Blood alcohol content (BAC) estimate
Blood alcohol content (BAC) is the concentration of alcohol in the bloodstream. It is commonly reported as a
percentage (for example, 0.08%), which corresponds to grams of alcohol per 100 mL of blood (g/dL). This calculator
provides an educational Widmark-style estimate based on drink amount, body size, and time since drinking began.
Real BAC can differ substantially from any estimate.
Important limitations and safety warning
BAC is affected by absorption timing (food in the stomach, drink spacing), body composition, hydration, sex-related
physiological averages, medications, illness, liver function, and many other factors. The model here is a simplified
approximation and is not medical advice and not legal guidance. Never use an estimate to decide whether it
is safe or legal to drive or operate machinery.
Step 1: Convert each drink to grams of ethanol
Each drink is entered by volume and ABV (alcohol by volume). First convert the drink volume to milliliters
if needed, then compute the volume of ethanol and convert to mass using the density of ethanol.
\[
1\ \text{fl oz} \approx 29.5735\ \text{mL}
\]
\[
V_{\text{ethanol}} = V_{\text{drink}}(\text{mL})\cdot \frac{\text{ABV}}{100}
\]
\[
m_{\text{ethanol}} = V_{\text{ethanol}}\cdot \rho_{\text{ethanol}}, \qquad
\rho_{\text{ethanol}} \approx 0.789\ \text{g/mL}
\]
The calculator totals the grams across all drinks:
\[
A = \sum_i m_{\text{ethanol},i}\quad (\text{grams})
\]
Step 2: Convert body weight to grams
Body weight is used to scale the estimate. If weight is entered in pounds, it is converted to kilograms and then to grams.
\[
1\ \text{lb} = 0.45359237\ \text{kg}
\]
\[
W(\text{g}) = W(\text{kg})\cdot 1000
\]
Step 3: Widmark distribution factor \(r\)
The Widmark model uses a distribution ratio \(r\), which approximates how alcohol distributes in body water. This calculator
provides typical educational presets and also allows a custom \(r\) value.
\[
r \approx
\begin{cases}
0.68 & \text{(male preset)}\\
0.55 & \text{(female preset)}
\end{cases}
\]
These are population averages, not precise measurements for an individual.
Step 4: Baseline BAC from total alcohol (instantaneous absorption limit)
A common Widmark-style baseline converts total alcohol grams into an initial BAC estimate (before accounting for time).
\[
\mathrm{BAC}_0 = \frac{A}{r\cdot W}\cdot 100
\]
Here, \(\mathrm{BAC}_0\) is expressed as a percent. This step assumes the alcohol is fully absorbed, which is not immediately true
in real drinking scenarios.
Step 5: Time model (absorption + elimination)
To produce a curve over time, the calculator uses a simple two-part model:
-
Absorption phase (first \(t_{\text{abs}}\) hours): alcohol entering the bloodstream increases linearly from 0 to \(A\).
-
Elimination phase (all times): BAC decreases approximately linearly at a constant metabolism rate \(\beta\).
The absorbed alcohol mass at time \(t\) is modeled as:
\[
A_{\text{abs}}(t) =
\begin{cases}
A\cdot \frac{t}{t_{\text{abs}}} & 0\le t \lt t_{\text{abs}}\\
A & t\ge t_{\text{abs}}
\end{cases}
\]
The BAC estimate at time \(t\) hours after the first drink is:
\[
\mathrm{BAC}(t) =
\max\!\left(0,\ \frac{A_{\text{abs}}(t)}{r\cdot W}\cdot 100\ -\ \beta t\right)
\]
A commonly used educational default is \(\beta \approx 0.015\%\) per hour, but real values vary widely.
Peak BAC and “time to zero” estimate
In this simplified model, BAC rises during the absorption interval (if intake dominates elimination) and then declines.
The “time to reach 0” is estimated by extending the linear elimination trend forward until BAC returns to zero.
If \(\mathrm{BAC}_{\text{now}}\) is the current estimate at time \(t_{\text{now}}\), then a rough remaining time is:
\[
t_{\text{remaining}} \approx \frac{\mathrm{BAC}_{\text{now}}}{\beta}
\]
This is a coarse approximation because elimination is not perfectly linear for all individuals and because absorption timing
depends strongly on drinking pattern and food intake.
How to read the visualizations
-
BAC curve: shows \(\mathrm{BAC}(t)\) over time. A vertical marker highlights the selected time since the first drink.
Hovering displays the estimated BAC at the cursor time. Zoom and pan help examine early rise vs later decline.
-
Threshold lines: optional reference lines (e.g., 0.02, 0.05, 0.08). These are included as generic context only; legal limits
and enforcement standards vary by region and situation.
-
Drink contribution bars: each bar represents grams of ethanol from one drink, computed from its volume and ABV. This helps identify
which drinks contribute the most alcohol mass.
Practical interpretation
The most useful educational outputs are the total grams of alcohol, the relative contributions of different drinks, and how a
constant-rate elimination assumption shapes the decline over time. Because individual variability is large, the correct safety decision is
not to “trust the estimate,” but to plan transportation and avoid risky activities after drinking.
