Blood Alcohol Content (BAC) Calculator

What is Blood Alcohol Content (BAC)?

Blood Alcohol Content (BAC) is a measure of the concentration of alcohol in an individual's bloodstream. It is typically expressed as a percentage, representing the weight of alcohol in a certain volume of blood. For example, a BAC of 0.08% means there are 0.08 grams of alcohol per 100 milliliters of blood.

The Widmark Formula for BAC Calculation

The Widmark formula is commonly used to estimate BAC:

\[BAC = \frac{A}{r \times W} - \beta t\]

Where:

• \(A\) = grams of alcohol consumed
• \(r\) = gender constant (0.68 for men, 0.55 for women)
• \(W\) = body weight in kilograms
• \(\beta\) = alcohol elimination rate (approximately 0.015 per hour)
• \(t\) = hours since drinking began

Step-by-Step BAC Calculation

1. Calculate grams of alcohol consumed: \[A = \text{volume (oz)} \times \text{alcohol content (%)} \times 29.5735 \text{ g/oz}\]
2. Convert body weight to kilograms: \[W_{kg} = \text{weight (lbs)} \times 0.453592 \text{ kg/lb}\]
3. Apply the Widmark formula: \[BAC = \frac{A}{r \times W_{kg}} - 0.015 \times t\]

Example Calculation

Let's calculate the BAC for a 180 lb man who consumed 5 beers (12 oz each, 5% alcohol) over 3 hours:

1. \(A = 5 \times 12 \text{ oz} \times 0.05 \times 29.5735 \text{ g/oz} = 88.72 \text{ g}\)
2. \(W_{kg} = 180 \text{ lbs} \times 0.453592 \text{ kg/lb} = 81.65 \text{ kg}\)
3. \(BAC = \frac{88.72}{0.68 \times 81.65} - 0.015 \times 3 = 0.134\%\)

Visual Representation

The red portion of the bar represents the calculated BAC (0.134%) relative to 1.00%.