Cmin Estimate Calculator
The formula
What the cmin (trough) tells you
The concentration just before the next dose — Cmax decayed across the dosing interval, adjusted for an absorption lag.
Calculation: Cmin = Cmax × e^(−k·(τ−lag)); trough-to-target comparison. Enter your inputs and every substitution is shown below the result.
Reading the result
For time-dependent antibiotics the trough is the MIC gate; for anticoagulants it is the bleeding question.
Rules of thumb: Vanc trough 10–20 mg/L; gent <2; phenytoin 10–20
Limitations and best practice
Drawn early, the trough is fiction: sample within 30 min before the next dose, at ≥3–4 half-lives of steady state.
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 not just dose to peak?
Does lag time help troughs?
Source & methodology
TDM consensus (Rybak VAN 2020).
How Cmin Estimate works — and what your result really means
Budgets fail on the numbers nobody wrote down — this tool forces every one of them into the open. There are plenty of pages about Cmin Estimate; almost none of them show the working. This one does: the formula, every input, a fully computed example, and a sensitivity analysis calculated live from this engine’s own defaults.
Trends beat snapshots. Cmin Estimate measured once tells you where you stand today; measured monthly against Cmax (mg/L) tells you which way the needle is moving — and direction is the actionable information in Medications & Dosing.
It helps to separate the mechanics from the interpretation. The mechanics are fixed: Cmin = Cmax × e^(−k·(τ−lag)); trough-to-target comparison. Anyone, anywhere, entering the same inputs will get the same 4.20 mg/L. The interpretation is where experience counts: whether 4.20 mg/L is good, normal or alarming depends on comparisons covered below, and that is the part most articles about Cmin Estimate never explain.
Every figure in the prose is generated by the engine rather than written beside it — the worked example resolves to predicted cmin = 4.20 mg/L on the default inputs, and the sensitivity section ranks the inputs that move the result — Interval first, at ≈14.9 % of the headline for a ten-percent error either way in that input — which is the thread the rest of this guide pulls on.
Inside the Cmin Estimate calculation: formula and every input
One formula, published in full: Cmin = Cmax × e^(−k·(τ−lag)); trough-to-target comparison. 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.
Cmax (mg/L) (example value 16) is a measured number in the unit named by the label; the formula does not convert for you. Figures of this kind carry safety consequences; when in doubt, use the conservative value and confirm with a professional.
t½ (h) (example value 7) is a plain measured quantity — the unit shown in the label is the unit the formula expects. If you are unsure what belongs in this field, look at the printed steps: the substitution shows exactly how the engine uses it.
Interval (h) (example value 14) is a measured number in the unit named by the label; the formula does not convert for you. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
Absorption lag (h) (example value 1) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
The default Cmin Estimate calculation, written out in full
Rather than describe the calculation, here it is end to end — every substitution in order, starting from the inputs above. Starting figures: Cmax (mg/L), t½ (h), Interval (h), Absorption lag (h). The endpoint of that chain is 4.20 mg/L of predicted cmin, sitting in the “Trough lands at 4.2 mg/L — below the typical 5 mg/L coverage floor: shorten the interval or raise the dose” band.
- k = 0.693/7.0 = 0.099 /h
- Decay = e^(−k×13.5) = 0.263
- Cmin = 16.0 × 0.263 = 4.20 mg/L
Decline factor — 0.263 e^(−k·window). Compare it against the main result of 4.20 mg/L before drawing conclusions.
Time in window — 13.5 h. This is the number experienced users quote when the headline alone would mislead.
Ratio to floor — 0.84. Read next to the headline, this is the figure that shows the shape of the trade-off.
k (/h) — 0.099. If your inputs change, this is usually the first companion figure to move.
Overwrite any input above and every line of this example updates with it — the substitution is live, not a screenshot of somebody else’s numbers.
Scenario table: Cmin Estimate at ±10 % and ±20 % of the key input
The honest version of any estimate is a corridor, and this one is cheap to produce: Cmin Estimate was recomputed at 5 points along the dominant input, with every other field left untouched.
| Interval setting | Predicted Cmin |
|---|---|
| 80 % of the example value | 5.55 mg/L |
| 90 % of the example value | 4.83 mg/L |
| example inputs | 4.20 mg/L |
| 110 % of the example value | 3.66 mg/L |
| 120 % of the example value | 3.19 mg/L |
Across 5 settings of Interval, the result spans 3.19 mg/L to 5.55 mg/L. 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 Interval alone; the substitution steps will follow your figures exactly.
Where Cmin Estimate is fragile — and where it is not
This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the predicted cmin was recalculated from scratch. It is the fastest honest answer to “what matters most in Cmin Estimate?” — and it is specific to these defaults, because sensitivity moves with the starting point.
- Interval: ten percent up gives 3.66 mg/L, ten percent down gives 4.83 mg/L — ≈14.9 % of the predicted cmin either way
- t½: ten percent up gives 4.75 mg/L, ten percent down gives 3.62 mg/L — ≈13.8 % of the predicted cmin either way
- Nudge Cmax by ±10 % and Cmin Estimate lands between 3.78 mg/L and 4.62 mg/L (sensitivity ≈10.0 %)
- Nudge Absorption lag by ±10 % and Cmin Estimate lands between 4.18 mg/L and 4.22 mg/L (sensitivity ≈0.5 %)
Interval is the dominant lever here: ten percent either way moves the result by about 14.9 %, from 3.66 mg/L to 4.83 mg/L. Measure that input from a document rather than from memory, and t½ is effectively tied with it (≈13.8 % for the same nudge), so verify the pair together. The rest of the inputs earn only a rounding-error of attention, and that asymmetry is the practical payoff of measuring rather than asserting.
Is your Cmin Estimate good — reading the result bands
A number on its own is trivia; a number against a range is intelligence. On the example inputs the band reads “Trough lands at 4.2 mg/L — below the typical 5 mg/L coverage floor: shorten the interval or raise the dose”; 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 Interval, ±10 % covers 3.66 mg/L to 4.83 mg/L. The practical reading rules: read the band as a starting hypothesis, then test it: change the two dominant inputs by ten percent and see whether the verdict survives. Verdicts that survive stress are the ones worth acting on.
The comparison worth making is not with somebody else’s Cmin Estimate but with the version of your own situation measured last quarter — same formula, same conventions, different inputs.
The errors that quietly break a Cmin Estimate figure
Drawn early, the trough is fiction: sample within 30 min before the next dose, at ≥3–4 half-lives of steady state. 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.
Copying a single headline number without checking the companion outputs. The tool reports Decline factor, Time in window and Ratio to floor alongside the main result precisely because Cmin Estimate in isolation misleads — the secondary columns are where outliers and trade-offs show up.
Attention is also misallocated between fields. Having measured this engine, we can say where it belongs: Interval first, everything else second.
A final trap is presentation: reporting Cmin Estimate 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.
Cmin Estimate verification checklist
- Confirm the example values are plausible for your own situation before replacing them.
- Verify each input against its original source document, not memory.
- Check Interval before anything else: it is the measured dominant input, ≈14.9 % of Cmin Estimate per ten percent.
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Repeat the ±10 % test on the inputs that matter and see whether the decision — not just the number — still holds.
A routine for decision-grade Cmin Estimate
Using a calculator well sounds trivial, but the difference between a decision-grade figure and a throwaway one lives entirely in the routine. The routine for Cmin Estimate takes a minute to learn and applies to every input above.
Step 1 — collect, then type. Everything this tool asks for is listed above (cmax (mg/l), t½ (h), interval (h), absorption lag (h)). Pull each figure from something you can point at — paperwork, a dashboard, a label — before touching a field. Guesswork at the input stage cannot be repaired at the interpretation stage. A result worth acting on survives having its two shakiest inputs halved.
Step 2 — compute the version you would not be embarrassed by. If a stranger audited your inputs, which set would you hand over? Enter that set, read the result, and treat everything else as upside. Suspiciously tidy answers deserve the same scrutiny as untidy ones.
Step 3 — play with the inputs on purpose. Ten percent up, ten percent down, one field at a time. Within a few minutes you will know this calculation better than most people who quote its results. If a result feels obviously right, that is the moment to check the inputs hardest.
Step 4 — compute a corridor, not a point. Three runs — worst, likely, best — turn Cmin Estimate from a snapshot into a range. Plan against the pessimistic end and treat the optimistic end as the upside story. A figure nobody can reproduce is a figure nobody will act on twice.
Step 5 — save the story with the figure. A number without its inputs and its date is unusable within a quarter. Record 4.20 mg/L, the assumptions behind it, and today’s date; your future self will be auditing a stranger’s arithmetic. A figure with a date beside it becomes evidence; without one it stays an anecdote.
Who actually uses Cmin Estimate — and when
Numbers earn their keep in conversations, and Cmin Estimate is no exception. In Health & Medical discussions around Medications & Dosing, this figure decides whether an option stays on the table: it converts an opinionated debate into an arithmetic one, and arithmetic is the only referee both sides accept. The point of transparency is that a reader can disagree with a specific line rather than with you.
The companion outputs — Decline factor and Time in window — exist for the second stage of that screen: the headline sizes the prize, while the companions describe the trade-off you are accepting to get it. If the verdict changes with a ten-percent nudge, report the nudge alongside the number.
Nothing here is stored or transmitted, so the habit of checking is free: open the page, re-enter current figures, compare with the number you saved last time. Most surprises in numbers are surprises about inputs, not about formulas.
Cmin Estimate — frequently asked questions
What affects Cmin Estimate the most?
The short answer: Interval. The longer answer is the sensitivity table on this page, where every numeric input was probed by ten percent and the predicted cmin recalculated — Interval moved it furthest, by roughly 14.9 % (3.66 mg/L to 4.83 mg/L).
Do t½ and interval matter equally?
On these inputs, yes: the two measured within a rounding error of each other — ≈14.9 % and ≈13.8 % of the predicted cmin per ten-percent change. Treat them as one pair to verify together rather than ranking them.
What is a typical Cmin Estimate?
There is no honest universal average for Cmin Estimate, but there is a reference point: the defaults on this page produce 4.20 mg/L (Trough lands at 4.2 mg/L — below the typical 5 mg/L coverage floor: shorten the interval or raise the dose). Replace the inputs with your own and compare — that comparison is the useful meaning of “typical”.
How do I calculate Cmin Estimate by hand?
Cmin = Cmax × e^(−k·(τ−lag)); trough-to-target comparison is the entire method. Work the inputs in that order — k = 0.693/7.0 = 0.099 /h — and you will reach 4.20 mg/L on the default figures, the same number this tool prints.
What happens to Cmin Estimate if interval changes by 10 %?
Try it in the form above and the printed substitution will follow you; the pre-computed answer for the defaults is 3.66 mg/L to 4.83 mg/L across the ten-percent probe, i.e. ≈14.9 % sensitivity on the predicted cmin.
Is the Cmin Estimate result of 4.20 mg/L good or bad?
Good and bad are comparisons, so the honest test is three questions: where does your own Cmin Estimate sit against the 4.20 mg/L reference above, how far would a plausible input error move it (≈14.9 % per ten percent on Interval), and what does the alternative option compute to?
How accurate is Cmin Estimate for me personally?
The formula encodes averages; body-composition and measurement error typically shifts results by a few percent in either direction. Use ranges and trends, and treat any single 4.20 mg/L as approximate.
How often should I check Cmin Estimate?
Whenever an input changes by more than a few percent, and otherwise on the rhythm of your decisions — before a purchase, a review, a renewal. Cmin Estimate is a snapshot, not a subscription; stale snapshots are the most common silent error in Health & Medical planning.
Why not just dose to peak?
Troughs govern accumulation toxicity and sub-MIC windows; peaks govern acute efficacy — both need a band.
Does lag time help troughs?
Extended-release absorption raises apparent troughs without changing AUC — a different risk profile.
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 Cmin Estimate
- Decline factor
- 0.263 e^(−k·window) on the example inputs — a companion figure printed beside the headline of Cmin Estimate so that no result is read in isolation.
- Time in window
- 13.5 h in the default Cmin Estimate calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Ratio to floor
- 0.84 on the example inputs — a companion figure printed beside the headline of Cmin Estimate so that no result is read in isolation.
- Predicted Cmin
- The primary output of this tool: 4.20 mg/L for the default inputs, computed exactly from Cmin = Cmax × e^(−k·(τ−lag)); trough-to-target comparison.
- Worked example
- Every substitution in order, from the example inputs to 4.20 mg/L — the audit trail for the headline figure.
- Verdict band
- The interpretation attached to a result (“Trough lands at 4.2 mg/L — below the typical 5 mg/L coverage floor: shorten the interval or raise the dose” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Cmin Estimate moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Method, sources and what this tool cannot tell you
The model is published arithmetic implemented exactly as written: Cmin = Cmax × e^(−k·(τ−lag)); trough-to-target comparison. Source of record: TDM consensus (Rybak VAN 2020). Any other implementation of this model should return the same figure for the same inputs. If one does not, the difference is in its assumptions — which this page prints and that one probably does not.
Treat the output as a precise answer to the question you typed: exact arithmetic, transparent formula, published source, no hidden rounding. The promise to the reader is narrow and testable: same inputs, same output, no silent rounding, and no figure presented without the formula that produced it.
After the number: what to do with it
Get one independent quote and reconcile it against this calculation; unexplained gaps are where hidden costs live.
The audience here is planners sizing a spend before committing money. 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.