Metabolic Mathematics

The Widmark Formula

NeonBAC Labs: Silo-01

The core engine behind NeonBAC is not based on guesswork, but on nearly a century of forensic toxicology. Every simulation our scanner runs is rooted in the mathematical principles established by Swedish physician Erik M.P. Widmark in the early 20th century.

A Scientific Milestone

In 1932, Widmark published his seminal work on the kinetics of alcohol distribution. He discovered that ethanol does not stay confined to the blood but distributes itself throughout the total body water. This insight allowed for the creation of a reliable predictive model that remains the global standard for legal and medical alcohol reconstruction.

Forensic Mathematical Model

FIGURE 1: THE WIDMARK EQUATION

BAC = [ (A × 5.14) / (W × r) ] - (β × H)
Forensic Analysis Note

Calculates peak concentration by balancing dosage (A) against body mass (W) and distribution (r), minus metabolism over time (H).

Core Metabolic Variables

FIGURE 2: PRIMARY FORENSIC VARIABLES

Dose (A) Weight (W) Ratio (r) Time (H)
Forensic Analysis Note

Biological and mathematical inputs that drive the peak BAC and elimination trajectory.

The Variables Explained

The Alcohol Dose (A)

This represents the total weight of alcohol consumed in ounces. Because different beverages have varying ABV (Alcohol by Volume) percentages, NeonBAC converts your drink log into pure ethanol weight before running the calculation.

Body Weight (W) and the r-Factor

Widmark identified that gender and body composition drastically change how alcohol is diluted. Men typically have a higher body water percentage (r = 0.73), while women typically have a lower ratio (r = 0.66) due to higher average adipose tissue. This "r" factor is why weight alone cannot predict BAC.

The Beta Constant (β)

This is the rate at which the liver eliminates alcohol. While it can vary, the average rate of 0.015% per hour is the unyielding "downward slope" of the metabolic timeline. No amount of coffee or cold showers can alter this biological constant.

Modern Implementation

While Erik Widmark used pen and paper, the NeonBAC engine uses these same equations to generate thousands of data points instantly. By simulating the "rising" absorption phase and the "linear" elimination phase, we provide a forensic-grade look at your metabolic journey.

Metabolic Trajectory

FIGURE 3: THE METABOLIC TIMELINE CURVE

First Sip Peak BAC Linear Elimination 0.000% BAC % TIME (HOURS)
Forensic Analysis Note

Metabolic trajectory showing the non-linear absorption phase (blue) followed by the zero-order linear elimination phase (pink). Note the "Peak BAC" occurs after the final consumption event, followed by a constant metabolic decay.

// FORENSIC_INTELLIGENCE_REPORT: FAQ

Q: IS THE WIDMARK FORMULA 100% ACCURATE?

While it is the global forensic standard, it provides a high-probability estimate. Individual variables like hydration, specific medications, or underlying health conditions can cause minor deviations from the statistical average.

Q: WHAT IS THE PURPOSE OF THE '5.14' VALUE?

This is a mathematical constant used to align liquid ounces of consumed alcohol with the total weight of blood in the human body (measured in pounds) to produce a decimal percentage result.

Q: WHY DOES THE FORMULA SUBTRACT TIME?

Metabolism is an active process that begins shortly after consumption. Subtracting elapsed time multiplied by the Beta Constant (0.015) accounts for the volume of alcohol the liver has already successfully eliminated from the system.

Sequential Record: SILO-02 14 Grams: Defining the "Standard Drink" →
⚠️ System Protocol: Critical Safety Notice ⚠️

NeonBAC simulations are mathematical estimates based on forensic averages (The Widmark Formula). Individual metabolism varies based on hydration, food intake, and biological health. These results are for educational and research purposes only.

NEVER USE THIS TOOL TO DETERMINE YOUR LEGAL ABILITY TO DRIVE. IF YOU HAVE CONSUMED ALCOHOL, DO NOT OPERATE A VEHICLE OR HEAVY MACHINERY.

NEONBAC EDUCATION LIBRARY