Medical
Estimated blood alcohol content
The Widmark estimate. Ethanol mass over body water volume, less the standard hourly clearance.
The Formula
BAC = (drinks x 14) / (r x kg x 10) - 0.015 x hours
The Widmark estimate. Ethanol mass over body water volume, less the standard hourly clearance.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| BAC | Estimated content | number | Grams of ethanol per decilitre of blood. |
| n | Standard drinks | count | Count of standard drinks, fourteen grams each. |
| rho | Water fraction | number | Share of body mass that is water, 0.68 men / 0.55 women. |
| W | Body mass | number | Body weight in kilograms. |
| t | Hours | number | Hours since the first drink. |
What Each Symbol Means
BACnumber
Estimated content
Grams of ethanol per decilitre of blood.
ncount
Standard drinks
Count of standard drinks, fourteen grams each.
rhonumber
Water fraction
Share of body mass that is water, 0.68 men / 0.55 women.
Wnumber
Body mass
Body weight in kilograms.
tnumber
Hours
Hours since the first drink.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate blood alcohol content page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Blood Alcohol Content, filed under Health. Every number the guide produces comes from substituting into this one line.