How to calculate alcohol concentration in human body

Answer 1

Calculating the alcohol concentration in the human body, often referred to as Blood Alcohol Concentration (BAC), involves determining the amount of alcohol in a person's bloodstream. BAC is typically expressed as a percentage (%), indicating the grams of alcohol per deciliter of blood. There are several methods for estimating BAC, including mathematical formulas and using breathalyzers. Here's a basic method for estimation:

Widmark Formula

One common way to estimate BAC is by using the Widmark formula:

\[ BAC = \frac{A}{r \cdot W} - \beta \cdot T \]

Where:

• BAC = Blood Alcohol Concentration (as a percentage)
• A = Total alcohol consumed (in grams)
• r = Alcohol distribution ratio (0.68 for men, 0.55 for women)
• W = Body weight (in grams)
• β = Alcohol elimination rate (typically about 0.015 per hour)
• T = Time since drinking began (in hours)

Steps to Calculate BAC

1. Determine the Total Alcohol Consumed (A):

   • Convert the volume of alcoholic beverages consumed into grams.
   • For example, a standard drink in the U.S. contains about 14 grams of pure alcohol, which is equivalent to:
     • 12 oz of beer (approximately 5% alcohol)
     • 5 oz of wine (approximately 12% alcohol)
     • 1.5 oz of distilled spirits (approximately 40% alcohol)

2. Calculate Body Weight (W):

   • Convert body weight from pounds to grams (1 lb ≈ 453.592 grams).

3. Select the Appropriate Distribution Ratio (r):

   • Use 0.68 for men and 0.55 for women.

4. Determine Time Since Drinking Began (T):

   • Note how many hours have passed since the drinking started.

5. Plug the values into the Widmark formula and solve for BAC.

Example Calculation

1. Alcohol Consumed: 3 standard drinks (3 x 14g = 42g)
2. Body Weight: Person weighs 180 lbs (180 lbs x 453.592 = 81,646 grams)
3. Distribution Ratio: For a male, r = 0.68
4. Time: Assume T = 2 hours
5. Elimination Rate: β = 0.015

Plugging these values into the formula:

\[ BAC = \frac{42}{0.68 \cdot 81646} - (0.015 \cdot 2) \]

Calculating the first part:

\[ BAC = \frac{42}{55559.68} - 0.03 \approx 0.000754 - 0.03 \approx -0.029246 \text{ (Negative BAC indicates not enough consumption to register)} \]

In this case, the BAC would need to be interpreted carefully, indicating the person is sober.

Important Considerations

• Individual variations (metabolism, food intake, tolerance) will significantly affect BAC.
• The above formula provides a rough estimate but should not be used for legal or medical purposes.
• Legal BAC limits for driving vary by region (often 0.08% in many places).

Conclusion

BAC can be estimated using the Widmark formula and taking into consideration various factors, but it's important to be aware that these calculations are estimates and many variables can influence actual BAC. For precise measurements, breathalyzers or blood tests should be employed.