SOLVETUTORMATH SOLVER

Instrument MI-04-052 · Health

BAC Calculator (Blood Alcohol Content)

Drinks, body weight, sex and hours elapsed go in; an estimated blood alcohol reading comes out — the same Widmark arithmetic forensic toxicologists have used since 1932.

Instrument MI-04-052
Sheet 1 OF 1
Rev A
Verified
Type 04 — Alcohol SER. 2026-04052

Estimated BAC (%)

0.0472

BAC = alcohol_g ⁄ (weight_g × r) × 100 − 0.015 × hours (Widmark)

The working Every figure verified twice
  1. bacOut = max(0, 3·14 ⁄ (80·1000·0.68)·100 − 0.015·(7200 ⁄ 3600)) = 0.0472
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

Blood alcohol content is the concentration of alcohol in a person's bloodstream, given as a percentage: a reading of 0.08 means eight-hundredths of a gram of alcohol per hundred millilitres of blood. The estimate this instrument produces traces back to Erik Widmark, a Swedish physician who in 1932 published the distribution model still cited in forensic toxicology textbooks today, after measuring how ingested ethanol spreads through body water in his subjects.

Widmark's insight was that alcohol dissolves almost entirely in water, not fat, so a given dose reaches a higher concentration in a body with less water relative to its weight. He folded that into a single distribution ratio, r — set here at 0.68 for the male option and 0.55 for the female one — then subtracted a steady clearance rate of roughly 0.015 percent per hour, the average pace at which a liver removes alcohol once absorption has finished.

None of this is a measurement of what is actually in your blood right now. It is an arithmetic model built from population averages, and every average hides a spread: genetics, medication, illness and simple differences between livers all shift the true clearance rate up or down. Roadside and courtroom use of Widmark's method has always paired it with an actual breath or blood sample; the equation alone estimates, it does not confirm.

BAC=alcoholgweightg×r×1000.015×hours\mathrm{BAC} = \frac{\text{alcohol}_g}{\text{weight}_g \times r} \times 100 - 0.015 \times \text{hours}alcoholg=drinks×grams per drink\text{alcohol}_g = \text{drinks} \times \text{grams per drink}
alcohol_g is total grams of alcohol consumed (drinks multiplied by grams per drink); weight_g is body weight converted to grams; r is the Widmark distribution ratio, 0.68 or 0.55 depending on the Sex setting; hours is elapsed time since the first drink; the result is floored at zero rather than allowed to go negative.
  • Enter Standard drinks consumed — the counter defaults to 3 for a quick reference point.
  • Check Alcohol per drink (g); 14 grams is the US standard-drink figure, but adjust it for stronger pours or other countries.
  • Set Body weight in kilograms, pounds or stone.
  • Choose Sex, Male or Female, which sets the Widmark distribution ratio the formula uses.
  • Enter Hours since first drink, then read Estimated BAC (%) — the working underneath shows every term.

Worked example — three drinks, 80 kg, two hours

Three standard drinks at 14 grams each total 42 grams of alcohol. For an 80 kilogram man, r is 0.68, so the pre-clearance reading is 42 divided by 80,000 times 0.68, times 100, which comes to 0.0772 percent — a substantial figure from three drinks in a body that size.

Two hours have passed since the first drink, so the equation subtracts 0.015 times 2, or 0.03, leaving an estimated BAC of 0.0472 percent. That lands under the 0.08 percent limit used for driving in most US states, but the same three drinks taken by a lighter or female drinker, or finished faster, would land higher — this is one reading on a curve, not a fixed verdict for 'three drinks'.

Questions

How accurate is a Widmark-based BAC estimate?

It is a population-average estimate, not a lab result. Actual breath or blood tests commonly diverge from the calculated figure by a wide margin, because drinking pace, stomach contents, hydration and individual liver enzyme activity all shift the true concentration in ways the arithmetic cannot see.

Why does changing Sex change the answer?

It changes the distribution ratio, r, used in the formula — 0.68 for the male setting and 0.55 for the female one. Alcohol spreads through body water, and at equal weight, women's bodies average a higher proportion of fat to water, so the same dose distributes into a smaller volume and reads a higher concentration.

Why is my actual test result different from this figure?

This formula assumes drinking has stopped and clearance is already underway at a fixed average pace. A real breath or blood test captures whatever is happening at that exact moment, including alcohol still being absorbed, food slowing that absorption, and a metabolism that may run faster or slower than the average this equation assumes.

Does the calculator know whether I ate beforehand?

No. Widmark's equation treats absorption as already complete and clearance as already begun at a constant rate; it has no field for food. Eating before or during drinking slows and lowers the true peak concentration, so a fasted reading and a fed reading from identical drinks can differ noticeably from what this estimate shows.

Can this figure tell me whether it's safe to drive?

No — treat it strictly as an educational estimate. Legal limits, personal tolerance and actual impairment do not track a single calculated decimal, and the only reliable way to know a real blood alcohol reading is a calibrated breath or blood test administered by trained personnel.

What counts as one 'standard drink'?

In the United States it's 14 grams of pure alcohol — about a 12-ounce beer near 5 percent, a 5-ounce glass of wine near 12 percent, or a 1.5-ounce shot of 40 percent spirits. Other countries define a standard drink at different gram weights, so adjust Alcohol per drink (g) if you're calculating outside the US.

References

Read this first: This instrument computes a screening figure from population formulas — it is not a diagnosis, and it cannot see the whole picture a clinician can. Use it to inform a conversation, not to replace one.