Trough Level Estimator (Cmin = Cmax · e^(-kτ)) | Online Free Tool

Trough Level Estimator (Cmin = Cmax · e^(-kτ)) | Online Free Tool | Elysia Tools

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

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

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

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

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

Key facts

Overview

When to use

How it works

Use cases

Examples

1. One half-life from peak to next dose

2. Longer interval produces a deeper trough

FAQ

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