Drug Accumulation Calculator
The formula
What the accumulation r tells you
How many times above the first dose the plateau lands when the interval is shorter than the half-life — the geometric series of residual drug.
Calculation: R = 1/(1−e^(−kτ)); plateau Cmax/Cmin from single-dose curve. Enter your inputs and every substitution is shown below the result.
Reading the result
Twice-daily dosing of a once-daily drug doubles the plateau before any dose is missed — R is the number that predicts that.
Rules of thumb: R≈1.4 (τ=t½/2); R≈2 (τ=t½); R→∞ when clearance saturates
Limitations and best practice
Nonlinear (capacity-limited) clearance voids the geometric series: phenytoin’s R explodes instead of converging.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Why do weekends feel like withdrawal with some drugs?
Does food change R?
Source & methodology
Multiple-dose PK (Levy 1966).
How Drug Accumulation works — and what your result really means
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. Drug Accumulation is the kind of number people argue about from memory. This page ends that argument with arithmetic you can watch happen: enter your figures, get Accumulation ratio in real time, and see every substitution printed below.
It helps to separate the mechanics from the interpretation. The mechanics are fixed: R = 1/(1−e^(−kτ)); plateau Cmax/Cmin from single-dose curve. Anyone, anywhere, entering the same inputs will get the same 3.93. The interpretation is where experience counts: whether 3.93 is good, normal or alarming depends on comparisons covered below, and that is the part most articles about Drug Accumulation never explain.
The number itself is the easy part. What takes judgement is knowing which inputs are facts in your situation and which are guesses wearing a decimal point — a distinction this page makes explicit for every field above.
Every figure in the prose is generated by the engine rather than written beside it — the worked example resolves to accumulation ratio = 3.93 on the default inputs, and the sensitivity section ranks the inputs that move the result — Dosing interval first, at ≈9.6 % of the headline for a ten-percent error either way in that input — which is the thread the rest of this guide pulls on.
The Drug Accumulation formula, explained
One formula, published in full: R = 1/(1−e^(−kτ)); plateau Cmax/Cmin from single-dose curve. Anything you can read, you can reproduce in a spreadsheet, and that reproducibility is the whole point of printing it rather than hiding it behind a button.
Half-life (h) (example value 26) is a quantity rather than a category — precision here is cheap and worth having. If you are unsure what belongs in this field, look at the printed steps: the substitution shows exactly how the engine uses it.
Dosing interval (h) (example value 11) is a measured number in the unit named by the label; the formula does not convert for you. The example value is there to demonstrate the mechanics, not to describe your situation — overwrite it.
Dose (mg) (example value 106) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Figures of this kind carry safety consequences; when in doubt, use the conservative value and confirm with a professional.
Vd (L) (example value 53) is a plain measured quantity — the unit shown in the label is the unit the formula expects. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
Drug Accumulation with real numbers, step by step
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Half-life (h), Dosing interval (h), Dose (mg), Vd (L). Run to the end, the accumulation ratio resolves to 3.93 — Dosing every 11 h with a 26-h half-life multiplies plateau exposure ×3.9 — peak 7.9 and trough 5.9 mg/L on the bands this tool uses.
- k = 0.693/26 = 0.027 /h
- R = 1/(1−e^(−kτ)) = 3.93
- Cmax,ss = (D/Vd)/(1−e^(−kτ)) = 7.87 mg/L
Plateau Cmax — 7.87 mg/L. This is the number experienced users quote when the headline alone would mislead.
Plateau Cmin — 5.87 mg/L. Compare it against the main result of 3.93 before drawing conclusions.
Swing Cmax/Cmin — 1.34. If your inputs change, this is usually the first companion figure to move.
First-dose Cmax — 2.00. Compare it against the main result of 3.93 before drawing conclusions.
Re-running with your own figures is instant; re-running by hand once is the best way to know the tool is telling you the truth.
The Drug Accumulation corridor: your result across a realistic band
Single-point answers invite false confidence, so the same engine was run across a band around the input that matters most here. Each row is a full recalculation of Drug Accumulation, not an interpolation.
| Dosing interval setting | Accumulation ratio |
|---|---|
| 80 % of the example value | 4.78 |
| 90 % of the example value | 4.31 |
| example inputs | 3.93 |
| 110 % of the example value | 3.63 |
| 120 % of the example value | 3.37 |
Across 5 settings of Dosing interval, the result spans 3.37 to 4.78. A decision that only works at one row of this table is a decision waiting for an input to move. Reproduce it in the form above by editing Dosing interval alone; the substitution steps will follow your figures exactly.
Where Drug Accumulation is fragile — and where it is not
Generic advice says “it depends on your inputs”; this section says exactly how much. Each field was perturbed by ±10 % in isolation and the accumulation ratio recomputed, so the ranking below is measured rather than asserted. Read it as a map of where Drug Accumulation is fragile — drawn for the example inputs, which is the map you want when deciding what to measure carefully.
- Dosing interval: ten percent up gives 3.63, ten percent down gives 4.31 — ≈9.6 % of the accumulation ratio either way
- Nudge Half-life by ±10 % and Drug Accumulation lands between 3.60 and 4.27 (sensitivity ≈8.6 %)
Dosing interval is the dominant lever here: ten percent either way moves the result by about 9.6 %, from 3.63 to 4.31. That is where a careless figure does the most damage, so check it against a source, and treat Half-life as the second priority (≈8.6 % per ten percent). The rest of the inputs earn only a rounding-error of attention, and that asymmetry is the practical payoff of measuring rather than asserting.
Reading the result: bands, zones and thresholds
The value above only becomes useful the moment you know what it is being measured against. On the example inputs the band reads “Dosing every 11 h with a 26-h half-life multiplies plateau exposure ×3.9 — peak 7.9 and trough 5.9 mg/L”; your own figures place you on a different rung of the same ladder. The sensitivity list shows how far a modest input error moves you along that ladder: for Dosing interval, ±10 % covers 3.63 to 4.31. The practical reading rules: ask what would have to change to move you one band. If the answer is “a small, plausible input difference”, the band itself is not the finding — the uncertainty is.
Where Drug Accumulation sits next to similar measures: this tool answers “how much is the Drug Accumulation”, while the related calculators answer “what do I do about it”. Reading the result alone tends to over-weight a single snapshot; pairing it with the companion tools above turns the number into a decision.
Common mistakes with Drug Accumulation (and the fix)
Nonlinear (capacity-limited) clearance voids the geometric series: phenytoin’s R explodes instead of converging. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Mixing units between tools. Metric and imperial entry paths round differently — keep one system top to bottom.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Dosing interval dominating — a careful figure there beats false precision everywhere else.
A final trap is presentation: reporting Drug Accumulation to more decimal places than the inputs support. The tool prints what the arithmetic gives; you should quote only what your least precise field justifies.
A quick check for any Drug Accumulation figure
- Recompute once with the dominant input deliberately set low, and see whether the decision changes.
- Compare the result with one independent method or published benchmark.
- Put Dosing interval under a magnifier; the sensitivity table above is the reason why.
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Verify each input against its original source document, not memory.
- Repeat the ±10 % test on the inputs that matter and see whether the decision — not just the number — still holds.
How to use the Drug Accumulation tool properly
The tool does the arithmetic; the routine below is what makes the arithmetic trustworthy. Five steps, a minute total — and afterwards you will know not just what the number is, but which assumption produced it.
Step 1 — gather before you type. Drug Accumulation depends on half-life (h), dosing interval (h), dose (mg), vd (l). Collect them from a source document — a statement, a report, an invoice, a log — rather than from memory, because recalled inputs are the single largest cause of wrong results. If the verdict changes with a ten-percent nudge, report the nudge alongside the number.
Step 2 — baseline before exploration. Get one defensible Accumulation ratio on screen before you start nudging numbers. Without a baseline, every variation looks interesting and none of them means anything. If the answer changes your behaviour, it deserves a second run with different assumptions.
Step 3 — isolate your variables. Change one field, observe, revert. The live sensitivity list does the ranking for the default inputs; verify it against your own, because dominance shifts when the starting point shifts. Write the figure down before moving on; memory flatters whichever number you saw last.
Step 4 — ask what would have to be true. Take the result you want and work backwards through the inputs until you find the assumption that produces it; then decide honestly whether that assumption is defensible. Note the assumption you are least sure about; that is where the real risk lives.
Step 5 — record the context, not just the number. Note today’s date and the inputs alongside the 3.93 output. Six months from now the context is what turns this figure into a trend. Repeating a calculation with the same numbers proves only that the arithmetic is reliable — which is worth knowing.
Who actually uses Drug Accumulation — and when
Most Medications & Dosing disagreements are arithmetic disagreements in disguise. When Accumulation ratio of 3.93 sits on the table with its working shown, the conversation stops being about who sounds more confident and starts being about which input is wrong. When two sources disagree, it is almost never the arithmetic that differs.
Used properly this is a five-minute filter that saves weeks. Compute Drug Accumulation, reject what fails, and only then bring in the expensive analysis for the survivors. When two sources disagree, it is almost never the arithmetic that differs.
There is a personal-administration use people overlook: periodic self-checking. Drug Accumulation quietly drifts as life changes — rates move, bodies change, costs compound — and re-running it a few times a year catches drift while correction is still cheap. The fastest sanity test is to guess the answer first and see how far the calculation disagrees.
Drug Accumulation — frequently asked questions
What affects Drug Accumulation the most?
The short answer: Dosing interval. The longer answer is the sensitivity table on this page, where every numeric input was probed by ten percent and the accumulation ratio recalculated — Dosing interval moved it furthest, by roughly 9.6 % (3.63 to 4.31).
Which matters more: half-life or dosing interval?
For Drug Accumulation, Dosing interval wins the head-to-head (≈9.6 % against ≈8.6 % per ten-percent change). Knowing which input dominates is the difference between careful work and merely slow work.
What is a typical Drug Accumulation?
There is no honest universal average for Drug Accumulation, but there is a reference point: the defaults on this page produce 3.93 (Dosing every 11 h with a 26-h half-life multiplies plateau exposure ×3.9 — peak 7.9 and trough 5.9 mg/L). Replace the inputs with your own and compare — that comparison is the useful meaning of “typical”.
How do I calculate Drug Accumulation by hand?
Three steps: write the formula (R = 1/(1−e^(−kτ)); plateau Cmax/Cmin from single-dose curve), insert your values, and simplify. The worked example section shows exactly that chain for the default inputs; replicating it once on paper teaches you more about Drug Accumulation than any number of calculator runs.
What happens to Drug Accumulation if dosing interval changes by 10 %?
The engine was re-run with that field moved by ten percent while everything else stayed fixed: the accumulation ratio goes across 3.63 to 4.31, a swing of roughly 9.6 % around the 3.93 baseline. That ratio is the practical definition of how much this input matters.
Is the Drug Accumulation result of 3.93 good or bad?
Neither, on its own — the label “Dosing every 11 h with a 26-h half-life multiplies plateau exposure ×3.9 — peak 7.9 and trough 5.9 mg/L” is the band this figure falls in for the example inputs, and your own inputs will place you elsewhere on the same ladder. Judge the number against your history and your alternatives, and remember that a ten-percent error in Dosing interval alone moves it by ≈9.6 %.
Can Drug Accumulation be negative or empty?
Yes, and that is informative rather than broken: a negative Drug Accumulation usually means the inputs encode an outflow or a shortfall, and the verdict band above labels exactly that situation instead of hiding it.
What affects Drug Accumulation the most?
Sensitivity depends on where you start, but the inputs Half-life (h) and Dosing interval (h) typically move Drug Accumulation further than the rest because they enter the formula multiplicatively. If you can only measure two things well, measure those and hold the others at conservative defaults.
Why do weekends feel like withdrawal with some drugs?
If the half-life is long and the interval shorter, steady state persists past a skipped dose — the reverse effect: accumulation persists.
Does food change R?
It changes F and absorption rate, which shifts peaks; the R arithmetic depends only on kτ.
Can this tool see the numbers I type?
It cannot. There is no submission step: the calculation happens in your browser and the result disappears when you close the page. Treat the fields above as a scratchpad rather than a form.
Glossary for Drug Accumulation
- Plateau Cmax
- 7.87 mg/L for the Drug Accumulation worked case; it sits next to the main result because it carries context the headline leaves out.
- Plateau Cmin
- 5.87 mg/L for the Drug Accumulation worked case; it sits next to the main result because it carries context the headline leaves out.
- Swing Cmax/Cmin
- 1.34 on the example inputs — a companion figure printed beside the headline of Drug Accumulation so that no result is read in isolation.
- Accumulation ratio
- The primary output of this tool: 3.93 for the default inputs, computed exactly from R = 1/(1−e^(−kτ)); plateau Cmax/Cmin from single-dose curve.
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- The plain-language label — here “Dosing every 11 h with a 26-h half-life multiplies plateau exposure ×3.9 — peak 7.9 and trough 5.9 mg/L” — mapping the computed figure onto experience-based ranges for Health & Medical.
- Sensitivity (±10 %)
- How far the Drug Accumulation moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Methodology, sources and limits
The model is published arithmetic implemented exactly as written: R = 1/(1−e^(−kτ)); plateau Cmax/Cmin from single-dose curve. Source of record: Multiple-dose PK (Levy 1966). Specialist software layers extra coefficients on top of the same algebra; none are hidden here, and that transparency is what makes a disagreement traceable to a specific input instead of a black box.
Treat the output as a precise answer to the question you typed: exact arithmetic, transparent formula, published source, no hidden rounding. The sensitivity table above is part of that promise rather than a bonus: it lets you see how much of the result depends on how carefully you measured.
Next steps after the calculation
Save the number together with its inputs and today’s date; a Drug Accumulation figure without context is unusable the moment an input changes.
The audience here is people who need one trustworthy number before their next decision. Everything you need to defend the result — formula, substitution, sensitivity, source — is printed above, so the only remaining variable is the honesty of your inputs.