The math behind the estimate

1 · Ethanol mass per drink

Each drink is converted to grams of pure ethanol from its volume, alcohol by volume, and the density of ethanol (0.789 g/mL at 20 °C).

grams = volume_mL × (ABV% / 100) × 0.789

A U.S. standard drink is defined as 14 g of ethanol, the figure used to display the standard-drink count (NIAAA).

2 · Total body water (Watson)

Ethanol distributes into body water, not body mass, so the volume of distribution is derived from total body water (TBW) rather than a fixed Widmark r factor. TBW is estimated with the sex-specific Watson anthropometric regressions from age, height, and weight.

male:   TBW_L = 2.447 − 0.09516·age + 0.1074·height_cm + 0.3362·weight_kg
female: TBW_L = −2.097 + 0.1069·height_cm + 0.2466·weight_kg

A physiological floor of 0.35 × weight keeps implausible inputs from driving TBW unrealistically low. Source: Watson, Watson & Batt, Am J Clin Nutr 1980, the equations endorsed for blood-alcohol work in ANSI/ASB BPR 122 (2024).

3 · From grams to whole-blood concentration

Concentration in body water is converted to whole blood using the mean water content of blood (F_water): 0.825 for males and 0.838 for females. The small difference reflects lower haematocrit in female blood. Dividing ethanol grams by this apparent distribution volume yields the whole-blood percentage.

Vd_L  = TBW_L / F_water          (F_water = 0.825 male, 0.838 female)
BAC%  = (grams_in_body / Vd_L) × 0.1

See Jones, WIREs Forensic Science 2019 for absorption, distribution, and the F_water derivation.

4 · Absorption

Gastric emptying controls how fast ethanol reaches the bloodstream. Each drink is absorbed linearly over a window that widens with stomach contents; the absorbed fraction ramps from 0 to 1 across the window and is then complete.

absorbed_fraction(t) = clamp( (t − t_finish) / window , 0 , 1 )

window:  empty 30 min · light meal 75 min · full meal 120 min

Windows follow OSAC 2020-S-0003, Guidelines for Performing Alcohol Calculations.

5 · First-pass metabolism (bioavailability)

Food increases pre-systemic (gastric and hepatic) metabolism, so not all ingested ethanol reaches the circulation. The absorbed mass is scaled by a bioavailability factor that lowers peak BAC and the area under the curve on a fuller stomach.

bioavailability:  empty 1.00 · light meal 0.95 · full meal 0.90

6 · Elimination (Michaelis–Menten)

The liver clears ethanol via alcohol dehydrogenase, which saturates at low concentrations. Rather than a pure zero-order rate, BACtrack uses Michaelis–Menten kinetics so clearance is effectively constant through the normal range and tapers smoothly to first-order near zero — removing the artifact where a small drink would clear to exactly 0.000%.

rate(C) = Vmax × C / (Km + C)          Km ≈ 0.002 %BAC (~2 mg/100 mL)

Vmax by weekly intake (U.S. standard drinks):
  rare       < 3 / week        0.012 %/hr
  moderate   3–14 / week        0.015 %/hr
  frequent   14–35 / week       0.018 %/hr
  dependent  problem drinking   0.025 %/hr

Because C is normally far above Km, rate(C) sits within a few percent of Vmax across the usual range, then falls off gradually below ~0.02%. Higher Vmax for frequent and dependent drinkers reflects CYP2E1 (MEOS) induction. All rates lie inside the evidence-based 0.010–0.035 %/hour span (alcoholics 0.025–0.035) reported by Jones, Forensic Sci Int 2010;200:1–20.

7 · Why kidney function is not an input

92–98% of ethanol is metabolized by the liver; only 2–10% leaves unchanged via urine, breath, and sweat. Renal function (eGFR) therefore has no meaningful effect on blood-alcohol clearance and is deliberately excluded to avoid implying a precision the model does not have.

Profile inputs

Your profile sets the constants used in each step above. Age, height, weight, and sex determine total body water (Watson). Stomach contents set the absorption window and bioavailability. Drinks per week sets the elimination rate (Vmax). Toggle BAL or BAC in the header to display the same estimated whole-blood concentration as mg/dL or as a percentage.

Stomach · empty

30 min · 100% bioavailability

Stomach · light meal

75 min · 95% bioavailability

Stomach · full meal

120 min · 90% bioavailability

Drinks/wk · under 3

0.012 %/hr clearance

Drinks/wk · 3–14

0.015 %/hr clearance

Drinks/wk · 14–35

0.018 %/hr clearance

Drinks/wk · problem drinking

0.025 %/hr clearance

Limitations

These are population formulas, not measurements. Real individuals vary in body composition, enzyme activity, gastric emptying, and drinking history, and the model assumes drinks are fully consumed at the stated finish time. Estimates are for educational interest only and must never be used to decide whether it is safe or legal to drive.