BAC Calculator

How the Widmark formula turns drinks into a number

Every BAC calculator you have used runs the same equation, published by Erik Widmark in 1932. It treats the body as a container of water, works out how concentrated the alcohol is in that water, and then subtracts what the liver has cleared since the first drink.

BAC = (grams of alcohol x 100) / (body weight in grams x r) - (0.015 x hours)

The top of the fraction is the alcohol you swallowed, converted to grams. The bottom is the water in your body, which is your weight in grams multiplied by a factor r that stands for the share of your body that behaves like water. The last term is the liver, working at a steady rate while the clock runs.

The result is a percentage in the sense used on every police report and every state statute: grams of ethanol per 100 milliliters of blood. A reading of 0.08 means 0.08 grams per deciliter, which is the same as 80 milligrams per deciliter, and that is the number the law cares about in all 50 states.

Weight and the r factor: why two people differ

Weight enters twice, once as pounds converted to grams and once through r. A 180 pound man weighs 81,647 grams, because 180 x 453.592 = 81,647. Multiply by r of 0.68 and his alcohol distributes into about 55,520 grams of body water. That is the denominator the formula uses.

The r factor is not a moral judgement, it is a body composition shortcut. Men carry more water and less fat per pound, so alcohol dilutes into a larger volume and the concentration falls. Women carry more fat per pound and less water, so the same drink lands in a smaller tank. The standard values are 0.68 for men and 0.55 for women, and they come from population averages rather than from you.

The gap between the 180 pound man and the 140 pound woman is 20,593 grams of water, which is 37% less dilution for the woman. That single difference is why the same three drinks can put one person under the limit and the other well over it.

Grams of alcohol, not drinks

A drink is not a unit, which is why the formula works in grams. The National Institute on Alcohol Abuse and Alcoholism defines a US standard drink as about 14 grams of pure alcohol, and its standard drink guide lists what that looks like in a glass.

To get grams from any container, multiply the volume in ounces by the alcohol by volume, convert to milliliters, and multiply by the density of ethanol, which is 0.789 grams per milliliter. A 12 ounce beer at 5% works out as 12 x 0.05 = 0.6 fluid ounces of alcohol, 0.6 x 29.57 = 17.7 milliliters, and 17.7 x 0.789 = 14.0 grams. A 16 ounce craft beer at 7% gives 16 x 0.07 = 1.12 fluid ounces, 1.12 x 29.57 = 33.1 milliliters, and 33.1 x 0.789 = 26.1 grams.

This is where most estimates go wrong. A pint of 7% beer is not one drink, it is nearly two, and a mixed drink poured at home is often three. Count the grams, not the glasses, and the formula has a chance of being close.

Time only moves the number down at a fixed rate

The liver clears alcohol at roughly 0.015 per hour, and that rate does not speed up because you drink water, eat bread or walk around the block. It also does not slow down much when you stop drinking. The clock and the liver are the only two things in the last term of the formula, which is why the clearing time for any level is that level divided by 0.015.

The effects column follows the impairment chart in NHTSA's ABCs of BAC guide, which lists the level at which each effect is usually first observed. Read it as a description of a population, not a promise about any one person.

The practical consequence is that a long night does not end when the glass empties. Someone who finishes their last drink at midnight at an estimated 0.10 is still near 0.08 at 1:20 in the morning, and still above zero until almost 7 in the morning. Sleep is not metabolism, it is just time passing while the liver works.

Worked example: three beers over two hours

Take a 180 pound man who drinks three 12 ounce beers at 5% between 8 and 10 pm, and check the number at 10 pm.

• Alcohol: 3 x 14 = 42 grams
• Body weight: 180 x 453.592 = 81,647 grams
• Water volume: 81,647 x 0.68 = 55,520 grams
• Peak BAC: 4,200 / 55,520 = 0.0756
• Two hours of clearance: 0.015 x 2 = 0.030
• At 10 pm: 0.0756 - 0.030 = 0.0456

That is under the 0.08 limit, and it still means impaired judgement and slower reactions. The same 42 grams in a 140 pound woman gives 63,503 x 0.55 = 34,927 grams of water, so 4,200 / 34,927 = 0.1203 at peak and 0.1203 - 0.030 = 0.0903 at the two hour mark, which is over the limit and takes about 6 hours from the first drink to clear.

Change the pace and the peak moves without changing the total. The same three beers in one hour produce the same peak of 0.0756, but only one hour of clearance, so the reading at the end is 0.0606 rather than 0.0456. Drink them over four hours and the reading falls to 0.0156. Total grams set the height, hours set how far down the line you already are.

What the estimate is good for

The formula is useful for three things: understanding why a smaller person reaches a higher level on the same drinks, planning how long a celebration will run before anyone drives, and checking that a story about being fine after four drinks does not survive arithmetic. It is a teaching tool and a rough planner.

It is not useful for settling an argument about whether you are legal to drive. The estimate can sit 0.02 above or below a measured reading, which is the entire distance between 0.06 and 0.08, and it cannot see the things that matter most in a real stop: how fast you drank, what you ate, what medication you take and how your liver handles ethanol.

NHTSA's own guidance does not ask drivers to estimate. It says that if you plan to drink, you should plan not to drive, pick a sober driver, or use a taxi, a friend or public transit. A calculator that produces a number is not a permission slip, and the one thing it should never do is talk you into the driver's seat.

Why this cannot tell you whether you can drive

Impairment starts well below the legal limit. NHTSA's chart records a decline in visual tracking and in divided attention at 0.02, and reduced coordination and difficulty steering at 0.05. A person at 0.05 is not legal trouble in most states, and is still a worse driver than they were at zero.

Tolerance hides the impairment without removing it. A heavy drinker may feel normal at 0.10 while their reaction time and lane control are measurably worse, which is why officers test driving behavior rather than asking how someone feels. The formula has no term for tolerance at all.

Then there is the arithmetic of the traffic stop. A breath test measures what is in the blood at that moment, and a court reads the number from the instrument, not from a web page. If the reading is 0.08 or higher, the estimate you ran at home is irrelevant. The safe rule is the one NHTSA repeats: if you have been drinking, do not drive, and decide that before the first drink rather than after the last.

Food, medication and what the formula ignores

Food slows absorption, so the peak arrives later and lower than the formula predicts, but the total alcohol still has to be cleared. A meal before drinking buys time, not immunity. Carbonation does the opposite and speeds absorption, which is why a sparkling drink can hit harder than a flat one of the same strength.

Medication is the larger blind spot. Sedatives, antihistamines, sleep aids and pain medication can multiply the impairment of a given BAC without changing the number, and alcohol plus a depressant is a combination that shows up in a disproportionate share of impaired driving crashes. The formula treats all of that as invisible.

Biology adds the rest. Liver enzymes vary between people and between populations, drinking on an empty stomach raises the peak, and a person who drinks daily metabolizes alcohol differently from someone who drinks twice a year. NIAAA's alcohol metabolism overview explains how much of the variation comes from genetics rather than behavior, and it is a useful reminder that a single r value cannot capture a person.

This page is an educational estimate, not medical advice and not a fitness to drive test. For health concerns, talk to a clinician. For anything involving a vehicle, the answer is always the same: do not drive after drinking.