# Steady-State Concentration Calculator (Css = F·Dose / CL·τ) 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. > Canonical page: https://elysiatools.com/en/tools/steady-state-concentration - **Category:** Health - **Keywords:** pharmacokinetics, steady state, steady-state concentration, Css, accumulation, Cmax, Cmin, trough, peak concentration, bioavailability, clearance, dosing interval, drug monitoring, tdm, pk, drug ## 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. ## Inputs - **Dose per interval (mg)** (number): Dose administered at each interval. Must be positive. - **Bioavailability F** (number): Fraction of dose reaching systemic circulation. IV=1, oral<1. Range (0, 1\]. - **Clearance CL (L/h)** (number): Drug clearance in L/h. Must be positive. - **Dosing interval τ (h)** (number): Time between consecutive doses in hours. Must be positive. - **Half-life t½ (h, optional)** (number): Optional elimination half-life. Required for accumulation index and peak/trough. - **Volume of distribution Vd (L, optional)** (number): Optional Vd. Required with t½ for one-compartment peak/trough estimation. - **Decimal Places** (number) ## 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 - Enter the dose per interval, bioavailability, clearance, and dosing interval. - The calculator computes Css,avg using F·Dose / (CL·τ). - Optionally enter half-life and volume of distribution to calculate k, Rac, Cmax,ss, and Cmin,ss. - Review 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. ## Frequently asked questions ### 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. ## 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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