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Steady-State Concentration Calculator (Css = F·Dose / CL·τ)

· Last updated：2026-08-02

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

Estimate the average steady-state plasma concentration under repeated fixed-interval dosing: Css,avg = (F · Dose) / (CL · τ), where F is bioavailability (1 for IV, <1 for oral), CL is clearance, and τ is the dosing interval. If t½ and Vd are also provided, computes the one-compartment IV-bolus accumulation index Rac = 1/(1-e^(-kτ)), peak Cmax,ss, trough Cmin,ss, and time to ~94%/~97% of steady state (4/5 half-lives). Valid only for linear pharmacokinetics with fixed dose and interval — NOT for Michaelis-Menten drugs or non-linear kinetics. 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

Estimate average steady-state concentration for repeated fixed-interval dosing with Css,avg = F·Dose / (CL·τ). Add half-life and volume of distribution to calculate the one-compartment IV-bolus accumulation index, steady-state peak, trough, and time to approximately 94% or 97% of steady state.

When to use

  • Estimate average steady-state concentration from dose, bioavailability, clearance, and dosing interval.
  • Compare how changes in dose, clearance, or dosing interval affect Css,avg under linear pharmacokinetics.
  • Estimate steady-state peak and trough concentrations when half-life and volume of distribution are available.

How it works

  1. 1Enter the dose per interval, bioavailability, clearance, and dosing interval.
  2. 2The calculator computes Css,avg using F·Dose / (CL·τ).
  3. 3Optionally enter half-life and volume of distribution to calculate k, Rac, Cmax,ss, and Cmin,ss.
  4. 4Review the JSON result, including the estimated time to reach about 94% and 97% of steady state when the required inputs are provided.

Use cases

  • Pharmacokinetic calculations for repeated oral or IV dosing.
  • Therapeutic drug monitoring preparation and concentration estimates.
  • Teaching and checking steady-state, accumulation, peak, and trough relationships.

Examples

1. Estimate average theophylline concentration

Clinical pharmacology student

Background

A repeated oral theophylline regimen uses a 200 mg dose every 8 hours, with bioavailability of 0.9 and clearance of 2.8 L/h.

Problem

Calculate the average steady-state concentration without estimating peak or trough values.

How to use

Enter dose 200 mg, bioavailability 0.9, clearance 2.8 L/h, and interval 8 h. Leave half-life and Vd blank.

Dose: 200 mg; F: 0.9; CL: 2.8 L/h; τ: 8 h; decimal places: 4

Outcome

The calculator returns Css,avg = 8.0357 mg/L and indicates that peak and trough values were not calculated because half-life and Vd were not provided.

2. Calculate IV steady-state peak and trough

Pharmacokinetics learner

Background

An IV regimen gives 100 mg every 12 hours. Clearance is 5 L/h, volume of distribution is 50 L, and half-life is 6.93 hours.

Problem

Estimate average concentration, accumulation, steady-state peak, and steady-state trough.

How to use

Enter dose 100 mg, bioavailability 1, clearance 5 L/h, interval 12 h, half-life 6.93 h, and Vd 50 L.

FAQ

What does Css,avg mean?

Css,avg is the average plasma concentration at steady state during repeated fixed-interval dosing.

Which inputs are required?

Dose, bioavailability, clearance, and dosing interval are required.

Do I need half-life and Vd?

No. They are optional for Css,avg, but both are needed for the peak, trough, and accumulation estimates.

What model does this calculator use?

It uses linear pharmacokinetics with a fixed dose and interval. Peak and trough estimates use a one-compartment IV-bolus model.

Can it be used for nonlinear drugs?

No. It is not valid for Michaelis-Menten or other nonlinear pharmacokinetics.

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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Dose: 100 mg; F: 1; CL: 5 L/h; τ: 12 h; t½: 6.93 h; Vd: 50 L; decimal places: 4

Outcome

The result is Css,avg = 1.6667 mg/L, Rac = 1.4292, Cmax,ss = 2.8584 mg/L, and Cmin,ss = 0.8604 mg/L.