A half-life of 2 hours
Every figure on this page is a function of one number: 2 hours. Five of those is 10.0 hours, and down to one percent takes about 13 hours. No compound is named here and none is implied.
Educational arithmetic only. Not medical advice and not a dosing protocol.
| Half-lives elapsed | Remaining, exactly | Elapsed | Which is |
|---|---|---|---|
| 1 | 50.0000% | 2 hours | 2.0 hours |
| 2 | 25.0000% | 4 hours | 4.0 hours |
| 3 | 12.5000% | 6 hours | 6.0 hours |
| 4 | 6.2500% | 8 hours | 8.0 hours |
| 5 | 3.1250% | 10 hours | 10.0 hours |
| 6 | 1.5625% | 12 hours | 12.0 hours |
| 7 | 0.7813% | 14 hours | 14.0 hours |
| To | Remaining | Hours, about | Which is about |
|---|---|---|---|
| Down to a half | 50% | 2.0 hours | 2.0 hours |
| Down to a quarter | 25% | 4.0 hours | 4.0 hours |
| Down to a tenth | 10% | 6.6 hours | 6.6 hours |
| Down to a twentieth | 5.0% | 8.6 hours | 8.6 hours |
| Down to a hundredth | 1.0% | 13.3 hours | 13.3 hours |
| Interval | Intervals per half-life | Surviving the gap | Limit the peaks approach | Intervals to within 1% |
|---|---|---|---|---|
| 8 hours | 4.00 | 6.3% | 1.07x | 2 |
| 12 hours | 6.00 | 1.6% | 1.02x | 2 |
| 24 hours | 12.00 | 0.0% | 1.00x | 1 |
| 48 hours | 24.00 | 0.0% | 1.00x | 1 |
| 72 hours | 36.00 | 0.0% | 1.00x | 1 |
| 168 hours | 84.00 | 0.0% | 1.00x | 1 |
| 336 hours | 168.00 | 0.0% | 1.00x | 1 |
What is particular to this half-life
Two hours is short enough that the whole curve is over inside a working day: five half-lives is ten hours. At any of the intervals in the second table the previous amount has essentially gone before the next is due, so the accumulation limit is one - the series does not accumulate at all. This is the regime where repeat arithmetic has nothing to say.
Reading the third table
The second column is the whole story. It is the
interval divided by the half-life, and it is the only input to the three columns after it:
the fraction surviving a gap is 0.5 to that power, and the limit is one over
one minus that fraction. Two rows with the same figure in column two have identical
arithmetic however different the clock times are.
At a 2-hour half-life and a 24-hour interval, 12.00 half-lives pass between repeats, about 0.0% of one amount survives the gap, and the peaks approach about 1.00 times one amount after roughly 1 intervals. Every one of those four figures comes from the ratio and from nothing else.
Why the first table is exact and the other two are not
At whole multiples of a half-life the exponent is a whole number, so the remaining fraction is exactly one half to the power n - a rational number, computed as one. That is why the first table has figures like 3.1250% in it rather than 3.13%.
Everywhere else the exponent is fractional and the value is irrational. There is no exact decimal to print, so those tables are computed in floating point and labelled approximate. Exact and approximate sets out which figures across this whole site are which, and why the distinction is worth making rather than papering over.
What this page is not
It is not about a compound. No substance has a 2-hour half-life as far as this page is concerned; 2 hours is a number, chosen as one of ten points spanning the range this arithmetic is useful over. A published half-life belongs to the species, formulation, route and assay that measured it, and this site holds no such figure for anything.
It is also not a schedule. The intervals in the third table are parameters swept across a plausible range so that the shape of the function is visible. None of them is a proposal, and what this does not do is explicit about that.
Elsewhere on this site
- The worksheetAny half-life and any interval, rather than the seven tabulated here.
- The other nine half-life valuesSame three tables, a different number at the top.
- The same grid by intervalHold the interval fixed and sweep the half-life instead.