Blood Alcohol Content (Widmark Formula)

Estimates blood alcohol concentration from amount of alcohol consumed, body weight, and time elapsed since drinking.

Written by the Vorzep Team

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BAC ⟷A, m, sex, t

Alcohol A

Mass m

Hours t

BAC

Sex: Male (r = 0.68) Female (r = 0.55)

Solve for: BAC A m t

Result —

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BAC over Time elimination from peak

BAC(t) = C₀ − 0.015·t Current BAC Peak / Zero

Widmark Formula • A in g, m in kg, t in hours • BAC in %

Variables

Symbol	Quantity	Unit
BAC	Blood alcohol content	%
alcohol_grams	Grams of pure alcohol consumed	g
mass_kg	Body mass	kg
r	Widmark distribution factor (≈0.68 men, 0.55 women)
hours	Hours since drinking started	hours

What it means

The Widmark formula estimates blood alcohol concentration (BAC) from the amount of alcohol consumed, body weight, and time elapsed. It accounts for the distribution of alcohol in body water (r factor). The result is in %. It is used in forensic toxicology, legal cases, and by law enforcement. It provides an approximation, but actual BAC depends on many factors (food intake, metabolism, etc.). Understanding this formula helps individuals estimate their impairment and to make safe decisions about driving and alcohol consumption. It is also used in research on alcohol pharmacokinetics.

Worked example

Blood Alcohol Content (Widmark) – Two Detailed Examples

Real‑World

Scenario: A man weighing 80 kg consumes a standard drink (14 g of alcohol) and wants to estimate his blood alcohol content (BAC) after 1 hour using the Widmark formula. He uses the formula to understand his approximate BAC and ensure he is safe to drive. The calculation accounts for body weight, sex (via the distribution factor r), and alcohol elimination over time.

Parameter	Value
alcohol (g)	14
mass (kg)	80
r	0.68
hours	1

1BAC ≈ 0.01074% (using the Widmark formula as per the table)

Result 0.011% ✓ Below legal limit (typically 0.08%)

Scenario: A woman weighing 60 kg consumes one standard drink (14 g of alcohol). She calculates her BAC after 0.5 hours using the Widmark formula with r = 0.55 for women. She wants to know if she can drive safely. The result helps her make a responsible decision.

Parameter	Value
alcohol	14
mass	60
r	0.55
hours	0.5

1BAC ≈ 0.03878% (as per table)

Result 0.039% ✓ Still below legal limit

Insight: The Widmark formula estimates BAC based on alcohol consumed, body weight, sex, and time elapsed. The legal limit for driving in many places is 0.08% BAC. This formula is only an estimate and individual factors vary.

Common mistakes

Widmark formula: BAC = (alcohol_grams / (mass_kg × r)) × 100 − (0.015 × hours).
Alcohol grams: Volume (mL) × %ABV × 0.789 (density of ethanol).
r: Body water fraction – 0.68 for men, 0.55 for women (or 0.58 average).
Hours: Time elapsed since the start of drinking – assumes linear elimination.
Estimate: Many factors affect BAC (food, metabolism) – this is a rough guide.

Applications

The Widmark formula estimates blood alcohol concentration (BAC) based on the amount of alcohol consumed, body weight, sex (via the distribution factor r), and time elapsed. It is used in forensic science, legal contexts, and emergency medicine to determine impairment and toxicity. Law enforcement uses it to estimate BAC for DUI cases. Clinicians use it to assess alcohol poisoning risk. By understanding BAC, professionals can advise on safe drinking limits and support public health campaigns. This formula highlights the importance of body composition and time in alcohol metabolism, helping to prevent alcohol‑related harm.

Forensic analysis and legal proceedings for alcohol impairment
Clinical assessment of alcohol intoxication and overdose
Public health education on drinking limits and safety
Pharmacokinetic studies of alcohol metabolism
Workplace and occupational alcohol testing