The Widmark Formula Explained: The Science Behind Alcomato's BAC Calculator
BAC = (A ÷ (Bw × r)) × 100 − (0.015 × t). Alcomato runs this formula for you automatically. Enter your drinks below.
Use the Widmark BAC Calculator →Every BAC calculator, including Alcomato, is built on a single equation developed by Swedish scientist Erik M.P. Widmark in 1932. The Widmark formula is the gold standard for estimating blood alcohol concentration from known alcohol intake, and it remains the forensic standard used in DUI cases worldwide nearly a century later.
What Is the Widmark Formula?
The Widmark formula calculates the peak BAC that results from consuming a known amount of alcohol, adjusted for body weight, gender, and elapsed time. It is a mathematical model, not a medical measurement — it produces estimates, not exact readings. However, for population averages, it is highly accurate.
Erik Widmark derived the formula by measuring blood alcohol levels in hundreds of subjects after controlled alcohol doses, developing the concept of the "r-factor" to account for the proportion of body weight that distributes alcohol.
The Complete Equation
BAC = (A ÷ (Bw × r)) × 100 − (0.015 × t)
- A = grams of pure alcohol consumed (see grams formula)
- Bw = body weight in grams (kg × 1000)
- r = Widmark r-factor (0.68 for men, 0.55 for women)
- t = hours elapsed since drinking began
- 0.015 = average alcohol elimination rate per hour (% BAC/hr)
Alcomato implements the full Widmark formula. Enter your drinks, weight, gender, and time to get an instant BAC estimate.
Use the Widmark BAC Calculator →The Widmark r-Factor: 0.68 for Men, 0.55 for Women
The r-factor (also called the Widmark factor or volume of distribution) represents the proportion of body weight through which alcohol is distributed. Ethanol distributes only in body water — not fat tissue. Because:
- Men have approximately 68% of body weight as water-containing tissue → r = 0.68
- Women have approximately 55% of body weight as water-containing tissue → r = 0.55
This is why women typically reach higher BAC than men of the same weight drinking the same amount — their lower r-factor means alcohol is distributed through a smaller volume. The r-factor can also be lower in obese individuals (fat contains no water) and higher in muscular individuals (muscle is ~73% water).
How Grams of Alcohol Are Calculated
The Widmark formula requires grams of pure ethanol, not "drinks." To convert any drink to grams: Volume (ml) × ABV (decimal) × 0.789 = grams. For example, a 330ml 5% beer: 330 × 0.05 × 0.789 = 13.0g. For a full explainer, see our grams of alcohol formula guide. The 0.789 constant is ethanol's density in g/ml — see why 0.789 matters.
Metabolism and the 0.015%/hr Rule
The liver eliminates alcohol at a roughly constant rate (zero-order kinetics) above BAC 0.02%. The population average is 0.015% BAC per hour, which corresponds to approximately 7–10g of ethanol per hour for an average adult. Individual rates range from 0.010% to 0.020% per hour depending on:
- Liver health and enzyme levels (ADH, ALDH genotypes)
- Habitual drinking (heavy drinkers eliminate faster due to enzyme induction)
- Age, genetics, and nutritional status
The Widmark Formula in Practice: Worked Example
Scenario: 70kg Man, 2 Beers (330ml 5% each), 2 Hours Elapsed
- Alcohol: 2 × 13.0g = 26g of ethanol
- Body weight: 70,000g
- r-factor: 0.68 (male)
- Time: 2 hours
- Peak BAC (t=0): 26 / (70,000 × 0.68) × 100 = 0.0547%
- After 2 hours: 0.0547 − (0.015 × 2) = 0.0547 − 0.030 = 0.025%
| Time After Drinking | BAC Calculation | Estimated BAC |
|---|---|---|
| 0 hours (peak) | 26 / (70000 × 0.68) × 100 | 0.055% |
| 1 hour | 0.055 − 0.015 | 0.040% |
| 2 hours | 0.055 − 0.030 | 0.025% |
| 3 hours | 0.055 − 0.045 | 0.010% |
| 3.7 hours | 0.055 − 0.055 | 0.000% |
Use Alcomato's BAC calculator to run these Widmark calculations automatically for your exact weight, drinks, and time.
Run the Widmark Calculation →Limitations and Accuracy of the Widmark Formula
- Absorption phase: The formula assumes alcohol is fully absorbed. During the first 30–60 minutes, actual BAC may be lower than calculated because absorption is still ongoing.
- Individual variability: The r-factor is a population average. Lean, muscular individuals have higher r values; obese individuals have lower ones.
- Food effects: A full meal can slow absorption significantly, reducing peak BAC by 20–40% and delaying it by 60–90 minutes.
- Bariatric surgery: After gastric bypass, the formula significantly underestimates peak BAC. See bariatric spike math for details.
Frequently Asked Questions
Is the Widmark formula still scientifically valid?
Yes. Despite being 90+ years old, the Widmark formula remains the forensic standard for BAC estimation because its simplicity and accuracy are validated across thousands of studies. More complex pharmacokinetic models exist but offer marginal improvement for practical BAC estimation at the cost of requiring more individual parameters.
What r-factor should I use if I am between the standard values?
The standard values (0.68 male, 0.55 female) are population averages. If you have very low body fat, use a higher r-factor (up to 0.73). If you have high body fat percentage, use lower (down to 0.60 for men, 0.50 for women). The Alcomato calculator uses standard values; for more precision, consult the Watson formula, which estimates body water from height, weight, and age.
Does the formula work for all types of alcohol?
Yes, because the formula only uses grams of pure ethanol — not the drink type. Whether those grams came from beer, wine, vodka, or cocktails is irrelevant. The rate of absorption may differ slightly between drink types (carbonated drinks absorb faster), but the total grams processed is the same. See our article on carbonation and BAC spikes for the absorption rate differences.
Every BAC estimate on Alcomato uses the Widmark formula. Enter your specific details for a personalised calculation.
Calculate Your BAC Now →Disclaimer: This article provides educational information only. It does not constitute medical or legal advice. BAC calculators provide estimates, not exact measurements. Individual BAC varies based on numerous factors including body composition, metabolism, food intake, medications, and health conditions. Never rely solely on calculators to determine if you are safe to drive. The only safe BAC for driving is 0.00%. Always use alternative transportation after consuming alcohol. If you struggle with alcohol use, consult a healthcare professional or contact SAMHSA's National Helpline at 1-800-662-4357.