tmax and t1/2 or peak plasma time and elimination half-life of a drug often cause confusion. Frequently these terms tmax and t1/2 are used to understand many equations or topics in biopharmaceutics. Differences between tmax and t1/2 are:

**1. Definition of Peak plasma time or time for peak plasma concentration or time of peak plasma concentration or t**_{max} and t_{1/2}

_{max}and t

_{1/2}

The t _{max} (time of peak plasma concentration) is the time required to reach maximum drug concentration in the plasma after drug administration. t _{max} is peak plasma time. Simply, t _{max} is the time to reach C _{max}. C _{max} is the maximum (peak) plasma drug concentration attained after the oral administration of the drug. Also, at t _{max}, the drug absorption rate exactly equals the drug elimination rate.

On the other hand, t _{1/2} (elimination half-life) is the time required to decrease the drug concentration within the body by one-half during elimination. In other words, t _{½ }(elimination half-life) is the time required for the amount or concentration of a drug to decrease by one-half [1]. In pharmacokinetic, elimination half-life, t _{1/2} refers to the time required for half the dose of drug administered to be removed from the body.

2. The **t _{max}** is dependent on the elimination rate (k) and absorption rate constant (ka). while

**t**is dependent on the elimination rate (k) and volume of distribution (Vd).

_{1/2}3. At tmax, the concentration of a drug is in peak. While at t _{1/2}, the concentration of a drug may or may not in peak.

**4. Equations for tmax and t1/2**

The equation for calculating t _{max} (peak plasma time):

**𝑡 𝑚𝑎𝑥** = ln (𝑘𝑎 / 𝑘) / (𝑘𝑎−𝑘)

= 2.303 log (𝑘𝑎 / 𝑘)/ (𝑘𝑎−𝑘)

On the other hand, the equation for calculating t½:

t½ = 0.693 × (Vd /CL)

Where, Vd = Volume of distribution and CL = Clearance.

5. t _{max} is peak plasma time. On the other hand, t _{1/2} is the elimination half-life.

6. t _{max} (peak plasma time) is a rough marker of the average rate of drug absorption. On the other hand, t _{1/2} is an indicator of how fast a drug is eliminated from the body.

**Summary of the difference between tmax and t1/2**

t_{max} | t_{1/2} | |

1. | The time of peak plasma concentration is the time required to reach maximum drug concentration in the plasma after drug administration. | t _{1/2} (elimination half-life) is the time required to decrease the concentration of a drug within the body by one-half during elimination. |

2. | The t max is dependent on the absorption rate constant (ka) and elimination rate (k). | t _{1/2} is dependent on the volume of distribution (Vd) and elimination rate (k). |

3. | At t _{max}, the drug concentration is in peak. | At t _{1/2}, drug concentration may or may not in peak. |

4. | Equation for calculating t _{max}:
𝑡 𝑚𝑎𝑥 = ln (𝑘𝑎 / 𝑘) / (𝑘𝑎−𝑘) = 2.303 log (𝑘𝑎 / 𝑘)/ (𝑘𝑎−𝑘) | Equation for calculating t _{½}:
t |

5. | It is Peak plasma time. | It is an elimination half-life. |

6. | It is a rough marker of the average rate of drug absorption. | The half-life is a useful indicator of how fast a drug is removed from the body. |

7. |

This article may provide the answer to the following questions:

- First of all, the difference between tmax and t1/2.
- Second, the difference between the time of peak plasma concentration (tmax) and elimination half-life (t1/2).
- Third, what is the difference between peak plasma time and elimination half-life?
- Finally, what is peak plasma time or time for peak plasma concentration?

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**References**

- Shargel, L., & McGraw-Hill Education. (2016).
*Applied biopharmaceutics & pharmacokinetics*. New York: McGraw-Hill Education.