The number needed to treat is the number of patients who must receive a treatment for one of them to avoid a bad outcome that would otherwise have happened. It is the reciprocal of the absolute risk reduction, the difference between the control event rate and the experimental event rate. This calculator works out the absolute risk reduction, the relative risk reduction, and the number needed to treat (or the number needed to harm when the treatment increases risk), each with a 95% confidence interval.
Number needed to treat calculator
Turn the event counts from a trial or a pooled relative effect into an absolute risk reduction and the number of patients you would treat to prevent one extra event.
Number needed to treat (benefit)
8
Exact value 7.69. 95% interval 4.66 to 21.96.
Risk reduction
Absolute risk reduction13.0% (95% CI 4.6% to 21.4%)
Relative risk reduction40.6% (95% CI 15.7% to 58.2%)
Standard error of absolute risk reduction0.0431
Relative effect measures
Relative risk (treatment vs control)0.594 (95% CI 0.418 to 0.843)
Odds ratio0.498 (95% CI 0.314 to 0.791)
Event rates
Experimental event rate (treatment)19.0%
Control event rate32.0%
Report-ready text
The absolute risk reduction was 13.0% (95% CI 4.6% to 21.4%), giving a number needed to treat of 8 (95% CI 5 to 22). The relative risk was 0.59 (95% CI 0.42 to 0.84).
The number that turns statistics into a decision
The number needed to treat answers the question a clinician and a patient most want answered: how many people have to take this treatment for one of them to be spared a bad outcome? It is an absolute measure, and that is its strength. A risk ratio of 0.5 sounds dramatic, but halving a risk that was already tiny changes very little in real terms. The number needed to treat forces the baseline risk back into the picture, because it is built from the absolute risk reduction, the plain difference between the control event rate and the experimental event rate. Take the reciprocal of that difference and you have the count of patients treated per event avoided. This is why a systematic review that only reports relative effects leaves readers short; translating a pooled relative measure into an absolute one is a core reporting step, and it pairs naturally with our comparison of odds ratios and risk ratios.
When to use it, and when it misleads
Reach for the number needed to treat when you are communicating the practical size of a benefit, especially to a non-statistical audience, and when you weigh a benefit against a harm by comparing it with a number needed to harm. Be cautious in three situations. First, it is meaningless without a stated time horizon, because event rates grow with follow-up. Second, it is anchored to the baseline risk you used, so a single number does not transfer between a high-risk and a low-risk population. Third, it should not be pooled directly across studies; pool the relative effect first in a meta-analysis, then convert to an absolute scale at a chosen baseline. Our walkthrough of running a meta-analysis end to end shows where that conversion fits, and the meta-analysis pooling calculator produces the pooled relative effect you start from.
A worked example and interpreting the size
Imagine a trial where 12% of the control arm has a stroke over two years and 8% of the treatment arm does. The absolute risk reduction is 0.12 minus 0.08 = 0.04, so the number needed to treat is 1 / 0.04 = 25. Twenty-five people must take the treatment for two years to prevent one extra stroke. Now suppose a different drug also cuts a 12% risk but only to 11%; the absolute risk reduction is 0.01 and the number needed to treat is 100, far less impressive despite a similar-sounding relative claim. There is no universal threshold for “good”: a number needed to treat of 5 to prevent a stroke is excellent, while a 5 to relieve a mild, self-limiting symptom may not be worth the cost or the side effects. Read the value against the seriousness of the outcome and the harms, the same balancing that underpins grading the certainty of evidence.
Common mistakes researchers make
The biggest error is misreading the confidence interval. The number needed to treat is a reciprocal, and reciprocals misbehave near zero. When the interval for the absolute risk reduction crosses zero, inverting it produces a broken range that runs from a number needed to treat, out to infinity, and back through a number needed to harm; the honest report is “not estimable” rather than a tidy pair of limits, which is why this calculator falls back to the absolute risk reduction interval in that case. A second mistake is quoting the figure with no follow-up time. A third is rounding down for show; round up, because you cannot treat a fraction of a person, and rounding down overstates the benefit. The fuller background is in our explainer on what the number needed to treat means in practice, and translating effects this carefully is part of our statistical analysis service.
How it works
The two event rates come straight from the counts: the experimental event rate is the treatment events divided by the treatment total, and the control event rate is the control events divided by the control total.
EER = eE / nE
CER = eC / nC
ARR = CER - EER
RRR = ARR / CER
NNT = 1 / ARR (report 1 / |ARR| as NNH if ARR < 0)
The standard error of the absolute risk reduction treats each arm as a binomial proportion, and the confidence interval is the usual normal-approximation interval.
SE(ARR) = sqrt( EER(1-EER)/nE + CER(1-CER)/nC )
95% CI(ARR) = ARR ± 1.96 × SE(ARR)
Inverting the bounds of the absolute risk reduction gives the interval for the number needed to treat. When that interval crosses zero the inverted interval is discontinuous and spans both benefit and harm, so it is reported as undefined, which is the well-known limitation of a confidence interval on a reciprocal.
Frequently asked questions
- How do you calculate the number needed to treat?
- Take the event rate in the control arm minus the event rate in the treatment arm to get the absolute risk reduction, then take the reciprocal. If the absolute risk reduction is 0.10, the number needed to treat is one divided by 0.10, which is 10. Rounding up to a whole number is the convention because you cannot treat a fraction of a patient.
- What is the difference between number needed to treat and number needed to harm?
- They use the same calculation but point in opposite directions. When the treatment lowers the event rate the absolute risk reduction is positive and the reciprocal is the number needed to treat for one extra good outcome. When the treatment raises the event rate the difference is negative and the reciprocal of its size is the number needed to harm, the number of people treated to cause one extra bad outcome.
- Why does the confidence interval for the number needed to treat look strange?
- The number needed to treat is the reciprocal of the absolute risk reduction, and reciprocals behave badly near zero. When the confidence interval for the absolute risk reduction includes zero, inverting it produces a discontinuous range that runs from a number needed to treat through infinity to a number needed to harm. In that case the interval is reported as undefined and the underlying interval for the absolute risk reduction is shown instead.
- What is a good number needed to treat?
- Lower is better because fewer people must be treated to produce one extra good outcome, but there is no universal threshold. The acceptable value depends on the seriousness of the outcome prevented, the cost, and the harms of treatment. A number needed to treat of 5 to prevent a stroke is excellent, while the same value to relieve a mild symptom may not justify the treatment.
- Can I get a number needed to treat from a pooled odds ratio or risk ratio?
- Yes, but you also need a baseline risk to anchor it to. A relative measure on its own does not fix the absolute benefit, because the same risk ratio produces a very different number needed to treat in a high-risk population than in a low-risk one. Apply the pooled relative effect to a chosen control event rate, work out the new treatment risk, and take the reciprocal of the difference.
- Why does the number needed to treat depend on follow-up time?
- The number needed to treat is tied to the period over which the event rates were measured. A value of 20 over one year is not the same as 20 over five years, because more events accumulate with longer follow-up. Always report the time horizon alongside the number needed to treat, otherwise the figure cannot be compared between trials or acted on sensibly.
The guides behind this tool
More review and meta-analysis tools
Meta-analysisPool study effect estimates with fixed-effect and random-effects models, with the heterogeneity statistics shown.Open tool Heterogeneity (I-squared)Quantify how much your studies disagree: Cochran's Q, I-squared, H, and the between-study variance tau-squared.Open tool Odds ratio / risk ratioTurn a 2x2 table of events into an odds ratio, risk ratio, and risk difference, each with a 95% confidence interval.Open tool