Blood Alcohol Content (BAC) Formula
Calculate estimated Blood Alcohol Content using the Widmark formula.
Accounts for body weight, gender, alcohol consumed, and time elapsed.
The Formula
The Widmark formula estimates blood alcohol content based on alcohol consumed, body weight, gender, and time.
BAC is expressed as a percentage (grams of alcohol per 100 mL of blood).
The body eliminates alcohol at approximately 0.015% per hour.
Variables
| Symbol | Meaning |
|---|---|
| BAC | Blood Alcohol Content (%) |
| A | Total alcohol consumed (grams) |
| W | Body weight (grams) |
| r | Widmark factor: 0.68 for men, 0.55 for women |
| t | Time since drinking started (hours) |
| 0.015 | Average alcohol elimination rate (% per hour) |
Calculating Alcohol in Grams
To find grams of alcohol in a drink:
Where 0.789 is the density of ethanol in g/mL.
| Drink | Typical Volume | ABV | Alcohol (g) |
|---|---|---|---|
| Beer | 355 mL / 12 oz | 5% | 14.0 g |
| Wine | 150 mL / 5 oz | 12% | 14.2 g |
| Spirit (shot) | 44 mL / 1.5 oz | 40% | 13.9 g |
Unit Conversions
- Weight in kg to grams: multiply by 1,000
- Weight in lbs to grams: multiply by 453.6
- Volume in oz to mL: multiply by 29.57
Example 1 (Metric)
A man weighing 80 kg (80,000 g) drinks 3 beers over 2 hours. Each beer contains 14 g of alcohol. Estimate his BAC.
Total alcohol: A = 3 × 14 = 42 g
BAC = (A / (W × r)) - (0.015 × t)
BAC = (42 / (80,000 × 0.68)) - (0.015 × 2)
BAC = (42 / 54,400) - 0.030
BAC = 0.0772 - 0.030
BAC ≈ 0.047% (below the 0.08% legal limit in most jurisdictions)
Example 2 (Imperial)
A woman weighing 130 lbs drinks 2 glasses of wine over 1 hour. Each glass contains 14.2 g of alcohol. Estimate her BAC.
Convert weight: 130 × 453.6 = 58,968 g
Total alcohol: A = 2 × 14.2 = 28.4 g
BAC = (28.4 / (58,968 × 0.55)) - (0.015 × 1)
BAC = (28.4 / 32,432.4) - 0.015
BAC = 0.0876 - 0.015
BAC ≈ 0.073%
BAC Effects
| BAC % | Typical Effects |
|---|---|
| 0.02 - 0.03% | Slight relaxation, mild mood changes |
| 0.04 - 0.06% | Relaxation, lowered inhibitions |
| 0.07 - 0.09% | Impaired balance, speech, and reaction time |
| 0.10 - 0.12% | Significant impairment of motor control |
| 0.13 - 0.15% | Gross impairment, blurred vision |
| 0.16%+ | Severe impairment, potential medical emergency |
When to Use It
Use the BAC formula for:
- Educational understanding of how alcohol affects the body
- General awareness of how different factors influence BAC
- Understanding why body weight and gender affect alcohol tolerance
Important: This formula provides only a rough estimate.
Actual BAC varies based on many factors including food intake, metabolism, medications, and individual physiology.
Never rely on a formula to determine whether it is safe to drive. When in doubt, do not drive.
This formula is for general educational purposes only. It is not medical or legal advice. Never use this formula to make decisions about driving or operating machinery.