The back-end calculation in the Widmark Blood Alcohol Content (BAC) formula subtracts 0.015 percentage points for every hour since your first drink, after first building a peak estimate from your drinks, body weight, and sex. The full equation reads BAC% = (standardDrinks × 14 ÷ (r × weightKg × 1000)) × 100 − 0.015 × hours, where r is the Widmark distribution ratio — 0.68 for men and 0.55 for women. The peak portion converts your standard drinks into grams of pure alcohol (one US standard drink contains about 14 g of pure alcohol), divides that mass by the volume of body water available to dilute it, and multiplies by 100 to express the answer as a percentage. The back-end subtraction then models how the liver eliminates alcohol at roughly 0.015 percentage points per hour, and the final number is clamped at zero because BAC cannot fall below nothing. That two-part structure — a dose-versus-body-water peak, minus a time-based elimination tail — is the skeleton of nearly every modern back-of-the-envelope BAC tool, almost a century after the Swedish chemist Erik M. P. Widmark worked out the original relationship between alcohol consumed, body size, and blood alcohol concentration in the 1920s and 1930s.
What the Two Halves of the Widmark Equation Do
The Widmark formula is built in two stages, and the back-end step only makes sense once the peak step has produced a starting number. The peak stage answers "how much alcohol is in your system if none of it has been metabolized yet." The back-end stage answers "how much has your liver already cleared since you took your first drink." Together they produce the single BAC percentage that the calculator reports.
For the peak stage, the calculation converts standard drinks to grams of alcohol, then divides that mass by an estimate of body water. Body water is approximated as your weight in kilograms multiplied by the sex-specific Widmark distribution ratio r — 0.68 for men and 0.55 for women — because men and women carry different average proportions of body water. Dividing grams of alcohol by that body-water volume gives the peak concentration, which is then multiplied by 100 to turn it into a percentage.
For the back-end stage, the formula multiplies 0.015 by the number of hours since the first drink and subtracts that product from the peak. The 0.015 figure is a population-average elimination rate — the amount of BAC the liver is assumed to clear per hour. If the resulting number is negative, the tool clamps it at zero, because a person's BAC cannot mathematically be less than zero percent. Adjusting any single input moves the answer in the direction you would expect: more drinks push it up, a longer wait pulls it down as your body metabolizes the alcohol, a heavier body dilutes the same alcohol across more body water, and switching from the male to the female ratio raises the estimate because women on average carry a smaller proportion of body water.
Inputs the Formula Expects
The back-end calculation needs four pieces of information, and each one moves the answer in a predictable direction.
| Input | Unit or value | Effect on the estimate |
|---|---|---|
| Standard drinks | count (14 g alcohol each) | More drinks raise the peak |
| Body weight | kilograms | Higher weight dilutes the same alcohol across more body water |
| Sex | Male (r = 0.68) or Female (r = 0.55) | Female ratio raises the estimate for the same inputs |
| Hours since first drink | hours | Longer time subtracts more from the peak |
A "standard drink" in the United States contains about 14 grams of pure alcohol, which is roughly a 12 oz beer at 5% alcohol by volume, a 5 oz glass of wine at 12% ABV, or a 1.5 oz shot of 40% spirits. If your drinks were stronger or larger than those benchmarks, count them as more than one standard drink before entering the number. The tool expects kilograms, so if you only know your weight in pounds, divide by 2.2046 to convert before typing it in.
Run the Numbers in the BAC Calculator
The BAC Calculator runs this entire calculation in your browser. Nothing you type is uploaded, so the numbers stay on your device.
- Pick your sex with the Male / Female toggle so the correct Widmark ratio (0.68 for men, 0.55 for women) is used.
- Enter the number of US standard drinks you have had, counting each 12 oz beer at 5%, 5 oz glass of wine at 12%, or 1.5 oz shot of 40% spirits as one drink.
- Enter your body weight in kilograms. If you only know pounds, divide by 2.2046 to convert.
- Enter the hours since your first drink — the elapsed time, not the planned time.
- Read the estimated Blood Alcohol Content, which updates instantly as you change any input.
The instant-update behavior is useful for exploring sensitivity. Raise the drink count and the number rises. Raise the hours and the number falls. Switch from male to female and the number rises for the same inputs, because the smaller body-water ratio concentrates the same grams of alcohol more tightly. Watching the number move while you edit the inputs is the quickest way to build intuition for which factors dominate the answer.
Worked Example: One Combination Step by Step
Suppose a man weighing 80 kg has had three standard drinks and it is now one hour since his first drink. With r = 0.68, the formula gives:
Step 1 — grams of alcohol: 3 × 14 = 42 g
Step 2 — body water denominator: 0.68 × 80 × 1000 = 54,400
Step 3 — peak BAC as a fraction: 42 ÷ 54,400 = 0.000772
Step 4 — peak BAC as a percentage: 0.000772 × 100 = 0.0772%
Step 5 — back-end subtraction: 0.0772 − (0.015 × 1) = 0.0772 − 0.015 = 0.0622%
That is the rough estimate the tool reports: about 0.062%. A 60 kg woman who has had two standard drinks two hours after starting, with r = 0.55, comes out to roughly 0.055% — and both numbers should be treated as educational, not as legal truths. For any other combination of inputs, the BAC Calculator does the arithmetic for you and reports the result instantly.
What the Widmark Formula Leaves Out
The back-end subtraction uses a single average elimination rate for everyone, and the peak step uses fixed sex-based body-water ratios. Real BAC also depends on food in the stomach, drinking speed, hydration, medications, liver health, genetics, and how accurately you counted your drinks. Two people who enter identical numbers into the tool can end up with very different readings on a calibrated breathalyzer.
| Factor | Included in the formula? | Real-world impact |
|---|---|---|
| Body water ratio | Yes, via r = 0.68 or 0.55 | Approximates average sex differences |
| Elimination rate | Yes, at 0.015 per hour | Population average only |
| Food in stomach | No | Can slow absorption meaningfully |
| Drinking pace | No | Fast drinking raises peak before elimination starts |
| Medications and liver health | No | Can raise or lower the elimination rate |
| Hydration, fatigue, genetics | No | Small effects on perceived impairment |
For a more formal description of the underlying model and its assumptions, the Wikipedia overview of Blood Alcohol Content walks through the Widmark derivation and the population-level ranges that real measurements produce. The takeaway for anyone using a calculator is the same: the formula is a deliberately simple model, and it shows its age in the factors it ignores.
Why This Estimate Must Not Guide Driving Decisions
The output of any back-end calculation that runs the Widmark formula is a rough educational estimate, not a measurement. It cannot account for the food in your stomach, the pace at which you drank, your medications, your liver function, or your genetics. Two people who enter the same numbers can end up with very different actual readings, and the only devices that measure true Blood Alcohol Content are calibrated breathalyzers and blood tests.
For that reason, the result from the BAC Calculator must never be used to decide whether you are below any legal limit or fit to drive. If you have been drinking, the safe answer is simply not to drive — arrange a taxi, a rideshare, or a sober driver instead. The tool is an educational aid that makes the rough math visible; it is not medical or legal advice, and it deliberately carries no claims about fitness to operate a vehicle.