Sensitivity Calculator
The formula
What the miss rate of the sick tells you
Sensitivity is the share of genuinely positive cases the test catches — its ability to avoid false reassurance.
Calculation: Sensitivity = TP ∕ (TP + FN). Enter your inputs and every substitution is shown below the result.
Reading the result
88% sensitivity means 12 of every 100 sick patients are told they look fine; triage tests aim above 95%.
Rules of thumb: Screening ≥95%, confirmatory labs ≥99% analytical sensitivity
Limitations and best practice
Confusing sensitivity with accuracy on rare disease: a test that flags everyone has 100% sensitivity and useless precision.
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
Does high sensitivity mean a positive result is reliable?
Sensitivity vs specificity trade-off?
Can sensitivity be estimated with no gold standard?
Source & methodology
Standard diagnostic-accuracy definitions (STARD).
Sensitivity: what this tool answers
You are here because you need a specific number, and you want to see how it was produced before you rely on it. Sensitivity 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 Sensitivity in real time, and see every substitution printed below.
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 Sensitivity.
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.
Nothing below is stock text pasted around a number: the worked example computes sensitivity = 89.4 % from this tool’s own defaults, and the sensitivity section ranks the inputs that move the result — True positives first, at ≈1.2 % 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.
Inside the Sensitivity calculation: formula and every input
One formula, published in full: Sensitivity = TP ∕ (TP + FN). 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.
True positives (sick & flagged) (example value 84) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. If you are unsure what belongs in this field, look at the printed steps: the substitution shows exactly how the engine uses it.
False negatives (sick & missed) (example value 10) 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.
Sensitivity on the example inputs: the complete substitution
The tool prints its own working; this is the same arithmetic on the example values, reproduced so you can follow it by hand. Starting figures: True positives (sick & flagged), False negatives (sick & missed). The computed sensitivity comes out at 89.4 %, which the interpretation band labels “Solid screen, but 10.6% of cases still walk through”.
- Total true cases = TP + FN = 84 + 10 = 94
- Sensitivity = 84 ÷ 94 = 89.4%
- High sensitivity → few false negatives → SnNOut (a Negative test rules Out)
Cases detected — 84. Read next to the headline, this is the figure that shows the shape of the trade-off.
Cases missed — 10. Read next to the headline, this is the figure that shows the shape of the trade-off.
Miss rate — 10.6 %. Read next to the headline, this is the figure that shows the shape of the trade-off.
Sensitivity needed for ≤5% misses at this FN count — 89.4 %. This is the number experienced users quote when the headline alone would mislead.
Keep this worked example open while you enter your own figures: matching the shape of the substitution is the fastest way to spot a unit or convention mistake.
The Sensitivity 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 Sensitivity, not an interpolation.
| True positives setting | Sensitivity |
|---|---|
| 80 % of the example value | 87.0 % |
| 90 % of the example value | 88.3 % |
| example inputs | 89.4 % |
| 110 % of the example value | 90.2 % |
| 120 % of the example value | 91.0 % |
That spread — 87.0 % at the low end, 91.0 % at the high — is what a careful read of Sensitivity looks like: a band you can state out loud, with the reason for each edge. Reproduce it in the form above by editing True positives alone; the substitution steps will follow your figures exactly.
Sensitivity: which inputs change Sensitivity the most
Nobody should have to guess which input matters. The engine was re-run once per field below — ten percent up, ten percent down, everything else frozen — and the results ranked by how far they moved the sensitivity. It is the fastest honest answer to “what matters most in Sensitivity?” — and it is specific to these defaults, because sensitivity moves with the starting point.
- True positives: ten percent up gives 90.2 %, ten percent down gives 88.3 % — ≈1.2 % of the sensitivity either way
- False negatives +10 % → Sensitivity = 88.4 % · −10 % → 90.3 % (the sensitivity shifts ≈1.1 %)
True positives is the dominant lever here: ten percent either way moves the result by about 1.2 %, from 88.3 % to 90.2 %. Measure that input from a document rather than from memory, and False negatives is effectively tied with it (≈1.1 % for the same nudge), so verify the pair together. The remaining fields can sit at safe defaults without materially changing the answer — knowing which is which is what separates a careful calculation from an anxious one.
What a Sensitivity of 89.4 % means in practice
A number on its own is trivia; a number against a range is intelligence. The verdict attached to the default calculation — “Solid screen, but 10.6% of cases still walk through” — is one band on a ladder your own figure may sit somewhere else on. The sensitivity list shows how far a modest input error moves you along that ladder: for True positives, ±10 % covers 88.3 % to 90.2 %. 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.
Placing this figure in context: calculators of this kind differ less in arithmetic than in what they choose to ignore. This one keeps True positives (sick & flagged) explicit so that the omissions are visible rather than hidden in a preset.
How people get Sensitivity wrong
Confusing sensitivity with accuracy on rare disease: a test that flags everyone has 100% sensitivity and useless precision. 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.
Chasing precision in False negatives (sick & missed) while True positives (sick & flagged) is still a guess. The sensitivity ranking above shows exactly where the accuracy budget should go.
Attention is also misallocated between fields. Having measured this engine, we can say where it belongs: True positives first, everything else second.
Another is comparing across contexts: a Sensitivity computed with one set of conventions should never be lined up against a figure computed with another. Check the inputs behind both before ranking them.
A quick check for any Sensitivity figure
- Check that every field the formula needs actually arrived from a document, not from recollection.
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Check True positives before anything else: it is the measured dominant input, ≈1.2 % of Sensitivity per ten percent.
- Confirm the example values are plausible for your own situation before replacing them.
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Confirm the answer against one independent method or published benchmark for Sensitivity.
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 Sensitivity takes a minute to learn and applies to every input above.
Step 1 — collect, then type. Everything this tool asks for is listed above (true positives (sick & flagged), false negatives (sick & missed)). 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. Write the figure down before moving on; memory flatters whichever number you saw last.
Step 2 — baseline before exploration. Get one defensible Sensitivity on screen before you start nudging numbers. Without a baseline, every variation looks interesting and none of them means anything. If a result feels obviously right, that is the moment to check the inputs hardest.
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. Half of a good calculation is knowing which input you would hate to be wrong about.
Step 4 — stress before you commit. A decision that survives a ten-percent squeeze on its two biggest inputs needs no luck to be sound. One that does not survive is a decision about hope, not about arithmetic. A figure with a date beside it becomes evidence; without one it stays an anecdote.
Step 5 — schedule the next run. In Science & Research the inputs drift quietly. Put a reminder a quarter out, re-enter the same fields, and read the change rather than the level. A calculation you cannot explain to somebody else is a calculation you cannot defend.
The real-world conversations Sensitivity settles
Numbers earn their keep in conversations, and Sensitivity is no exception. In Science & Research discussions around Statistics & Data Science, 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 inputs are the part of the work that nobody else can do for you.
Professionals in Statistics & Data Science use this style of calculation as a screening filter before spending real money or effort: a quick Sensitivity check eliminates weak options in minutes, and the survivors earn the deeper, slower analysis. Comparisons are cheap: run the identical calculation for the alternative and look at the gap.
Treat Sensitivity like a smoke alarm rather than a painting — its value is in being tested periodically, not in being admired once. Re-running a number costs seconds; retracting a decision costs considerably more.
The questions that come up most about Sensitivity
What affects Sensitivity the most?
The short answer: True positives. The longer answer is the sensitivity table on this page, where every numeric input was probed by ten percent and the sensitivity recalculated — True positives moved it furthest, by roughly 1.2 % (88.3 % to 90.2 %).
Do false negatives and true positives matter equally?
On these inputs, yes: the two measured within a rounding error of each other — ≈1.2 % and ≈1.1 % of the sensitivity per ten-percent change. Treat them as one pair to verify together rather than ranking them.
What is a typical Sensitivity?
On the worked example above Sensitivity comes out at 89.4 %. Treat that as one point on a distribution rather than a norm: the bands, the companion outputs and the sensitivity ranking tell you how wide the plausible range really is.
How do I calculate Sensitivity by hand?
Use the stated model — Sensitivity = TP ∕ (TP + FN) — and substitute in the order the tool prints (it starts from Total true cases = TP + FN = 84 + 10 = 94). On the example inputs the hand route lands on 89.4 %, exactly what the calculator shows. A spreadsheet reproduces it in two or three cells; doing it once by hand is what makes the automated answer trustworthy.
What happens to Sensitivity if true positives changes by 10 %?
The engine was re-run with that field moved by ten percent while everything else stayed fixed: the sensitivity goes across 88.3 % to 90.2 %, a swing of roughly 1.2 % around the 89.4 % baseline. That ratio is the practical definition of how much this input matters.
Is the Sensitivity result of 89.4 % good or bad?
The tool answers “what”, not “whether”: 89.4 % carries the verdict “Solid screen, but 10.6% of cases still walk through” for the default case, which is a starting interpretation rather than a verdict on your situation. Re-run with your own figures and compare the bands.
How do I calculate Sensitivity manually?
Write down the inputs, then follow the printed steps in order — Sensitivity = TP ∕ (TP + FN). A spreadsheet replicates it with two or three cells. The manual route is worth doing once to build intuition; after that the calculator saves time and eliminates transcription slips.
What affects Sensitivity the most?
Sensitivity depends on where you start, but the inputs True positives (sick & flagged) and False negatives (sick & missed) typically move Sensitivity 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.
Does high sensitivity mean a positive result is reliable?
No — that’s positive predictive value, which depends on prevalence. Sensitive tests still over-flag.
Sensitivity vs specificity trade-off?
Loosening the cutoff raises sensitivity and burns specificity; the ROC curve is that whole trade.
Does this Sensitivity tool store my numbers?
No. The entire calculation runs in your browser session; nothing entered above is transmitted or saved, which is the correct behaviour for sensitive Science & Research figures and the reason you can re-run this page as often as you like.
Key terms on this page
- Cases detected
- 84 on the example inputs — a companion figure printed beside the headline of Sensitivity so that no result is read in isolation.
- Cases missed
- 10 for the Sensitivity worked case; it sits next to the main result because it carries context the headline leaves out.
- Miss rate
- 10.6 % in the default Sensitivity calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Sensitivity
- The primary output of this tool: 89.4 % for the default inputs, computed exactly from Sensitivity = TP ∕ (TP + FN).
- Worked example
- The calculation written out in full so that nothing on this page has to be taken on trust.
- Verdict band
- The interpretation attached to a result (“Solid screen, but 10.6% of cases still walk through” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Sensitivity 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: Sensitivity = TP ∕ (TP + FN). Source of record: Standard diagnostic-accuracy definitions (STARD). 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.
This page is an estimation aid, not professional advice. The design rule is simple: two people entering identical figures must get identical answers. 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.
Turning this Sensitivity into a decision
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 Science & Research, a dated figure is a trend, and an undated one is a rumour.