Half-Life and Pharmacokinetics Calculator

Calculate plasma half-life, time to steady state, and accumulation ratio for hormones and drugs.

Molecule

Custom half-life (hours) (hours)

Initial concentration C0 (any units)

Time elapsed t (hours) (hours)

Dosing interval τ (hours) (hours)

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Why Hormone Half-Lives Span Five Orders of Magnitude

Half-life is set by clearance mechanism and protein binding, and hormones differ enormously in both.

Hormone	Half-life	Reason
Adrenaline	1–3 minutes	Rapid enzymatic degradation
Insulin	5–6 minutes	Hepatic first-pass extraction
Cortisol	66 minutes	Partly protein-bound
Thyroxine (T4)	7 days	99.97% protein-bound

Protein binding is the dominant factor. Only free hormone is cleared, so thyroxine's near-total binding to TBG makes it a circulating reservoir rather than a rapidly turned-over signal. Adrenaline, unbound and enzymatically destroyed, disappears in minutes.

This maps directly onto function. Fast signals need fast clearance or they cannot be switched off; sustained set-points benefit from long half-lives that buffer against fluctuation.

Clinical Consequences of Long Half-Life

T4's seven-day half-life explains several practical points at once. A missed dose changes concentration by only about 9%, so occasional non-adherence is well tolerated. But steady state takes five half-lives — roughly six weeks, which is why TSH should not be rechecked sooner after a dose change.

Half-lives elapsed	Fraction of steady state reached
1	50%
2	75%
3	87.5%
5	96.9%

The same arithmetic runs in reverse for washout, which is why stopping T4 takes weeks to show its full effect.

Why Measured Half-Life Can Mislead

Many hormones are secreted in pulses, so a single measurement reflects where in the pulse the sample fell rather than the average. Growth hormone and LH are the clearest cases — a single low GH result means little without provocation testing.

Cortisol adds a circadian layer: its concentration varies several-fold across the day, so a level is uninterpretable without the sampling time. Half-life describes elimination, not the secretion pattern that determines what is actually in the blood.

Worked Examples

Example 1: Cortisol t½=66min: C0=100, t=4hr

Ct=100×e^(-0.628×4)

Result: Ct=8.2 — 4hr=3.6 half-lives, <10% remains

Morning cortisol cleared by evening

Example 2: T4 t½=7 days: missed dose

C(24hr)=100×e^(-0.00412×24)

Result: C=90.7% — minimal change in 1 day

Safe to take missed dose next day (long t½)

Example 3: Why TSH is rechecked at six weeks

T4 half-life 7 days, dose increased

Result: Steady state at about 5 half-lives

Testing at two weeks captures a concentration still climbing toward its new plateau, risking an unnecessary further dose change.

Example 4: Why a single GH level is uninformative

Pulsatile secretion

Result: Provocation testing required

Growth hormone is released in bursts. A trough sample looks deficient and a peak sample looks normal, regardless of true status.

Common Mistakes

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Interpreting a single hormone level without timing

Pulsatile secretion and circadian rhythm mean one measurement may reflect timing rather than average concentration. Cortisol and growth hormone are the clearest examples.

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Rechecking TSH too soon after a dose change

Steady state takes about five half-lives, which for thyroxine is six weeks. Earlier testing reflects a concentration still rising.

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Forgetting that only free hormone is cleared

Protein binding is the main determinant of half-life. Thyroxine is 99.97% bound, which is why it persists for days.

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Assuming a missed dose matters equally for all hormones

A missed T4 dose shifts concentration about 9%. For a hormone with a minutes-long half-life the equivalent gap would be complete loss.

Frequently Asked Questions

Steady state concentration?

After 4-5 half-lives: plasma level reaches steady state (input=output). Accumulation ratio = 1/(1-e^(-k×τ)). Short t½ relative to dosing interval: less accumulation. Continuous infusion: reaches SS in 4-5 t½ regardless.

First-order kinetics?

Most hormones/drugs: concentration decreases exponentially (first-order). Constant half-life regardless of concentration. Zero-order (some drugs at high doses, ethanol): constant amount eliminated per time, t½ increases with concentration.

Why does thyroxine have such a long half-life?

Because it is 99.97% bound to plasma proteins and only free hormone is cleared. The bound fraction acts as a circulating reservoir.

How long until a hormone reaches steady state?

About five half-lives regardless of dose. For thyroxine that is roughly six weeks, which sets the interval for rechecking TSH.

Does missing one thyroxine dose matter?

Concentration falls only about 9% over a day, so occasional missed doses are well tolerated — a direct consequence of the long half-life.

Why can a single hormone measurement mislead?

Pulsatile secretion and circadian variation mean one sample may not represent average concentration. Timing and provocation testing are often required.