Half-Life Plotter

The elimination half-life is the time it takes for the amount of a compound in the body to fall by half. Most clinically relevant drugs — peptides included — follow first-order kinetics: the elimination rate is proportional to how much is present, so the decline is exponential rather than linear (Hallare & Gerriets, StatPearls). After one half-life 50% remains, after two 25%, after three 12.5%, and after 4–5 half-lives only 3–6% is left. This plotter applies that rule to every dose independently — each dose decays as dose × 0.5^(t/t½) — and sums the overlapping curves, a superposition that is mathematically exact for first-order elimination.

Why half-life shapes dosing intervals

The relationship between half-life and dosing interval determines the whole character of exposure. Dose more often than the compound clears and levels accumulate: with regular dosing, a plateau — steady state — is reached after roughly 4 to 5 half-lives, at which point elimination between doses balances the amount added and accumulation stops. This is why long-half-life peptides such as semaglutide (~1 week) are studied on weekly schedules but take about a month of dosing to reach their full plateau, while short-half-life peptides (minutes to hours) never accumulate at all — each dose is a discrete pulse that is gone before the next. The same arithmetic explains washout: after the final dose, roughly 94–97% is eliminated within 4–5 half-lives.

What the model leaves out

The chart is a teaching aid, not a pharmacokinetic simulation of any person. It assumes the full dose appears in the body instantly (no absorption phase, though subcutaneous injections absorb over hours), a single compartment (no distribution into tissues), and a half-life that never changes. It plots total milligrams, not plasma concentration — converting between the two requires the volume of distribution, which varies by compound and person. Published half-lives are population averages; individual clearance differs with kidney and liver function, body composition, and more. Use the shapes to understand accumulation and washout as concepts, not to predict levels — and note that nothing here evaluates whether any dose or schedule is appropriate (see the medical disclaimer).

What is "steady state"? When a compound is dosed at regular intervals, each new dose adds to what remains of the previous ones. Early on, the amount eliminated between doses is smaller than the amount added, so levels climb. Eventually elimination (which scales with concentration under first-order kinetics) catches up to the input rate, and the curve settles into a repeating peak-and-trough pattern. Pharmacology references place this at approximately 4 to 5 half-lives of regular dosing.

Why does the curve keep climbing at first? Because the dosing interval is shorter than the time needed to eliminate a full dose. If a compound with a 7-day half-life is dosed weekly, half of each dose is still present when the next arrives, so the doses stack. The shorter the interval relative to the half-life, the higher the eventual plateau relative to a single dose.

Does the chart show real blood concentrations? No. It plots total milligrams remaining in a one-compartment model with instantaneous absorption. Real pharmacokinetics involve an absorption phase, distribution into tissues (volume of distribution), and individual variation in clearance, so measured plasma concentrations differ from these idealized curves. The shape — accumulation toward a plateau — is the educational point, not the absolute numbers.

How long until a compound is effectively gone after the last dose? Under first-order elimination, roughly 94–97% of a compound is eliminated after 4 to 5 half-lives, at which point levels typically fall below any meaningful concentration. For a half-life of 5 days, that is about 3 to 4 weeks; for a half-life of 30 minutes, a few hours.