# Blood alcohol content (BAC) calculator

> Blood alcohol content (BAC) estimate by the Widmark formula from drinks, body weight and time, with the elimination curve and time back to zero.

النسخة التفاعلية: https://www.calcopenly.com/ar/health/blood-alcohol-calculator
الموضوع: حاسبات الصحة واللياقة

Blood alcohol content (BAC) is estimated with the Widmark formula: the alcohol drunk is spread through a share r of body weight, 0.73 for men and 0.66 for women, and about 0.015 percentage points are eliminated per hour. In US units, BAC % = fluid ounces of alcohol × 5.14 ÷ (weight in lb × r) − 0.015 × hours. One US standard drink holds 14 g, or 0.6 fl oz, of pure alcohol (NIAAA).

People use it to see how drinks, body weight and time interact. An 80 kg man who has had 3 standard drinks over 2 hours is estimated at 0.042 %, and the estimate reaches zero about 2 h 47 min later.

The result is an average-person model, not a measurement: food, drinking pace, medicines and liver function change real BAC, and impairment begins well below legal limits. It is not a basis for deciding whether to drive.

## المدخلات

- **Sex (for the formula)** (الخيارات: Male, Female)
- **Weight**
- **Count alcohol as** (الخيارات: Standard drinks, Volume and strength)
- **US standard drinks**: One US standard drink = 14 g alcohol: 12 fl oz beer at 5%, 5 fl oz wine at 12%, or 1.5 fl oz spirits at 40% (NIAAA).
- **Total volume drunk**
- **Alcohol by volume**
- **Time since the first drink**: Hours, or 1:30 for an hour and a half.

## النتائج

- Estimated BAC now (%) — النتيجة الرئيسية
- Estimate before elimination (%)
- Time until the estimate reaches 0
- Estimated BAC now (‰ (g/L))
- Pure alcohol (g)

## الصيغة

$$
\text{BAC}\% = \frac{A \times 5.14}{W \times r} - 0.015\,H\quad(A\ \text{fl oz alcohol},\ W\ \text{lb},\ r = 0.73\ \text{M} / 0.66\ \text{F},\ H\ \text{hours})
$$

## أمثلة محلولة

### Man, 180 lb, 3 standard drinks, 2 hours

- Sex (for the formula): Male
- Weight: 180 lb
- Count alcohol as: Standard drinks
- US standard drinks: 3
- Time since the first drink: 2
- **Estimated BAC now: 0.040 %**
- **Estimate before elimination: 0.070 %**
- **Time until the estimate reaches 0: 2 h 41 min 38 s**
- مصدر التحقق: ⁨Python 3.8 decimal: 1.8 × 5.14 / (180 × 0.73) − 0.015 × 2 = 0.04041; zero after 0.070411/0.015 − 2 h = 2.6941 h⁩

### Woman, 130 lb, a 750 mL bottle of 12% wine, 3 hours

- Sex (for the formula): Female
- Weight: 130 lb
- Count alcohol as: Volume and strength
- Total volume drunk: 750 mL
- Alcohol by volume: 12%
- Time since the first drink: 3
- **Estimated BAC now: 0.137 %**
- **Estimate before elimination: 0.182 %**
- **Time until the estimate reaches 0: 9 h 9 min 14 s**
- مصدر التحقق: ⁨Python 3.8 decimal: A = 750/29.5735295625 × 0.12 = 3.04326 fl oz; 3.04326 × 5.14 / (130 × 0.66) − 0.045 = 0.13731⁩

### Edge: one drink, 80 kg man, 5 hours later (floored at zero)

- Sex (for the formula): Male
- Weight: 80 kg
- Count alcohol as: Standard drinks
- US standard drinks: 1
- Time since the first drink: 5
- **Estimated BAC now: 0.000 %**
- **Time until the estimate reaches 0: 0 s**
- **Estimate before elimination: 0.024 %**
- مصدر التحقق: ⁨Python 3.8 decimal: 0.6 × 5.14 / (176.37 lb × 0.73) = 0.02395 < 0.015 × 5, so the estimate is 0⁩

### Edge: no drinks

- Sex (for the formula): Female
- Weight: 60 kg
- Count alcohol as: Standard drinks
- US standard drinks: 0
- Time since the first drink: 1
- **Estimated BAC now: 0.000 %**
- **Estimate before elimination: 0.000 %**
- **Pure alcohol: 0.0 g**
- مصدر التحقق: ⁨Definition: A = 0 gives BAC 0⁩

### Woman, 70 kg, 2 standard drinks, 1 hour

- Sex (for the formula): Female
- Weight: 70 kg
- Count alcohol as: Standard drinks
- US standard drinks: 2
- Time since the first drink: 1
- **Estimated BAC now: 0.046 %**
- **Estimate before elimination: 0.061 %**
- **Pure alcohol: 28.0 g**
- مصدر التحقق: ⁨Python 3.8 decimal: 1.2 × 5.14 / (154.32 lb × 0.66) − 0.015 = 0.04556; 1.2 fl oz × 29.5735 mL × 0.789 g/mL = 28.0 g⁩

## الأسئلة

### What is a standard drink?

In the US, a standard drink contains 14 g (0.6 fl oz) of pure alcohol: 12 fl oz of 5 % beer, 5 fl oz of 12 % wine or 1.5 fl oz of 40 % spirits, according to NIAAA. Other countries use different sizes; a UK unit is 8 g, so one US standard drink is 1.75 UK units. A 750 mL bottle of 12 % wine holds about 71 g of alcohol, roughly 5 US standard drinks.

### How is blood alcohol calculated?

With the Widmark formula. The alcohol drunk is divided by body weight times r, the share of the body that holds it (0.73 for men and 0.66 for women here), and about 0.015 percentage points are subtracted for each hour since drinking began. A 180 lb man who has 3 standard drinks (1.8 fl oz of alcohol) peaks at 1.8 × 5.14 ÷ (180 × 0.73) = 0.070 % and is estimated at 0.040 % two hours later.

### How long does it take for alcohol to leave your body?

At the average elimination rate of about 0.015 percentage points per hour, a BAC of 0.08 % takes roughly 5 hours 20 minutes to reach zero. One US standard drink takes about 1.3 hours to clear for a 100 kg man and 2.8 hours for a 50 kg woman by this estimate. Coffee, water and sleep do not speed elimination; the liver sets the pace, and individual rates vary.

### What BAC is the legal limit for driving?

0.08 % in every US state except Utah, which lowered its limit to 0.05 % in 2018, and 0.04 % for US commercial drivers. England, Wales and Northern Ireland use 80 mg per 100 mL of blood (0.08 %) and Scotland 50 mg (0.05 %). Impairment starts below these limits, so an estimate under the limit does not mean it is safe to drive.

### ما مدى دقة «⁨Blood alcohol content (BAC) calculator⁩»؟

تعتمد الدقة على مدخلاتك وافتراضات الطريقة. يستخدم الحساب العشري 50 رقمًا معنويًا، لكن التقديرات والأساليب العددية وبيانات المصدر قد تكون أقل دقة؛ تقريب القيم المعروضة لا يزيل هذه الحدود. أمثلة محلولة جرى التحقق منها بمصادر مستقلة: 5. مثلًا، يجري التحقق من «⁨Man, 180 lb, 3 standard drinks, 2 hours⁩» بالرجوع إلى ⁨Python 3.8 decimal: 1.8 × 5.14 / (180 × 0.73) − 0.015 × 2 = 0.04041; zero after 0.070411/0.015 − 2 h = 2.6941 h⁩.

### ما مصدر هذه الطريقة؟

Widmark EMP. Die theoretischen Grundlagen und die praktische Verwendbarkeit der gerichtlich-medizinischen Alkoholbestimmung (1932); NIAAA — What is a standard drink?; NIAAA — Understanding the dangers of alcohol overdose.

## المصادر

- Widmark EMP. Die theoretischen Grundlagen und die praktische Verwendbarkeit der gerichtlich-medizinischen Alkoholbestimmung (1932)
- [NIAAA — What is a standard drink?](https://www.niaaa.nih.gov/alcohols-effects-health/what-standard-drink)
- [NIAAA — Understanding the dangers of alcohol overdose](https://www.niaaa.nih.gov/publications/brochures-and-fact-sheets/understanding-dangers-of-alcohol-overdose)

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