Peak and Trough Calculator
The formula
What the cmax/cmin ss tells you
The plateau band a multiple-dose regimen lives in: steady-state peak and trough from the IV-bolus superposition model.
Calculation: IV-bolus multiple dose: Cmax,ss = F·D/Vd/(1−e^(−kτ)); Cmin = Cmax·e^(−kτ). Enter your inputs and every substitution is shown below the result.
Reading the result
Troughs drive toxicity for concentration-independent killers; peaks drive efficacy for concentration-dependent ones — the swing direction is the clinical decision.
Rules of thumb: Gentamicin peak 6–10, trough <2; vancomycin trough 10–20
Limitations and best practice
Oral dosing blurs the model: absorption flips the true peak later than the dose; treat this as the IV floor.
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 does trough matter before the next dose?
Can I change swing without changing AUC?
Source & methodology
Aminoglycoside/VAN consensus PK.
Peak and Trough explained: formula, worked example and honest limits
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. There are plenty of pages about Peak and Trough; 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.
Like most useful measures, Peak and Trough is a summary, and summaries hide as much as they reveal. The companion outputs and the input table are here to reopen what the headline compressed.
People rarely disagree about arithmetic; they disagree about assumptions that were never written down. Printing the substitution and the sensitivity ranking removes that category of disagreement for Peak and Trough.
Every figure in the prose is generated by the engine rather than written beside it — the worked example resolves to steady-state peak = 62.27 mg/L on the default inputs, and the sensitivity section ranks the inputs that move the result — Vd first, at ≈11.1 % of the headline for a ten-percent error either way in that input. Work down the page and by the end you could re-derive the result in a spreadsheet from memory.
Every input in Peak and Trough, and what it does to the answer
The engine implements a single stated model: IV-bolus multiple dose: Cmax,ss = F·D/Vd/(1−e^(−kτ)); Cmin = Cmax·e^(−kτ). There is no hidden coefficient and no login-gated precision — the formula printed is the formula executed, which is also what makes the result citable.
Dose (mg) (example value 968) is a measured number in the unit named by the label; the formula does not convert for you. Take this figure from a label, a report or a prescription — never from a guess.
Vd (L) (example value 20) 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.
t½ (h) (example value 6) 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.
Interval (h) (example value 13) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
Bioavailability F (0–1) (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 Peak and Trough 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: Dose (mg), Vd (L), t½ (h), Interval (h). The computed steady-state peak comes out at 62.27 mg/L, which the interpretation band labels “Plateau swings 62.3 → 13.9 mg/L between doses — meaningful trough carryover: the accumulation ratio is 1.3”.
- k = 0.693/6.0 = 0.116 /h
- Cmax,ss = 48.40 ÷ (1−e^(−1.50)) = 62.27
- Cmin = ×e^(−kτ) = 13.87 mg/L
Steady-state trough — 13.87. This is the number experienced users quote when the headline alone would mislead.
Peak:trough swing — 4.5 ×. Compare it against the main result of 62.27 mg/L before drawing conclusions.
Time to peak — IV bolus model: at dose time. If your inputs change, this is usually the first companion figure to move.
First-dose peak — 48.40. Compare it against the main result of 62.27 mg/L 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.
Scenario table: Peak and Trough at ±10 % and ±20 % of the key input
The honest version of any estimate is a corridor, and this one is cheap to produce: Peak and Trough was recomputed at 5 points along the dominant input, with every other field left untouched.
| Vd setting | Steady-state peak |
|---|---|
| 80 % of the example value | 77.84 mg/L |
| 90 % of the example value | 69.19 mg/L |
| example inputs | 62.27 mg/L |
| 110 % of the example value | 56.61 mg/L |
| 120 % of the example value | 51.89 mg/L |
That spread — 51.89 mg/L at the low end, 77.84 mg/L at the high — is what a careful read of Peak and Trough looks like: a band you can state out loud, with the reason for each edge. Reproduce it in the form above by editing Vd alone; the substitution steps will follow your figures exactly.
Where Peak and Trough 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 steady-state peak was recalculated from scratch. It is the fastest honest answer to “what matters most in Peak and Trough?” — and it is specific to these defaults, because sensitivity moves with the starting point.
- Vd +10 % → Peak and Trough = 56.61 mg/L · −10 % → 69.19 mg/L (the steady-state peak shifts ≈11.1 %)
- Dose +10 % → Peak and Trough = 68.50 mg/L · −10 % → 56.04 mg/L (the steady-state peak shifts ≈10.0 %)
- Bioavailability F: ten percent up gives 68.50 mg/L, ten percent down gives 56.04 mg/L — ≈10.0 % of the steady-state peak either way
- Nudge Interval by ±10 % and Peak and Trough lands between 59.88 mg/L and 65.30 mg/L (sensitivity ≈4.9 %)
- t½: ten percent up gives 64.99 mg/L, ten percent down gives 59.64 mg/L — ≈4.4 % of the steady-state peak either way
Vd is the dominant lever here: ten percent either way moves the result by about 11.1 %, from 56.61 mg/L to 69.19 mg/L. That is where a careless figure does the most damage, so check it against a source, and treat Dose as the second priority (≈10.0 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.
Is your Peak and Trough good — reading the result bands
Nobody acts on a bare figure — they act on a figure with a comparison attached. The default case lands in the “Plateau swings 62.3 → 13.9 mg/L between doses — meaningful trough carryover: the accumulation ratio is 1.3” band, and bands are deliberately wide because real situations overlap. Before treating the band as fact, note its width: ten percent either way on Vd already spans 56.61 mg/L to 69.19 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.
Related measures answer related questions, and the distinctions matter: Peak and Trough is the quantity, Steady-state peak is this tool’s reading of it, and the decision that follows belongs to neither of them separately.
Common mistakes with Peak and Trough (and the fix)
Oral dosing blurs the model: absorption flips the true peak later than the dose; treat this as the IV floor. 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 Steady-state trough, Peak:trough swing and Time to peak alongside the main result precisely because Peak and Trough in isolation misleads — the secondary columns are where outliers and trade-offs show up.
This model has its own particular trap: Vd carries ≈11.1 % of the response per ten percent of error, so effort spent elsewhere is largely decorative.
A final trap is presentation: reporting Peak and Trough 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.
Peak and Trough verification checklist
- Re-run the calculation with a ±10 % stress on the two most sensitive inputs.
- Check that every field the formula needs actually arrived from a document, not from recollection.
- Put Vd under a magnifier; the sensitivity table above is the reason why.
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Compare the result with one independent method or published benchmark.
- Repeat the ±10 % test on the inputs that matter and see whether the decision — not just the number — still holds.
Five steps from raw inputs to a figure you can defend
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 Peak and Trough takes a minute to learn and applies to every input above.
Step 1 — start from evidence. The inputs behind Peak and Trough are dose (mg), vd (l), t½ (h), interval (h), bioavailability f (0–1). Write them down with their source next to each one; if you cannot name where a figure came from, that is the input most likely to be wrong. Write the assumptions in the same file as the result, and future arguments take minutes instead of meetings.
Step 2 — enter the conservative case first. Resist the flattering scenario. Type the inputs you would defend in front of a sceptical reader, read the Steady-state peak (62.27 mg/L for the example values), and note the verdict band. Numbers are cheap to produce and expensive to retract; the extra minute is the cheapest insurance available.
Step 3 — measure what deserves measuring. The ranked levers above tell you where a careful figure pays off. Everything else can stay approximate, which is a licence to stop hunting for data you do not need. Say the answer out loud before you save it; if it sounds wrong, the model did not change, your understanding did.
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. The input you reach for first is usually the one you measured longest ago.
Step 5 — write the one-line memo. “Steady-state peak = 62.27 mg/L on this date, from these inputs.” That line is the entire deliverable; everything else on this page is how you earned the right to write it. Note the assumption you are least sure about; that is where the real risk lives.
From calculation to decision: where Peak and Trough earns its keep
Most Medications & Dosing disagreements are arithmetic disagreements in disguise. When Steady-state peak of 62.27 mg/L 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. The test of a good estimate is not that it feels right but that it changes what you do.
The audience for this page is people who need one trustworthy number before their next decision. In professional Medications & Dosing practice the pattern is always the same — screen with Peak and Trough, then invest slow analysis only in whatever survives the screen. A figure nobody can reproduce is a figure nobody will act on twice.
Treat Peak and Trough like a smoke alarm rather than a painting — its value is in being tested periodically, not in being admired once. One decimal place more than your data supports is one decimal place of fiction.
Quick answers: what searchers ask about Peak and Trough
What affects Peak and Trough the most?
Measured on this engine, Vd is the dominant lever: moving it ±10 % shifts the steady-state peak across 56.61 mg/L to 69.19 mg/L — about 11.1 % of the headline, with Dose next at ≈10.0 %. The ranked list in the sensitivity section is computed live, not asserted from a template.
Which matters more: dose or vd?
For Peak and Trough, Vd wins the head-to-head (≈11.1 % against ≈10.0 % per ten-percent change). Knowing which input dominates is the difference between careful work and merely slow work.
What is a typical Peak and Trough?
There is no honest universal average for Peak and Trough, but there is a reference point: the defaults on this page produce 62.27 mg/L (Plateau swings 62.3 → 13.9 mg/L between doses — meaningful trough carryover: the accumulation ratio is 1.3). Replace the inputs with your own and compare — that comparison is the useful meaning of “typical”.
How do I calculate Peak and Trough by hand?
IV-bolus multiple dose: Cmax,ss = F·D/Vd/(1−e^(−kτ)); Cmin = Cmax·e^(−kτ) is the entire method. Work the inputs in that order — k = 0.693/6.0 = 0.116 /h — and you will reach 62.27 mg/L on the default figures, the same number this tool prints.
What happens to Peak and Trough if vd changes by 10 %?
On these inputs a ±10 % change in vd takes Peak and Trough to 56.61 mg/L against the 62.27 mg/L example — around 11.1 % of the headline. The same test on every other field is in the sensitivity section.
Is the Peak and Trough result of 62.27 mg/L good or bad?
Good and bad are comparisons, so the honest test is three questions: where does your own Peak and Trough sit against the 62.27 mg/L reference above, how far would a plausible input error move it (≈11.1 % per ten percent on Vd), and what does the alternative option compute to?
How accurate is Peak and Trough 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 62.27 mg/L as approximate.
Does Peak and Trough change with age?
Yes — reference bands shift deliberately across the lifespan, which is why this tool prints an interpretation rather than a bare number. Re-read the bands each time inputs like Dose (mg) change materially.
Why does trough matter before the next dose?
Residual drug at the next dose is the accumulation the kidney sees; high troughs predict aminoglycoside toxicity.
Can I change swing without changing AUC?
Yes — same daily dose over more frequent, smaller intervals shrinks the swing.
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 Peak and Trough
- Steady-state trough
- 13.87 in the default Peak and Trough calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Peak:trough swing
- 4.5 × on the example inputs — a companion figure printed beside the headline of Peak and Trough so that no result is read in isolation.
- Time to peak
- IV bolus model: at dose time on the example inputs — a companion figure printed beside the headline of Peak and Trough so that no result is read in isolation.
- Steady-state peak
- The primary output of this tool: 62.27 mg/L for the default inputs, computed exactly from IV-bolus multiple dose: Cmax,ss = F·D/Vd/(1−e^(−kτ)); Cmin = Cmax·e^(−kτ).
- Worked example
- Every substitution in order, from the example inputs to 62.27 mg/L — the audit trail for the headline figure.
- Verdict band
- A named zone on the range of plausible results; the example inputs land in “Plateau swings 62.3 → 13.9 mg/L between doses — meaningful trough carryover: the accumulation ratio is 1.3”, and your inputs may not.
- Sensitivity (±10 %)
- How far the Peak and Trough 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: IV-bolus multiple dose: Cmax,ss = F·D/Vd/(1−e^(−kτ)); Cmin = Cmax·e^(−kτ). Source of record: Aminoglycoside/VAN consensus PK. 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. Nothing is smoothed, weighted or adjusted behind the scenes; where judgement enters, this page says so and names the input responsible.
What to do with your Peak and Trough next
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
Whoever you are (people who need one trustworthy number before their next decision), the next step is the same: replace the example inputs with your own, note the date, and re-run whenever a figure moves. In Health & Medical, a dated figure is a trend, and an undated one is a rumour.