Tool
Half-life calculator & visualizer
Enter a half-life and a dosing interval - see relative level over repeated equal doses, the accumulation ratio, and approximately how long steady state takes to reach. Arithmetic only, no mg or dose inputs.
Your numbers
How long the level takes to fall by half. Not a dose recommendation - a physical property of the compound and the person taking it.
How often an equal dose is repeated. This tool does not suggest a schedule - it only draws what a given interval would produce.
Level over repeated doses
Accumulation ratio
2x
steady-state peak ÷ one dose's own peak
~90% steady state
4
doses in, ≈558.1 h (23.25 d)
Half-life 168 h (7 d). Dosed every 168 h (7 d). Steady state (about 90%) is reached after roughly 4 doses, around 558.1 h (23.25 d) after the first dose. Accumulation ratio 2x: at steady state, the peak level after each dose is about 2 times one dose's own peak, and the trough between doses is about 1 times it.
- Elimination rate constant (k)
- 0.0041 per hour
- Steady-state peak(right after each dose)
- 2x
- Steady-state trough(right before the next dose)
- 1x
- ≈97% of steady state
- 849.9 h (35.41 d)
Accumulation ratio = 1 ÷ (1 − e^(−k·τ)), where k = ln(2) ÷ half-life and τ is the dosing interval. Time to steady state depends only on half-life, not on the interval - the same reason a rule of thumb like "about 4-5 half-lives" gets taught regardless of how often a dose repeats.
Results update in the address bar, so you can copy the link to save or share a calculation. Nothing is stored, and there is no account.
How the maths works
Half-life is the time it takes a level to fall by half. Under repeated equal dosing, that same number sets both how fast a dose disappears and how fast the level climbs toward a plateau.
1. One dose, decaying
First-order elimination means the level falls by the same fraction every hour, not the same amount - so it halves every half-life: 100% → 50% after one half-life → 25% after two → 12.5% after three, and so on. As a formula, level = 100% × e^(−k·t), where k = ln(2) ÷ half-life.
2. Repeated doses stack
Give an equal dose every τ (tau) hours, and each new dose adds its own decaying 100%-peak on top of whatever is left from every earlier dose. Early on the doses barely overlap. Eventually what decays between doses equals what the next dose adds, and the peaks and troughs stop climbing - that is steady state.
3. The accumulation ratio
At steady state, the peak right after each dose is a fixed multiple of a single dose's own peak:1 ÷ (1 − e^(−k·τ)). Dose exactly one half-life apart and that multiple is exactly 2. Space doses out much further than the half-life and it drops toward 1 - almost no accumulation. Pack doses in much closer together than the half-life and it climbs well past 2.
Common questions
What does this tool actually calculate?
Arithmetic on two numbers you type in: a half-life and a dosing interval. It plots relative level as a percentage of one dose's own peak, assuming simple first-order elimination and equal repeated doses - the same model used to teach the "4-5 half-lives to steady state" rule of thumb. It does not know what compound you have, what dose you take, or whether any schedule is appropriate.
What is the accumulation ratio?
How much higher the steady-state peak is than the peak from a single dose alone: 1 ÷ (1 − e^(−k·τ)), where k = ln(2) ÷ half-life and τ (tau) is the dosing interval. Dosing exactly one half-life apart gives a ratio of 2. Dosing much slower than the half-life gives a ratio close to 1 - almost no accumulation. Dosing much faster gives a much larger ratio.
How is "time to steady state" calculated?
As the time for the peak-to-peak envelope to reach a given fraction of its eventual steady-state value, using the same exponential time constant as single-dose elimination: t = −ln(1 − fraction) × half-life ÷ ln(2). At 50% that is exactly one half-life; at 90% about 3.3 half-lives; at 97% about 5. This is why steady state is commonly described in half-lives, not in doses or days - it does not depend on the dosing interval.
How do I calculate half-life in Excel?
Build it from LN, EXP and POWER - Excel has no dedicated half-life function. To find the amount left after a given time from a known half-life: =start*0.5^(time/half_life). To find the half-life itself from two measured amounts at two times: =(time2-time1)*LN(0.5)/LN(amount2/amount1). With a full decay dataset, plot LN(amount) against time and take half-life = LN(2)/ABS(slope), where slope comes from Excel's SLOPE function or a linear trendline.
Why is there no mg or dose input?
Because the shape of this curve - the accumulation ratio, the time to steady state - depends only on half-life and dosing interval, never on how large the dose is. Adding a dose amount would not change any number this tool reports; it would only invite treating the output as a personal dosing plan, which it is not.
Where do the preset half-life values come from?
Each preset is the elimination half-life stated in that drug's current FDA-approved prescribing information on DailyMed, fetched and cited on this page. They describe the approved product, not any compounded or research-labelled version sold under the same name.
Is this medical or dosing advice?
No. It performs arithmetic on the numbers you enter and states the standard first-order elimination model behind that arithmetic. It does not recommend a dose, an interval, or a schedule, and real elimination in a real person can deviate from this simplified model. If you take a prescription medicine, follow your prescriber and the product label, not a calculator on the internet.