DrugTheGuide
Pharmacokinetics

First-order kinetics

dC/dt = −ke × C

Drug elimination in which the rate of elimination is directly proportional to the current drug concentration. A constant fraction of drug is eliminated per unit time — the half-life is constant and dose-independent. Most drugs follow first-order kinetics at therapeutic concentrations.

Core equations

Differential form
dC/dt = −ke × C
Rate of change of concentration is proportional to current concentration C
Integrated form (IV bolus)
C(t) = C₀ × e−ke × t
Exponential decay from initial concentration C₀
Half-life (constant)
t½ = 0.693 / ke
Independent of dose or starting concentration
Fraction remaining after n half-lives
f = (0.5)n
After 4 half-lives: 6.25%; after 5: 3.125% remains

The ke is related to clearance (CL) and volume of distribution (Vd) by ke = CL / Vd. See the elimination rate constant glossary entry for derivations and clinical examples. Use the half-life calculator to compute t½ from ke or clearance values.

First order kinetics is the dominant elimination model for the vast majority of drugs used in clinical practice. Under first-order conditions, a constant fraction of the drug is removed per unit time, which means doubling the dose produces a predictable doubling of the steady-state concentration — a property called dose proportionality or linear pharmacokinetics. This predictability is the foundation of rational dose adjustment: if a patient needs 50% higher drug levels, the clinician can increase the dose by 50%. In contrast, drugs following zero-order kinetics (e.g., phenytoin near its therapeutic range) lack this proportionality, making dose adjustment far more dangerous. The NCBI multiple-dose pharmacokinetics chapter ↗ and Drugs.com ↗ provide elimination kinetics data for approved medications. For regulatory context, the FDA NCA guidance ↗ describes how first-order parameters are estimated in drug development studies.

First-order vs zero-order kinetics

PropertyFirst-orderZero-order
Elimination rate Proportional to C (varies) Constant (independent of C)
Fraction eliminated/time Constant Varies (decreases as C falls)
Amount eliminated/time Varies (decreases as C falls) Constant
Half-life Constant (dose-independent) Increases as concentration increases
C vs time plot Exponential decay Linear decay
log(C) vs time Straight line (ln-linear) Curved
Common drugs Most drugs at therapeutic doses Phenytoin (high dose), ethanol, salicylate overdose

Clinical relevance

Dose proportionality

For first-order drugs, doubling the dose doubles the steady-state concentration. This predictability is essential for dose titration. Zero-order drugs lack this predictability — a small dose increase can cause a large concentration rise.

Time to steady state

4–5 half-lives to steady state on regular dosing, regardless of dose or interval. A drug with t½ = 4 h reaches steady state in ~20 h; one with t½ = 72 h takes ~15 days. See the steady-state glossary entry.

Washout after stopping

After stopping a first-order drug, 97% is eliminated in 5 half-lives. Relevant for drug interactions, switching medications, and pre-operative management. Drugs with long half-lives (amiodarone t½ ~40–55 days) have very slow washout.

Accumulation prediction

Accumulation ratio = 1 / (1 − e^(−ke×τ)) where τ is the dosing interval. For a drug given at τ = t½, the accumulation ratio is ~2 (trough ≈ half of Cmax at steady state).

Frequently asked questions

What is first-order kinetics in pharmacokinetics?
First-order kinetics: the rate of drug elimination is proportional to the current concentration — dC/dt = −ke × C, where ke is the elimination rate constant. The integrated equation gives C(t) = C₀ × e−ke×t. Because a constant fraction is eliminated per unit time, the half-life (t½) is constant (t½ = 0.693/ke) regardless of starting dose. Most drugs at therapeutic doses follow first-order kinetics. See NCBI StatPearls — basic pharmacokinetics ↗ for derivation.
How does first-order kinetics differ from zero-order kinetics?
First-order: rate ∝ concentration; constant fraction eliminated per unit time; constant half-life. Zero-order: rate = constant; constant amount eliminated per unit time; variable half-life (increases with concentration) — occurs when elimination pathway is saturated. Key zero-order examples: phenytoin at high doses ↗ (saturable CYP2C9 metabolism — Michaelis-Menten), ethanol (saturated alcohol dehydrogenase, ~10 mL/h elimination rate), salicylate in overdose. See elimination rate constant and PK basics guide for full comparison.
What drugs are known exceptions to first-order kinetics?
Key clinical exceptions: Phenytoin — Michaelis-Menten kinetics; at doses near Vmax (Km for CYP2C9 is ~4–5 mg/L), small dose increases → large level increases; use TDM and consult NCBI pharmacotherapy resource ↗. Ethanol — ADH is saturated at all drinking concentrations (~10 mL ethanol/h). High-dose aspirin/salicylate — glycine and glucuronide conjugation pathways saturate above ~1 g/day. High-dose IV methotrexate — tubular secretion saturable. See the narrow therapeutic index glossary entry for why saturable kinetics increases toxicity risk.
How many half-lives does it take to reach steady state?
For first-order kinetics, steady state is reached in ~4–5 half-lives (97% at 5 × t½). The half-life alone determines time to steady state — not the dose or dosing interval. This is critical clinically: a drug with t½ = 20 h (e.g. methadone) takes ~4 days to reach steady state; a drug with t½ = 2 h (e.g. ibuprofen) reaches steady state in ~10 h. See the steady-state glossary entry and half-life calculator tool. For loading dose calculation to rapidly achieve target levels, see loading dose ↗.
How does first-order kinetics relate to bioavailability and volume of distribution?
For a one-compartment oral model with first-order absorption and elimination: C(t) = (F·D·ka)/(Vd·(ka−ke))·(e−ke·t − e−ka·t). The AUC = F·D / CL; Cmax depends on both ka and ke; Vd scales peak concentration. See the one-compartment model glossary entry and the half-life calculator for interactive simulation. The PK basics guide covers ADME in full context.