NNT from the absolute reduction, with the relative one shown beside it.
Absolute and relative, side by side
A 50% relative reduction. NNT is 7; inverting the relative figure gives 2 — a 3.33x overstatement.
Treatment 15.0000% · control 30.0000% · absolute difference 15.0000pp
Number needed to treat = 7
Treat 7 people to prevent one event. Exactly, it is 6.66667 — always rounded UP, because a fraction of a person is not treated.
Number needed to treat
7
1 ÷ absolute reduction
Absolute reduction
15.0000pp
the number NNT inverts
Relative reduction
50.0000%
the number that gets published
Relative risk
0.50000
treatment ÷ control
Odds ratio
0.41176
not the same as RR
Difference CI
-26.149 to -3.411pp
Newcombe, 95%
p-value
0.011085
z = -2.5400
NNT from the relative figure
2
the common error
Inverting the relative reduction gives 2. The real answer is 7. A factor of 3.3333. The relative reduction of 50.0000% is the figure that appears in abstracts and press releases; it contains no information about how many people have to be treated, because it has been divided by a baseline risk the reader is not told. Only the absolute reduction can be inverted.
The same 50.0000% reduction at every baseline risk
Every point on this curve produces the identical relative-reduction headline. The NNT ranges from single digits on the right to hundreds on the left, so two trials reporting the same percentage can describe treatments with completely different clinical value. This is why a relative figure quoted without its baseline cannot be acted on.
NNT is always rounded up, never to the nearest whole number. An NNT of 6.67 is reported as 7: treating 6 people does not reliably prevent an event, and rounding down claims a benefit the arithmetic does not support. The exact value is printed above so the rounding is visible rather than silent.
An NNT belongs to a time horizon and a population, not to a drug. The same treatment has a different NNT over one year and over five, and a different one again in a higher-risk group, because the baseline risk it divides into is different. An NNT quoted without the follow-up period and the population it came from is not transferable — and it is not a substitute for the harms, which have their own number.
What this tool shows
Two trials can report the identical “50% reduction” and have numbers needed to treat of 7 and 1,000. NNT is 1 ÷ the ABSOLUTE risk reduction. Inverting the relative reduction — the figure abstracts and press releases quote — gives 2 in both cases. The tool computes both and prints the ratio, so the error is a number rather than a warning.
NNT from the absolute risk reduction, rounded up as convention requires
Absolute and relative risk reduction side by side
The NNT you would get from the relative figure, and the factor between them
Relative risk, odds ratio and the risk difference from the same table
A Newcombe confidence interval for the difference, and the two-proportion p-value
The NNT curve across baseline risk at your own relative reduction
NNT and NNH The relative trap Rounded up CI included
Updated 12 September 2026 · Works in any browser, no installation
NNT = 1 ÷ (control event rate − treatment event rate) — the reciprocal of the ABSOLUTE risk reduction, rounded up. It answers “how many people must receive this treatment for one of them to avoid the outcome”, and it is the only summary of a trial that is directly countable. The relative risk reduction cannot be inverted, because it has already been divided by a baseline the reader is not told.
At a glance
Formula shown
ARR = CER − EER, where CER is the control event rate and EER the experimental event rate. NNT = 1/ARR, always rounded UP to the next whole person. RRR = ARR/CER = 1 − RR, which is the figure most often published. Inverting RRR gives 1/RRR = CER/ARR, which differs from NNT by exactly the factor CER — so the error equals the baseline risk, and is largest when the outcome is rare. When ARR is negative the same arithmetic gives the number needed to harm.
Scenario support
Reading a trial result, comparing two treatments with different baseline risks, translating a published relative reduction into something countable, teaching evidence appraisal, and deciding whether an effect is large enough to act on.
Educational estimate
Planning support from the values you enter — not professional advice.
The same headline, a 500-fold difference
Two trials. Both report a 50% reduction. One has an NNT of 7 and the other an NNT of 1,000, and nothing in either abstract distinguishes them.
Trial one: 30% of the control arm had the event, 15% of the treatment arm. The absolute reduction is 15 percentage points, so NNT = 1/0.15 = 6.67, reported as 7.
Trial two: 0.2% of the control arm, 0.1% of the treatment arm. The absolute reduction is 0.1 percentage points, so NNT = 1/0.001 = 1,000.
Both are exactly a 50% relative reduction. Divide 0.15 by 0.30 and you get 0.5. Divide 0.001 by 0.002 and you get 0.5. The relative figure has already divided out the baseline, and with it the information you needed.
Inverting the relative figure gives 2 in both cases. That is the shortcut, and it is wrong by a factor of 3.33 in the first trial and 500 in the second. The size of the error is exactly the baseline risk, so it is worst when the outcome is rare — which is when relative figures are most likely to be quoted, because they look most impressive.
The tool prints the wrong answer next to the right one with the ratio between them, because knowing the shortcut exists is not the same as seeing what it costs on the numbers in front of you.
An NNT belongs to a baseline risk, not to a drug
The curve in the tool holds the relative reduction fixed and varies the baseline. Every point on it produces the identical published percentage, and the NNT runs from single digits to hundreds.
So the same treatment has different NNTs in different populations. A statin in a high-risk secondary-prevention group and the same statin in a low-risk primary-prevention group have the same relative effect and completely different numbers needed to treat, because the baseline it divides into is different.
And different NNTs over different follow-up periods. Risk accumulates with time, so a five-year NNT is smaller than a one-year NNT for the same treatment. An NNT without its time horizon is not interpretable, and the horizon is omitted far more often than it is stated.
Which means NNTs from different trials cannot simply be compared. Two treatments with NNTs of 20 and 50 may be equally effective, tested in populations at different risk. Comparing relative reductions is the fairer comparison there; comparing NNTs is the fairer one within a population.
The useful move is to re-derive it for your own baseline. Take the relative reduction from the trial, apply it to the risk in the patient in front of you, and invert THAT absolute reduction. The tool’s curve does exactly this and shows the whole range at once.
Always rounded up, never to the nearest
A small convention with a real justification, and one that some calculators get wrong.
An NNT of 6.67 is reported as 7, not as 6. Treating six people does not reliably prevent one event — the expected number prevented is 6 × 0.15 = 0.9. Rounding down claims a benefit the arithmetic does not deliver.
The exact value is still worth printing. It is what a further calculation should use, and rounding an intermediate value before multiplying it into a cost or a population estimate introduces error that compounds.
An NNT below 1 is possible and means something specific. An absolute reduction above 100% is impossible, but a reduction of 60 percentage points gives an NNT of 1.67 — treat two people, prevent more than one event. Rounding to 2 is still correct.
And when the arms are identical the NNT is infinite. Not undefined, not zero: no number of people treated produces a benefit that is not there. The tool reports infinity rather than dividing by zero and printing something arbitrary.
The number needed to harm is the same arithmetic
When the treatment arm does worse, the absolute reduction is negative and the same formula gives the number needed to HARM: how many people must be treated for one additional bad outcome.
The tool switches the label automatically rather than reporting a negative NNT, which is not a quantity anyone can use.
Every treatment has both. A drug with an NNT of 20 for the benefit and an NNH of 15 for a serious adverse effect is doing more harm than good in that population, and neither number alone says so. Benefit and harm are computed from different outcomes in the same trial, and both belong in the report.
They are rarely presented together, and when they are, the harms are usually reported as relative figures while the benefits are absolute, or the reverse — which makes the comparison meaningless in exactly the way this page is about.
The likelihood of being helped or harmed is the ratio NNH ÷ NNT, and it is the number that actually answers “is this worth it”. Above 1 the benefit is more likely than the harm; below 1 it is not.
An NNT has a confidence interval, and it can be strange
NNT is a reciprocal, and reciprocals of intervals behave in ways that catch people out.
Invert the interval for the absolute risk reduction, not the interval for the relative one. The tool reports a Newcombe interval for the difference, which is the correct input.
If that interval contains zero, the NNT interval is not a range at all. It splits into two pieces running to infinity in both directions — from some NNT for benefit, through infinity, to some NNH for harm. This is the standard result and it is why NNT intervals are often omitted from papers where the effect is not significant.
So an NNT from a non-significant trial should not be quoted as a point estimate. It is compatible with benefit, no effect and harm simultaneously, and a single number conceals all three possibilities.
Even a significant result gives an asymmetric interval. Because the transformation is a reciprocal, the upper NNT bound is much further from the estimate than the lower one. Reporting “NNT 25 (95% CI 14–140)” is normal, and the width is real rather than a sign of an error.
Reporting a treatment effect so it can be acted on
Five things. The first three are almost always missing from the sentence that reaches a reader.
Give the absolute numbers. “Reduced events from 30% to 15%” is complete. “Reduced events by 50%” is not, and cannot be made complete by the reader.
Give the time horizon. An NNT over five years and over one year differ by roughly the ratio of the periods, and the horizon is frequently omitted.
Give the population. The baseline risk that produced this NNT belongs with it, so a reader can re-derive one for their own patient.
Give the harms in the same units. Benefits as absolute figures and harms as relative ones is the commonest asymmetry in trial reporting, and it always favours the treatment.
And give the interval, or say the result was not significant. An NNT from a trial whose confidence interval for the difference spans zero is a number with no direction, and presenting it as a point estimate is the most misleading thing on this list.
Method. NNT is computed as the reciprocal of the absolute risk reduction, measured against the control arm as baseline, and the exact unrounded value is reported alongside the conventional rounded-up figure. The suite pins the two worked cases numerically — a common outcome where inverting the relative reduction is wrong by a factor of 10/3, and a rare one where the identical published percentage makes it wrong by exactly 500 — rather than describing the error. The confidence interval for the difference uses Newcombe’s method, built from two Wilson intervals, for the reason the Wilson interval beats Wald on a single proportion. The suite also verifies that a relative risk is near-invariant when both event counts are scaled while the absolute reduction changes in every case. That engine is verified on every change against 75 assertions. The count and the per-case breakdown are published on the formula verification page.
Related calculators
Where this goes next:
Relative RiskRisk ratio and odds ratio from one table with the divergence between them plotted: they agree to half a percent at a 1% baseline, and at an 80% baseline the odds ratio is exactly half the risk ratio.
Two-Proportion Z-TestCompares two rates with the pooled z-test and a Newcombe interval for the difference, and shows that z² equals the 2×2 chi-square statistic exactly — so the “z-test or chi-square” question has no content.
Odds RatioOdds ratio, relative risk, risk difference and number needed to treat from one 2x2 table — because an odds ratio of 6.00 can describe a relative risk of 1.50.
Sensitivity and SpecificitySensitivity, specificity, PPV, NPV, likelihood ratios and MCC from a 2×2 table, with predictive values recomputed across the prevalence range — a 99%/99% test has a PPV of 50% at 1% prevalence and 9% at 0.1%.
Confidence IntervalIntervals for a mean or a proportion using t at every sample size and Wilson rather than the textbook Wald formula — with both methods shown, because Wald returns [0,0] at zero successes.
Effect SizeCohen d, Hedges g and the overlap between groups, with a sample-size control that moves the p-value while leaving the effect size fixed — the same d gives t = 1.29 at n=30 and 23.57 at n=10,000.
An educational tool, not clinical guidance. An NNT describes one outcome in one trial population over one follow-up period, and says nothing about harms, costs, or whether the treatment is appropriate for a particular person — decisions about treatment belong with a qualified clinician who can see the whole picture.
Published NNT from the absolute risk reduction with the relative figure beside it and the ratio between them. Two trials reporting the identical '50% reduction' have NNTs of 7 and 1,000; inverting the relative reduction gives 2 for both.
The size of that error is exactly the baseline risk, so it is worst when the outcome is rare - which is when relative figures are most likely to be quoted. Pinned numerically at a factor of 10/3 on the common-outcome case and exactly 500 on the rare one.
Added the curve that holds the relative reduction fixed and varies the baseline: every point produces the identical published percentage while the NNT runs from single digits to hundreds.
NNT is rounded UP rather than to the nearest whole number, with the exact unrounded value printed so the convention is visible. Identical arms return infinity rather than a divide-by-zero artefact.
The number needed to harm is the same arithmetic with the sign reversed, and the tool switches the label rather than reporting a negative NNT.
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