The halflife of a substance is the time taken for half of the dose to be eliminated or metabolised.
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The halflife of a substance, usually denoted by
t_{1/2}, is the time taken for half of the dose to be eliminated or metabolised. The shorter the halflife of a
drug, the quicker it is eliminated. The half life of a drug can be influenced by many individual factors, such as metabolic, and genetic.
When the drug concentration is around 5% it is said to be negligible, therefore around 4 or 5 half lives must elapse until the drug is eliminated.*
*This is not to say the drug cannot be detected via drug test.
Drug tests will be able to identify trace amounts of a drug even a few days after it has been consumed.
[top]Calculating halflife
T half life  amount of drug  3hr HL  8hr HL  1850hr HL  46day HL 

  morphine  MDMA  Clonazepam  Fluoxetine 
0  100%  0  0  0  0 
1  50%  3  8  1850  46 
2  25%  6  16  36100  812 
3  12.5%  9  24  54150  1218 
4  6.25%  12  32  72200  1624 
5  3.125%  15  40  90250  2030 
  15 hours  40 hours  ~4 to 10 days  34 weeks 
The above table shows how long it would take to eliminate 4 different
drugs from the body.
Opiates and
stimulants tend to have shorter half lives then
benzodiazepines, although there are many exceptions. Anti
depressants and antipsychotics tend to have very long half lives.
An example using dosages instead of percent: if the halflife of a drug is, say, 4 hours and you ingest 1g (1,000mg), then after 4 hours you'll have 500mg, a half of 1g, in your system, after 8 hours you'll have 250mg, a half of 500mg, and after 12 hours you'll have 125mg, etc.
[top]Mathematics
More formally, the total concentration of a substance in the body can be calculated by
C_{t}=C_{0} e^{kt}
Where:
 C_{t} is the concentration at time t
 C_{0} is the initial concentration
 k is the elimination constant, given by k= log(2)/t_{1/2}. [Where log is taken to base e, giving a value of log(2)=0.693. The value 0.7 can be used without a great deal of loss of precision]
[top]Important things to know about the halflife model
There are several important points to me made here. Firstly, this is a mathematical model, and pharmacological
elimination kinetics do not necessarily follow it exactly, although for a large range of substances at a large range of doses it is a good approximation [needs referencing  D]. Some drugs,
alcohol and shortacting
barbiturates more closely follow zeroth order elimination profiles, i.e. a fixed amount of the drug is metabolised in a unit of time until the drug is totally elimiated. An example of this is that alcohol is metabolised at roughly the rate of one unit (10mg of
ethanol) per hour.
Secondly, halflives can vary wildly between different people. This is especially true, for instance, if an enzyme is involved in metabolism, and the quantity of enzyme present in individuals varies according to genetics.
Thirdly, some drugs are metabolised into active metabolites. Indeed some
prodrugs are not pharmacologically active themselves, but are metabolised to pharmacologically active agents. An example of this is
heroin which is metabolised to
morphine. Other drugs such as the
benzodiazepine chlordiazepoxide (
Librium) have relatively short halflives themselves but have metabolites with much longer halflives.
There are other complications, such as when there are different metabolic pathways to different metabolites, and this is the subject of
pharmacokinetics.