Alcohol: Calculations

Calculations

The amount of alcohol in a drink

As a rule of thumb we can assume that a glass of wine, a beer and a tot of spirits each contains roughly the same amount of alcohol, namely 10 grams. However, it is often necessary to be more precise about the exact amount of alcohol in a drink. If the strength of a beverage expressed as v/v% is known, the amount of alcohol in gram can be calculated. As an example a 100 ml glass containing white wine with an alcohol content of 12% will be used for the following measurements: 100 ml wine will therefore contain 12 ml alcohol. The specific gravity of alcohol is 0,79, in other words 1 ml alcohol weighs 0,79 g. Therefore the alcohol content of 100 ml wine will be 12x6 0,79 = 9,48 g.

The Widmark formula

The Widmark formula is used to calculate the amount of alcohol in grams ingested by an individual to produce a specific blood-alcohol concentration at a given time. It is important to realise that it does not reflect any alcohol already absorbed and eliminated, nor any alcohol ingested but not absorbed.

A = px c x r x 10

A:The amount of alcohol in gram in the body at a given time to cause the blood alcohol concentration

P: the mass of the person in kg

C:the blood alcohol concentration in g% or g/dl

R:the Widmark or distribution factor

As mentioned above, alcohol is water-soluble. The higher the water content of a tissue or body, the more alcohol can be dissolved in the tissues, and the lower the blood-alcohol level will be. As males generally have more muscle tissue than females, the same quantity of alcohol ingested by a male and female of the same mass (all other factors being equal) will result in a lower level in the male than in the female. This ``r'' or distribution factor is 0,6 for females and 0,7 for males.

The reason why this formula must be multiplied by 10 is its German origin. In Germany an alcohol-level is expressed in promille, that is g/l. In order to express the g% or g/dl value as used in South Africa, we multiply by 10.

Take the example of a man weighing 70 kg and a blood-alcohol level of 0,08g%. Based on the Widmark formula this level represents the following amount of alcohol ingested:

= p x c x r x 10

=70 x 0,08 x 0,7 x 10

=39,20 g

This represents roughly 4 drinks

Reverse calculations

When using this formula it is important to remember that it also represents alcohol already absorbed by the body. As we can safely assume that all alcohol will be absorbed after 2 hours, this formula can only be applied if no alcohol was ingested in the 2-hour period before specimen collection. If alcohol was taken in during this period, the amount and its impact on the blood-alcohol level must be taken into account.

This formula is based on the principle that alcohol elimination occurs at a constant level of between 0,01 and 0,02g% per hour. This value is also called the B60 value, and we generally use an average value of 0,015g%/h.

Let us take as example someone arrested at 22:00 with a blood-alcohol level of 0,10g% at the time of the arrest. The incident occurred at 19:00, 3 hours previously. If we use the formula:

Ci=Ca + (B60 x t)

Ci:   concentration at time of incident

Ca: concentration at time of arrest

t:hours between these events

 β60: 0,015g%/h

We find that:

Ci    = Ca + (B60 x t)

=0,10 g% + (0,015 g%/h x 3h)

=0,10 g% + 0,045 g%

=0,145 g%

As said before, we can use this formula only if no more alcohol was consumed during the period between the incident and the time of specimen collection, except if we take that alcohol into account.