are stable and worth knowing.
Do not use it to decide whether to drive, operate machinery, or take any action where a real BAC matters. The formula ignores food in your stomach, the speed you drank, your liver enzymes, medication and the fact that alcohol is still being absorbed for the first 30 to 90 minutes. Real measured BAC can differ from the estimate by 0.02 to 0.04 percentage points in either direction.
If you drank, do not drive. A calculator that says 0.04% can be hiding a true value of 0.07%. The safe decision does not depend on the estimate.
The formula and the intuition behind it
Widmark's model treats alcohol as if it dissolves evenly through the water in your body, then leaves at a steady rate.
The symbols mean:
- A
- Total alcohol consumed, in grams. Three 10 gram drinks give
30grams. - W
- Body weight in grams. A 75 kg person is
75000grams. - r
- The Widmark factor, the fraction of your body that behaves like water for alcohol. About
0.68for men and0.55for women, because women carry a higher fraction of fat, which holds little alcohol. - \beta
- The elimination rate, about
0.015percentage points of BAC removed per hour. Roughly one standard drink per hour for many adults. - t
- Hours since the first drink.
The first term is peak BAC if all the alcohol were absorbed instantly. Dividing by W \times r spreads the alcohol through your body water: more water means more dilution and a lower number. The second term subtracts steady elimination. Because \beta is constant, the decline is a straight line, not a curve. That is the model's single most useful fact: your body clears alcohol at a fixed pace, and drinking water or coffee does not speed it up.
A worked example with the demo numbers
75 kg man, three drinks, two hours
- Total alcohol:
3 × 10 = 30grams. - Body water term:
75000 × 0.68 = 51000grams. - Peak concentration before elimination:
30 / 51000 = 0.000588, which is0.0588%by mass. - Elimination over two hours:
0.015 × 2 = 0.030percentage points. - Estimated BAC now:
0.0588 - 0.030 = 0.0288%, round to0.029%.
To find hours until sober, set BAC to zero and solve for time: 0.0588 / 0.015 = 3.9 hours from the first drink. To reach a 0.05% limit, solve (0.0588 - 0.05) / 0.015 = 0.59 hours, so about 35 minutes after the first drink. That short window is why a legal-looking dinner can still leave you over a limit.
The model assumes all 30 grams are already in your blood at hour zero. In reality absorption takes time, so your true early BAC is lower and your true peak comes later, often around 45 to 90 minutes after you finish.
Reading the decay chart
The chart below traces the demo man's estimated BAC from the first drink until he returns to zero. The line is straight because elimination is constant at 0.015% per hour.
Two features matter. First, the slope never changes: nothing you eat or drink bends this line. Second, the starting height, peak BAC, is set entirely by drinks, weight and the r factor. Add one more 10 gram drink and the peak rises by 10 / 51000 = 0.0196%, pushing the sober time out by about 0.0196 / 0.015 = 1.3 hours.
How weight and sex reshape the number
Because BAC divides by W \times r, both weight and sex move the peak sharply. The table shows peak BAC for the same three 10 gram drinks across four people, before any elimination.
| Person | Weight (kg) | r | Peak BAC (%) |
|---|---|---|---|
| Man | 90 | 0.68 | 0.049 |
| Man | 75 | 0.68 | 0.0588 |
| Woman | 75 | 0.55 | 0.0727 |
| Woman | 60 | 0.55 | 0.0909 |
The lightest woman reaches nearly double the peak of the heaviest man on identical drinks. The widget below lets you move these inputs and watch the whole line shift.
Common mistakes
The errors below inflate confidence in a number that deserves none.
- Assuming a "standard drink" is standard. A UK unit is 8 grams, the common European definition is 10 grams, a US drink is 14 grams. A pint of strong craft beer can hold three US drinks. Counting glasses, not grams, is the most frequent error.
- Treating time from the first drink as time since finishing. The formula subtracts elimination from hour zero, but absorption is still climbing early. Your real peak may arrive after you thought you were declining.
- Believing you can lower BAC faster. Coffee, water, exercise and cold air do not change \beta. Only time removes alcohol.
- Reading the estimate as your true BAC. Individual r values range from about 0.60 to 0.75 in men and 0.49 to 0.62 in women. That spread alone shifts the answer by 15 to 20 percent.
Related tools
If you are working through other everyday health numbers, two nearby tools use the same honest, formula-first approach. The Dose & Rate Converter handles mg/kg doses and mg to mL volumes, which share the same body-weight scaling idea you saw with W here. The Pregnancy Due Date Calculator estimates a due date from a last period, conception or IVF transfer.
Frequently asked questions
How accurate is a Widmark BAC estimate?
Treat it as a range, not a point. Because the r factor and elimination rate vary between people, and because food and timing shift absorption, a real breath or blood test can differ from the estimate by roughly 0.02 to 0.04 percentage points. That is enough to cross a legal limit.
Why does the same drink affect women more?
The r factor is lower for women, about 0.55 against 0.68, because a higher fraction of body mass is fat, which holds little water. Less water means less dilution, so the same grams of alcohol produce a higher concentration. In the table above, a 75 kg woman peaks at 0.073% while a 75 kg man peaks at 0.059%.
How long until I am sober?
Divide your peak BAC by 0.015 to get hours from the first drink. A peak of 0.0588% clears in about 3.9 hours. This is an average; some people clear closer to 0.010% per hour, which would stretch the same case to 5.9 hours.
Does eating before drinking change my BAC?
Food slows absorption, so it lowers and delays your peak, but it does not remove alcohol. Your total exposure over time is similar; the curve is just flatter. The Widmark model does not include food, so it tends to overstate early BAC for someone who ate a full meal.
Can I use this to decide whether to drive?
No. The estimate is educational only, and its error bar is wider than the gap between many legal limits. If you drank, do not drive.
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