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Calculate the drug accumulation index R under repeated fixed-interval dosing with linear first-order elimination: R = 1 / (1 - e^(-kτ)), where k = ln2 / t½ and τ is the dosing interval. R is the ratio of the steady-state peak concentration to the peak concentration after the first dose — it quantifies how much the body burden rises at steady state versus a single dose. For example, dosing once per half-life (τ = t½) gives R = 2. The term e^(-kτ) is the fraction of peak concentration remaining at the end of one interval. Valid only for linear first-order elimination with fixed dose and interval — NOT for Michaelis-Menten drugs (phenytoin) or non-linear kinetics. Not medical advice.
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Calculate the drug accumulation index R for repeated fixed-interval dosing with linear first-order elimination. Enter the elimination half-life and dosing interval to calculate R, the ratio of the steady-state peak concentration to the peak after the first dose, along with k and the fraction remaining between doses.
Background
A student wants to verify the standard accumulation result when the dosing interval matches the elimination half-life.
Problem
Calculate R for a half-life of 8 hours and a dosing interval of 8 hours.
How to use
Enter 8 for Half-life t½, 8 for Dosing interval τ, and select 4 decimal places.
{"halfLife":8,"interval":8,"decimalPlaces":4}Outcome
The calculator returns R = 2, k = 0.0866 h⁻¹, and a fraction remaining of 0.5.
Background
An analyst is comparing accumulation at an interval that is three times the known 8-hour half-life.
Problem
Determine the accumulation index for a 24-hour dosing interval.
How to use
Enter 8 for Half-life t½, 24 for Dosing interval τ, and select 4 decimal places.
{"halfLife":8,"interval":24,"decimalPlaces":4}R is the ratio of the steady-state peak concentration to the peak concentration after the first dose.
A positive half-life in hours and a positive dosing interval in hours are required.
k is the first-order elimination rate constant, calculated as ln2 divided by the half-life, and expressed in h⁻¹.
The accumulation index is R = 2, and the fraction remaining at the end of the interval is 0.5.
No. It is valid only for linear first-order elimination with fixed doses and intervals, not nonlinear kinetics such as Michaelis-Menten elimination.
Outcome
The calculator returns R = 1.1429, k = 0.0866 h⁻¹, and a fraction remaining of 0.125.