How many half-lives to reach steady state?

5 half-lives: 97% of steady-state; 4 half-lives: 94%. This applies to both reaching steady state and elimination (97% of drug eliminated after 5 t₁/₂).

How is steady-state concentration calculated for multiple dosing?

Css,avg = F × Dose / (CL × τ) where F = bioavailability, CL = clearance (L/hr), τ = dosing interval (hr). Css,max = (F × Dose / Vd) / (1 − e^(−ke×τ)).

Drug Half-Life & Multi-Compartment Model Calculator

Constant	Symbol	Value	Units
Speed of light	c	2.99792458×10⁸	m/s
Planck's constant	h	6.62607015×10⁻³‴	J·s
Boltzmann constant	kʙ	1.380649×10⁻²³	J/K
Avogadro's number	Nₐ	6.02214076×10²³	mol⁻¹
Gravitational constant	G	6.6743×10⁻¹¹	N·m²/kg²
Gas constant	R	8.31446	J/(mol·K)
Elementary charge	e	1.602176634×10⁻¹⁹	C
Electron mass	mₑ	9.1093837015×10⁻³¹	kg
Proton mass	mₚ	1.67262192369×10⁻²⁷	kg
Fine-structure constant	α	7.2973525693×10⁻³	dimensionless

Formula Definitions

The Drug Half-Life & Multi-Compartment Model Calculator works by applying a well-defined formula to the values you enter. Understanding the formula behind the calculation helps you interpret the result and check that your inputs are correct. Below we break down the key components that drive the Drug Half-Life.

The core formula used by this calculator is:

Result = f(physical quantities, constants, conditions)

Each variable in the formula has a specific meaning:

physical quantities — Measured values with units entered into the Drug Half-Life.
constants — Physical or chemical constants (e.g. CODATA values, gas constant, Avogadro's number).
conditions — Temperature, pressure, concentration, or environmental state of the system.
Result — Computed physical or chemical quantity with associated units.

Note: Compare results with standard reference values or published experimental data.

How to Use This Calculator

Enter the physical or chemical quantities. Enter the physical or chemical quantities with correct units into the Drug Half-Life & Multi-Compartment Model Calculator input fields.
Verify conditions. Verify or adjust the conditions such as temperature, pressure, concentration, or environmental parameters.
Apply the scientific formula. Press Calculate to apply the scientific formula or physical law.
Compare with reference values. Review the result and compare it with standard reference values, CODATA constants, or published experimental data.

Glossary and Definitions

Physical quantity: A measurable property of a physical system, expressed as a numeric value with units.
Constant: A fixed, well-defined value (e.g. a CODATA constant) used across scientific calculations.
Significant figures: The digits in a measurement that carry meaning, reflecting the precision of the instrument.
Reference value: A published standard or experimental value used to validate a calculated result.
Drug half-life calculator: A key concept referenced by the Drug Half-Life: Calculate drug concentration over time for one-, two-, and three-compartment pharmacokinetic models. Predict steady-state concentrations for multiple dosing.
Two compartment model: A key concept referenced by the Drug Half-Life: Calculate drug concentration over time for one-, two-, and three-compartment pharmacokinetic models. Predict steady-state concentrations for multiple dosing.
Steady state concentration: A key concept referenced by the Drug Half-Life: Calculate drug concentration over time for one-, two-, and three-compartment pharmacokinetic models. Predict steady-state concentrations for multiple dosing.
Multiple dosing PK: A key concept referenced by the Drug Half-Life: Calculate drug concentration over time for one-, two-, and three-compartment pharmacokinetic models. Predict steady-state concentrations for multiple dosing.

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