Blood Alcohol Concentration (BAC) is a key measure used in Australia to determine the level of alcohol in a person’s bloodstream. It plays a crucial role in enforcing drink-driving laws and promoting road safety. While breathalysers and blood tests provide direct measurements, it is also possible to estimate BAC using mathematical formulas. One of the most widely recognized methods is the Widmark formula, which offers a practical way to approximate BAC based on personal factors and alcohol consumption. This blog explains the BAC formula, how it works, and what Australians should know about it.
The Widmark Formula: A Tool to Estimate BAC
Developed by Swedish scientist Erik M.P. Widmark in the early 20th century, the Widmark formula estimates BAC by considering:
- The amount of alcohol consumed (in grams)
- Body weight (in grams)
- A gender-specific constant reflecting alcohol distribution in the body
- Time elapsed since drinking began (to account for metabolism)
The formula is:BAC=Alcohol consumed in gramsBody weight in grams×r×100−(0.015×hours since drinking began)\text{BAC} = \frac{\text{Alcohol consumed in grams}}{\text{Body weight in grams} \times r} \times 100 – (0.015 \times \text{hours since drinking began})BAC=Body weight in grams×rAlcohol consumed in grams×100−(0.015×hours since drinking began)
Where:
- rrr = Widmark’s constant (approximately 0.68 for males and 0.55 for females)
- 0.015% per hour is the average rate at which the body metabolises alcohol
Breaking Down the Formula
- Alcohol consumed in grams: Calculated by multiplying the number of standard drinks by grams of alcohol per drink. In Australia, a standard drink contains 10 grams of pure alcohol.
- Body weight in grams: Your weight in kilograms multiplied by 1,000.
- Gender constant (r): Reflects differences in body water content affecting alcohol distribution.
- Metabolism factor: Accounts for the reduction of BAC over time as your body processes alcohol.
Example Calculation
Imagine a 70 kg male who has consumed 4 standard drinks over 2 hours. Here’s how the BAC estimate works:
- Calculate alcohol consumed:
4 drinks × 10 grams = 40 grams - Convert body weight:
70 kg × 1,000 = 70,000 grams - Apply Widmark constant for males:
r=0.68r = 0.68r=0.68 - Calculate initial BAC:
4070,000×0.68×100=4047,600×100≈0.084%\frac{40}{70,000 \times 0.68} \times 100 = \frac{40}{47,600} \times 100 \approx 0.084\%70,000×0.6840×100=47,60040×100≈0.084%
- Subtract metabolism over 2 hours:
0.084%−(0.015×2)=0.084%−0.03%=0.054%0.084\% – (0.015 \times 2) = 0.084\% – 0.03\% = 0.054\%0.084%−(0.015×2)=0.084%−0.03%=0.054%
Estimated BAC is approximately 0.054%, which is just above the legal limit of 0.05% in Australia.
Important Considerations
- The Widmark formula provides an estimate and cannot replace actual breath or blood testing.
- Individual factors such as metabolism rate, health, medications, and food intake can affect accuracy.
- The formula assumes consistent drinking over the time period, which may not reflect real drinking patterns.
- Always err on the side of caution and avoid driving if you have consumed any alcohol.
The Widmark formula is a valuable tool for estimating Blood Alcohol Concentration and understanding how alcohol consumption relates to legal limits in Australia. While it offers insight into how your body processes alcohol, it should be used cautiously and never as a substitute for official testing or responsible decision-making. When in doubt, the safest choice is to avoid driving after drinking.