Estimating Blood Alcohol Content: How the Widmark BAC Formula Works

Every number you see for blood alcohol content (BAC) on a calculator comes from a single 1932 equation. Erik Widmark, a Swedish physician, worked out that the alcohol in your blood is roughly the amount you drank divided by the part of your body that holds water, minus whatever your liver has already cleared. Pharmacology courses still teach his model first, because it is simple enough to do by hand and honest about what it cannot know.

I want to walk through that math, show you one worked example, and then be very direct about its limits. A BAC estimate is a teaching figure. It is not a breathalyser, and it is never a reason to get behind the wheel.

The Widmark formula, in plain terms

The formula needs three things: how many grams of pure alcohol you drank, how much of your body is water, and how much time has passed.

Pure alcohol is the starting point. A drink is a volume times an alcohol-by-volume percentage, and ethanol weighs about 0.789 grams per millilitre. So a 350 ml beer at 5% ABV is 350 × 0.05 × 0.789, or roughly 13.8 grams of ethanol.

Body water is the denominator. Alcohol distributes into water, not fat, so Widmark uses a distribution ratio he called r: about 0.68 for men and 0.55 for women. You multiply your body weight in grams by r to get the effective body water the alcohol spreads through. A heavier person, or a person with a higher r, dilutes the same alcohol into more water and lands at a lower concentration.

Time is the subtraction. Your liver clears alcohol at a fairly steady pace, modelled as a flat 0.015 percent per hour. After three hours, the formula simply removes 0.045 from the peak.

Put together, BAC as a percentage is:

(grams of alcohol ÷ (body weight in grams × r)) × 100 − (0.015 × hours)

That is the whole engine behind the BAC calculator. The grams of ethanol, the r division, and the per-hour subtraction are the only moving parts.

A worked example: two drinks, 70 kg man, one hour

Let me run a concrete case so the numbers stop being abstract.

A 70 kg man has two standard beers — say two 350 ml cans at 5% ABV — over one hour.

Each beer is 350 × 0.05 × 0.789 ≈ 13.8 g of ethanol. Two of them is about 27.6 g.
His body water is 70,000 g × 0.68 = 47,600 g.
Peak BAC before metabolism: (27.6 ÷ 47,600) × 100 ≈ 0.058%.
Subtract one hour of clearing: 0.058 − 0.015 = 0.043%.

So roughly 0.043% after an hour, drifting back toward zero at 0.015 per hour, which puts him near 0.000 about three hours later. Now hold the drinks fixed and imagine a 55 kg woman: her denominator is 55,000 × 0.55 = 30,250 g, and her peak jumps to about 0.091% — more than half again as high from the identical two beers. That single swap is the clearest argument against matching anyone drink for drink.

Why weight, sex, and time pull the number around

Three levers move every BAC estimate, and the worked example shows each one.

Body weight sets the size of the water pool. Double the weight and you roughly halve the concentration, because the same alcohol spreads through twice the water. This is why a small person feels two drinks far more sharply than a large one.

Sex enters through r. The 0.55-versus-0.68 gap reflects a population average: women tend to carry a smaller share of body water relative to mass. It is a statistical ratio, not a fixed fact about any one person, and it is one of the reasons two people with identical inputs can still test very differently.

Time is the only lever working in your favour. At 0.015 per hour, a peak of 0.06 takes four hours to clear on paper. There is no shortcut — coffee, a cold shower, and fresh air change how you feel, not how fast your liver works.

What the 0.08 limit actually means

The calculator lines your estimate up against four real driving thresholds: zero tolerance, 0.02, 0.05, and the US federal 0.08. In the United States, 0.08% BAC is the per-se limit, meaning you are legally over the line at that number regardless of how you feel. Many countries set 0.05, and quite a few use zero tolerance for new or commercial drivers.

Here is the trap. In the worked example the man's estimate sat near 0.043 — comfortably under 0.08 on screen. But the Widmark model assumed every gram of alcohol was already absorbed and distributed, which is rarely true an hour in. Real BAC is often still climbing while the estimate says it is falling. The number under 0.08 on your screen can be over 0.08 in your blood.

The disclaimer that matters more than the math

This is the part I will not soften. A Widmark estimate ignores food in your stomach, how fast you absorbed each drink, hydration, medication, liver health, and your own genetics. Any of those can push your real BAC well above what the tool shows. The "back to 0.000" time is the earliest theoretical clearing under an optimistic flat rate — treat it as the soonest it could be true, never as a green light.

So: never drink and drive. The only safe BAC before driving is zero. If you have been drinking, wait, call a taxi, or arrange a ride. Use this calculator to understand alcohol metabolism, to teach the Widmark formula, or to settle a curiosity about how quickly an evening adds up — not to decide whether you are okay to drive. You are not, and no estimate can tell you otherwise.

There is one harmless extra use. Alcohol carries about 7 kcal per gram, and the tool already computes your ethanol grams. If you track intake, multiply that figure by seven and feed your day into the calorie calculator to see how a couple of drinks reshape an energy budget. That is the kind of question a BAC estimate can honestly answer.

Made by Toolora · Updated 2026-06-13