The relationship between the half life
and the elimination rate constant

When the drug elimination is a first-order process, the plasma drug concentration can be described by the following equation:

After one half life Cp will be equal to 1/2 Cp0

By rearrangement, and determining the anti-In of both sides of the equation:

t1/2 =

0.639

k

OR

k =

0.639

t1/2
Cp= Cp0 e-kt

1

2
Cp0 = Cp0 e-kt1/2

1 Cp0

2 Cp0
= e -kt 1/2
-ln 2 = -kt1/2
-0.693 = -kt1/2