To calculate bac the way forensic science has done it for ninety years, you need four things: the alcohol in grams, your weight, a factor called r, and a clock. This guide shows how to calculate bac with nothing hidden — every multiplication printed — through three full cases, including a man and a woman who drink exactly the same drinks and land in different legal worlds. The formula is Erik Widmark’s, from the early 1930s; the arithmetic is yours to check with a pencil.

The bac formula, in grams

The bac formula in its original form:

BAC% = A ÷ (W × r) × 100 − β × t

A is pure alcohol consumed, in grams — one standard drink is 14 g. W is body weight, in grams. r is the distribution factor: alcohol dissolves in body water, not fat, and r is the water share of body weight — 0.68 for men, 0.55 for women in Widmark’s fitting. β is the elimination rate, about 0.015 per hour, and t is hours since the first drink. Units check: grams of alcohol spread through (grams of body × water share) gives a concentration; × 100 states it as the familiar percent. Anyone learning how to calculate blood alcohol level is learning this one line and the honesty notes at the end of this guide.

Case one: the same-drinks pair

Four standard drinks each, over two hours. A = 4 × 14 = 56 g for both.

Same drinks, same hours, and her estimate is nearly double his — because the alcohol is identical while the water it dissolves in is not: 34,927 g against 55,520 g. This pair is the single most instructive computation in the whole subject: it is why “we had the same” is not a defence, a comfort, or a fact about BAC. To calculate blood alcohol level honestly you must run your own row of this table, with your own weight and your own r.

Case two: five drinks, three hours, 190 lb man

A = 5 × 14 = 70 g. W = 86,183 g; body water = × 0.68 = 58,604 g. Peak = 70 ÷ 58,604 × 100 = 0.119%. Elimination = 0.015 × 3 = 0.045. BAC = 0.119% − 0.045 = 0.074%. Notice what the third hour bought: without it the reading would be 0.089%; time is the only ingredient in the formula that ever subtracts.

Case three: two drinks, half an hour, 120 lb woman

A = 28 g. W = 54,431 g; body water = × 0.55 = 29,937 g. Peak = 28 ÷ 29,937 × 100 = 0.094%. Elimination = 0.015 × 0.5 = 0.0075. BAC = 0.086% — over the 0.08% per se limit, on two standard drinks, inside half an hour, in a small body. Small denominators are the whole story of this case, and of a great many real ones.

The imperial twin — and why your calculator disagrees slightly

American practice usually runs the same bac calculation formula in ounces and pounds: BAC% = (A_oz × 5.14) ÷ (W_lb × r) − 0.015 × H, with A_oz at 0.6 fl oz per standard drink and the forensic r pair 0.73 (men) / 0.66 (women). That is the version the hub calculator runs. On case one’s pair it returns 0.064% and 0.104% — a few thousandths under the grams form, because the higher r pair assumes a slightly wetter average body. Neither is “the true one”: they are the same equation fitted to different reference populations, and the distance between them is a useful, honest picture of how wide any estimate’s error band runs. When you calculate my bac searches promise a single exact figure, that band is what they are not showing you.

The formula’s terms are people-shaped

Every symbol hides a body. A is only as good as your drink count — and the standard-drink guide in this series shows how real pours quietly double it. r is an average water share; a lean athlete and a sedentary person of the same sex and weight do not share it. β ranges 0.010–0.025 across measured people, and the formula cannot know yours. t assumes the drinks spread across it, while a fast hour front-loads the peak. The equation is exact; its inputs are estimates. That is not a reason to distrust the method — it is the method’s own finding, printed in its terms, and it is why its output frames decisions about understanding an evening, never about driving after one: the only safe BAC for driving is 0.00.

Widmark himself: where the constants came from

Erik Mikael P. Widmark (1889–1945) was a Swedish pharmacologist who spent the 1920s doing something nobody had done carefully: giving known doses of alcohol to subjects and measuring, hour by hour, what appeared in their blood. His 1932 monograph set out the framework this guide uses — the distribution factor r, fitted from those experiments (his subjects’ body water is the ancestor of every 0.68 and 0.55 printed since), and the constant elimination rate β, which his curves showed falling in a straight line rather than a curve. Courts adopted the method because it could run in both directions: forward, from drinks to BAC, and backward, from a measured BAC to an earlier one. Nearly a century of forensic practice has refined the inputs — the Watson body-water equations of 1980 let modern practitioners estimate r from age, height and build rather than sex alone — but the equation on this page is recognisably the one Widmark published.

Case four: running the formula backwards

Forensic practice more often runs the equation in reverse. A driver is tested at a station some time after the stop; the legal question is the BAC at the wheel. On the falling limb, the reconstruction adds back what the liver removed in between: BAC_then = BAC_now + β × Δt. Worked: a test reads 0.050% at 1:30 a.m.; the driving was two hours earlier. At the average rate, BAC_then = 0.050 + (0.015 × 2) = 0.080%. But β is a range, and the honest reconstruction is a range: at 0.010/hr it returns 0.070%, at 0.025/hr, 0.100%. Courts hear both ends of that band argued, which is exactly what an estimate with unknown inputs deserves. The backward use also carries a condition the forward use hides: it is only valid once absorption is complete. Run it while the driver was still absorbing and the arithmetic invents a peak that never happened.

The error band, priced on case one

Return to the woman of case one — 140 lb, four drinks, two hours — and vary only the assumptions, holding her evening fixed:

One woman, one evening, and defensible estimates from 0.104% to 0.140% — every one of them over the 0.08% line, but spread across a band wide enough to matter in a courtroom or a conscience. That band is not sloppiness; it is the true information content of the inputs any calculator is given. A result quoted to three decimals (0.104%) describes the arithmetic, not the woman. Read every BAC estimate — this guide’s included — as the centre of a band at least this wide, and the formula becomes what Widmark built it to be: a disciplined way to reason about alcohol in a body, with its uncertainty printed in its own terms.

Check yourself: three verifications

The method is only learned when the pencil moves. Three cases, answers computed by the same steps — cover the right-hand column and run them.

The second row is the one to sit with: a large body, a long evening, five full drinks — and the estimate lands exactly on the 0.08% line, 0.080%, before the error band of the previous section is even applied. “Big and slow about it” is a description of a drinking pattern, not a protection the formula recognises. If your pencil disagreed with any row, the likeliest culprits are the two this guide keeps flagging: a weight converted carelessly, or an r taken from the wrong column.

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