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Trough Level Estimator (Cmin = Cmax · e^(-kτ))

· Last updated：2026-08-04

This tool is for informational purposes only and does not constitute medical, financial, or legal advice; consult a qualified professional for advice.

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.

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Written by the Elysia Tools team

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category
Health
Input types
number
Output type
json
Sample coverage
4
API ready
Yes

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.

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

  1. 1Enter the measured peak concentration Cmax in mg/L.
  2. 2Enter the elimination half-life t½ and the time from the peak to the next dose τ, both in hours.
  3. 3The tool calculates k = ln2 / t½ and applies Cmin = Cmax · e^(-kτ).
  4. 4The 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.

Examples

1. One half-life from peak to next dose

Clinical pharmacokinetics learner

Background

A measured peak concentration is 15 mg/L, the elimination half-life is 8 hours, and the next dose is 8 hours after the peak.

Problem

Estimate the trough concentration after exactly one half-life.

How to use

Enter cmax = 15, halfLife = 8, tau = 8, and decimalPlaces = 4.

{"cmax":15,"halfLife":8,"tau":8,"decimalPlaces":4}

Outcome

The estimated Cmin is 7.5 mg/L. Half of the peak remains, with a peak-to-trough drop of 7.5 mg/L.

2. Longer interval produces a deeper trough

TDM analyst

Background

The measured peak is 15 mg/L and the half-life is 8 hours, but the next dose is 12 hours after the peak.

Problem

Estimate the lower trough expected after an interval of 1.5 half-lives.

How to use

Enter cmax = 15, halfLife = 8, tau = 12, and decimalPlaces = 4.

FAQ

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.

Hub

Pharmacokinetic Teaching and Dose-Model Checks

Explore pharmacokinetic formulas, model assumptions, and result consistency for teaching or QA without giving medication dosing or clinical advice.

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{"cmax":15,"halfLife":8,"tau":12,"decimalPlaces":4}

Outcome

The estimated Cmin is 5.3033 mg/L. About 35.36% of the peak remains, with a peak-to-trough drop of 9.6967 mg/L.