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Drug Half-Life Calculator

Applies first-order elimination kinetics to a drug's half-life: elimination rate constant, fraction and amount of a dose remaining after a given time, times to steady state and to 97% elimination, and, for repeated dosing, the accumulation ratio and the approach to steady state.

When to use

You know a drug's elimination half-life and want how much remains after some hours, how long washout or steady state takes, or how much a regular dosing interval causes accumulation.

Do not use when: Elimination is not first-order (saturable kinetics such as phenytoin or ethanol), active metabolites or multi-compartment distribution dominate the time course, or a dosing decision is being made; results are informational and not medical advice. For radioactive or chemical decay use half-life.

Formula

k = ln(2) / half_life_hours; fraction_remaining = e^(−k × hours_elapsed); amount_remaining_mg = dose_mg × fraction_remaining; percent_eliminated = 100 × (1 − fraction_remaining); time_to_steady_state = 5 × half_life_hours; time_to_eliminate_97_percent = ln(100 / 3) / k; accumulation_ratio = 1 / (1 − e^(−k × dosing_interval_hours)); fraction_at_steady_state = 1 − e^(−doses_taken × k × dosing_interval_hours)

One-compartment model with first-order (linear) elimination: each half-life removes half of what remains, so 50 / 75 / 87.5 / 93.75 / 96.9% is eliminated after 1–5 half-lives regardless of dose; the accumulation ratio assumes equal doses at fixed intervals with complete absorption. Results are informational only and not a substitute for clinical judgement or medical advice.

Inputs

Parameter	Type	Unit	Required	Description
`half_life_hours`	number	h	yes	Terminal elimination half-life in hours (minutes ÷ 60, days × 24). Range: > 0, ≤ 100000
`dose_mg`	number	mg	default 100	Amount of a single dose in mg (any unit works, outputs scale with it); the default 100 makes amounts read as percentages. Range: > 0, ≤ 10000000
`hours_elapsed`	number	h	no	Hours after the dose at which the remaining fraction is evaluated; defaults to one half-life. Range: ≥ 0, ≤ 1000000
`dosing_interval_hours`	number	h	no	Interval between repeated equal doses; enables the accumulation ratio and steady-state outputs. Range: > 0, ≤ 100000
`doses_taken`	integer		no	Number of doses given so far at that interval; reports the fraction of the steady-state level reached (needs dosing_interval_hours). Range: ≥ 1, ≤ 10000

Outputs

Output	Type	Unit	Description
`elimination_rate_constant_per_hour`	number	1/h	k = ln 2 / half-life.
`half_lives_elapsed`	number		hours_elapsed / half_life_hours.
`fraction_remaining`	number		e^(−k × hours_elapsed) = 0.5^(half-lives elapsed).
`amount_remaining_mg`	number	mg	dose_mg × fraction remaining.
`percent_eliminated`	number	%	100 × (1 − fraction remaining).
`time_to_steady_state_hours`	number	h	5 × half-life, the usual rule of thumb (96.9% of the plateau reached).
`time_to_eliminate_97_percent_hours`	number	h	ln(100/3) / k ≈ 5.06 half-lives, when 3% of a dose remains.
`accumulation_ratio`	number		R = 1 / (1 − e^(−k τ)): steady-state level relative to the first dose; only when dosing_interval_hours is given.
`fraction_at_steady_state_after_n_doses`	number		1 − e^(−n k τ); only when dosing_interval_hours and doses_taken are given.
`schedule`	list		Hours, percent remaining and amount remaining at 0–10 half-lives after a single dose.

Example

Half-life 6 h, 200 mg, 24 h later, every 12 h, 3 doses: {"half_life_hours":6,"dose_mg":200,"hours_elapsed":24,"dosing_interval_hours":12,"doses_taken":3} → {"elimination_rate_constant_per_hour":0.1155,"fraction_remaining":0.0625,"amount_remaining_mg":12.5,"percent_eliminated":93.75,"time_to_steady_state_hours":30,"accumulation_ratio":1.333,"fraction_at_steady_state_after_n_doses":0.9844,"time_to_eliminate_97_percent_hours":30.35}

Half-life 12 h, 500 mg, 36 h later: {"half_life_hours":12,"dose_mg":500,"hours_elapsed":36} → {"elimination_rate_constant_per_hour":0.0578,"half_lives_elapsed":3,"amount_remaining_mg":62.5,"percent_eliminated":87.5,"time_to_steady_state_hours":60}

GET https://tttkmbb.com/api/v1/calculate/drug-half-life?half_life_hours=6&dose_mg=200&hours_elapsed=24&dosing_interval_hours=12&doses_taken=3

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/drug-half-life (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/drug-half-life · Markdown: https://tttkmbb.com/medical/drug-half-life.md · JSON definition: https://tttkmbb.com/medical/drug-half-life.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="drug-half-life"
OpenAPI operationId: calculate_drug_half_life_kinetics
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

FAQ

Is a drug gone after 5 half-lives?

About 3.1% remains after 5 and 0.1% after 10 half-lives; whether that is negligible depends on the drug's potency and the reason for the washout.

Does a bigger dose take longer to clear?

Not with first-order kinetics: the fraction remaining depends only on time, so doubling the dose doubles the amount at every time point but not the half-life.

What does the accumulation ratio mean?

The steady-state peak (and trough) is R times the peak (or trough) after the first dose; dosing every half-life gives R = 2, dosing every 2 half-lives gives 1.33.

Related calculators

Half-Life Calculator — General half-life and decay calculator (radioactive or chemical).
Dose by Weight Calculator — Weight-based dose that feeds the amount.
Creatinine Clearance Calculator — Renal function that lengthens the half-life of renally cleared drugs.