# Trough Level Estimator (Cmin = Cmax · e^(-kτ)) Predict the trough concentration Cmin from a measured peak concentration Cmax during therapeutic drug monitoring (TDM): Cmin = Cmax · e^(-kτ), where k = ln2 / t½ and τ is the time from the peak to the next dose. Inputs are the measured peak, the elimination half-life, and the dosing interval. Also reports the fraction of the peak remaining at the trough and the peak-to-trough drop. This tool takes a measured Cmax (the TDM workflow), unlike drug-half-life-dose (which derives C0 from Dose/Vd) and dosing-interval-designer (which outputs a dimensionless peak/trough ratio, not an absolute concentration). Valid for one-compartment first-order elimination with the peak measured post-distribution. Not medical advice. > Canonical page: https://elysiatools.com/en/tools/trough-level-estimator - **Category:** Health - **Keywords:** trough concentration, Cmin, peak concentration, Cmax, TDM, therapeutic drug monitoring, half-life, dosing interval, pharmacokinetics, pk, drug, medicine ## Overview Trough Level Estimator predicts the trough concentration Cmin from a measured peak Cmax, elimination half-life, and time from the peak to the next dose. It uses Cmin = Cmax · e^(-kτ), where k = ln2 / t½, and reports the remaining peak fraction and peak-to-trough drop for a one-compartment, first-order elimination model. ## Inputs - **Measured peak Cmax (mg/L)** (number): Measured peak plasma concentration (post-distribution). Must be positive. - **Half-life t½ (h)** (number): Elimination half-life. Must be positive. - **Time from peak to next dose τ (h)** (number): Dosing interval — time from the measured peak to the next dose. Must be positive. - **Decimal Places** (number) ## When to use - Estimate a post-dose trough concentration from measured therapeutic drug monitoring results. - Assess how a dosing interval compares with the drug's elimination half-life. - Quantify the fraction of the measured peak remaining and the concentration drop before the next dose. ## How it works - Enter the measured peak concentration Cmax in mg/L. - Enter the elimination half-life t½ and the time from the peak to the next dose τ, both in hours. - The tool calculates k = ln2 / t½ and applies Cmin = Cmax · e^(-kτ). - The JSON result includes Cmin, elimination rate constant k, fraction remaining, peak-to-trough drop, and the calculation method. ## Use cases - Therapeutic drug monitoring calculations using a measured post-distribution peak. - Comparing trough depth for different times from peak to the next dose. - Checking concentration retention and peak-to-trough changes in pharmacokinetic exercises. ## Frequently asked questions ### What inputs does the estimator require? It requires a positive measured peak Cmax, a positive half-life, and a positive time τ from the peak to the next dose. ### What units are used for the result? Cmax, Cmin, and the peak-to-trough drop are reported in mg/L. Half-life, τ, and k use hours and h⁻¹. ### What model does this calculation use? It uses one-compartment first-order elimination with the peak measured after distribution. ### What does the fraction remaining mean? It is the proportion of the measured peak concentration expected to remain at the trough. ### Can this tool replace clinical judgment? No. It is a pharmacokinetic estimation tool and is not medical advice. ## Related tools - [A-a Gradient (Alveolar-Arterial O₂)](https://elysiatools.com/en/tools/a-a-gradient-calculator): Calculate the alveolar-arterial O₂ gradient to distinguish hypoxemia causes. PAO₂ = FiO₂×(P_atm−47) − PaCO₂/0.8; A-a = PAO₂ − PaO₂. Normal ≈ (Age+10)/4. Elevated → V/Q mismatch, shunt, diffusion impairment. 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