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. $BAC=\frac{88.72}{0.68\times 81.65}-0.015\times 3=0.134\mathrm{\%}$

Visual Representation

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