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The maths behind the curve — Widmark's equation, the Watson body-water formula, and an honest account of everything the model cannot see.
Last updated: July 2026
An estimate is not a measurement. Everything below produces a modelled number from a handful of inputs. Only a breath or blood test measures anything. No estimate — however carefully computed — is a clearance to drive.
Nearly every blood-alcohol estimate in existence descends from work published by Swedish chemist Erik Widmark in 1932. His insight was that alcohol distributes itself through the water in your body, so the concentration you end up with depends on how much water you have to dilute it in.
Where A is the mass of alcohol consumed, W is body mass, r is the "distribution ratio" (roughly, the fraction of you that behaves like water), β is the elimination rate, and t is time elapsed.
The weak point is r. Widmark used fixed averages — about 0.68 for men, 0.55 for women. Those constants are the reason simple online calculators are so often wrong: they treat every body of the same sex as identical.
In 1980, Watson, Watson and Batt published regression equations estimating total body water (TBW) from ordinary anthropometric measurements — age, height, weight and sex. That lets you compute a personal distribution ratio instead of borrowing a population average.
Total body water converts to a distribution ratio by dividing by body mass and by the water content of blood (≈0.806):
The payoff is that two people of the same weight but different height, age or composition no longer get the same answer — which, physiologically, they shouldn't.
This is why a BAC feature asks for date of birth, sex, height and weight. Not to profile you — those four numbers are the formula. Without them there is no personal estimate, only a population guess.
A single equation gives you one number. A live curve needs to model two processes running at once, and they behave very differently.
A drink doesn't hit your bloodstream instantly. It absorbs from the stomach and small intestine over roughly 30–90 minutes, quickly at first and then tailing off — first-order kinetics. Each drink follows its own absorption curve from its own timestamp, which is why logging when matters as much as logging what.
Elimination works the opposite way. The enzyme doing the work is saturated at any meaningful concentration, so it clears alcohol at a near-constant 0.015 % per hour regardless of how much is present — zero-order kinetics.
One subtlety that simple models routinely get wrong: elimination is a single global term, not per drink. Your liver does not clear four drinks four times faster than one. Sum the absorption curves, then subtract one steady drain from the total. Getting this backwards inflates the estimate badly on heavy nights — which is the direction you least want to be wrong in.
An honest estimate comes with an honest error bar. None of the following are visible to the maths:
| Factor | Effect on the real number |
|---|---|
| Stomach contents | A full stomach can substantially delay and lower the peak. The model sees only the drink. |
| Individual elimination rate | Genuinely varies, roughly 0.010–0.025 %/hr. A fixed constant is an average, not you. |
| Medication | Several common drugs interact with alcohol metabolism, and some are dangerous with alcohol regardless of BAC. |
| Liver health and drinking history | Both shift elimination in ways no formula derived from height and weight can capture. |
| Actual pour size | A "glass of wine" is not a fixed quantity. Estimated inputs give estimated outputs. |
| Tolerance | Changes how impaired you feel — not how impaired you are, and not the number at all. |
The correct way to hold the output, then: a well-founded approximation of a trend, useful for seeing the shape of a night as it happens. Not a reading. Not evidence. Not permission.
SipWiser uses the Watson body-water formula for the distribution ratio, models each logged sip as its own first-order absorption curve from its own timestamp, and applies a single global zero-order elimination term to the total. Everything is computed on your device — the inputs never need to leave it.
The projected sober time is that same curve extended forward to zero. For what that projection is and isn't good for, see how long until you're sober.
SipWiser logs each sip and draws the curve as it happens — computed on-device, offline-first, and built to help you drink less, never more.
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