Number Needed to Treat (NNT) Calculator with Confidence Interval
Calculate the number needed to treat (NNT) or harm (NNH) from event rates, 2 × 2 event counts or events per patient-year, with ARR, RRR, relative risk and 95% confidence intervals (Wald or Newcombe).
How it works
ARR = CER − EER · NNT = 1 ÷ ARR, rounded up to a whole patient · RRR = ARR ÷ CER · RR = EER ÷ CER · 95% CI for ARR (Wald) = ARR ± 1.96 × √(CER(1 − CER)/n₁ + EER(1 − EER)/n₂) · 95% CI for NNT = 1 ÷ upper ARR limit to 1 ÷ lower ARR limit · Per patient-years: risk = 1 − e^(−events ÷ patient-years × years)
The number needed to treat is how many patients must receive a treatment instead of the comparison for one extra patient to avoid the outcome over the study period. It is the reciprocal of the absolute risk reduction (ARR), the plain difference between the control event rate (CER) and the treatment event rate (EER). By convention (Cochrane Handbook) the NNT is rounded up to the next whole patient, and this calculator also shows the exact 1 ÷ ARR. When the treatment increases the outcome, the reciprocal is a number needed to harm (NNH, or NNTH). Choose Event counts to enter a 2 × 2 table: the calculator then gives the confidence interval for the ARR (Wald method as in Altman 1998 and MedCalc, or the more accurate Newcombe hybrid score method), turns its limits into an NNT interval, and adds relative risk with its log-method interval, the odds ratio and a two-proportion z-test P value. If the ARR interval includes zero, the NNT interval runs through infinity and is written NNTH x to ∞ to NNTB y. Choose Per patient-years for trials that report events per patient-year: each rate is turned into a risk over the time horizon with 1 − e^(−rate × years), the method ClinCalc and Omni use. If the outcome you count is a good one (cure, response), set it under More options so that the benefit is EER − CER. An NNT is only meaningful together with the comparator, the outcome, the follow-up time and the baseline risk of the patients it came from.
Worked example
With the default event rates, 20% of control patients and 12% of treated patients have the bad outcome. ARR = 20.00% − 12.00% = 8.00%, so 1 ÷ 0.08 = 12.50 and the NNT is 13 (rounded up). RRR = 8 ÷ 20 = 40.00% and RR = 12 ÷ 20 = 0.600. Out of 1,000 patients, 200 have the event without treatment and 120 with it, so 80 are prevented. Entered as event counts (40 of 200 versus 24 of 200), the Wald 95% CI for the ARR is 0.86% to 15.14%, so the 95% CI for the NNT is NNTB 6.6 to 116.6.
Sources: Cochrane Handbook, Chapter 15: Interpreting results (NNT rounding, NNTB/NNTH) · ClinCalc: Number Needed to Treat calculator and worked examples · MedCalc: Relative risk and NNT with confidence intervals (Altman 1998) · CMAJ: Tips for learners of evidence-based medicine, NNT confidence intervals · Newcombe hybrid score interval for a difference of proportions (McGill) · Omni Calculator: NNT from percentages or patient-years
Frequently asked questions
Why is the NNT rounded up?
An NNT counts whole patients, and the Cochrane Handbook says the convention is to round it up to the next whole number. If 1 ÷ ARR is 12.5, treating 12 patients is not quite enough to expect one prevented event, so 13 is reported. The exact reciprocal is also shown for use in further calculations.
How is the confidence interval for the NNT calculated?
First a confidence interval is found for the absolute risk reduction, here with the Wald formula ARR ± 1.96 × SE (the method in Altman 1998, MedCalc and most calculators) or with the Newcombe hybrid score method. The NNT limits are the reciprocals of those ARR limits, swapped in order: an ARR of 7% with a 95% CI of 2.92% to 11.08% gives an NNT interval of about 9.0 to 34.2.
What does an NNT interval with infinity in it mean?
If the ARR interval runs from a negative value to a positive one, the treatment might help, do nothing or harm. The NNT interval then goes from a number needed to harm, through infinity (no effect), to a number needed to benefit, written for example NNTH 4.8 to ∞ to NNTB 2.9. It means the result is not statistically significant.
What is the difference between NNT and NNH?
Both are 1 ÷ the absolute risk difference. NNT (or NNTB) is used when the treatment lowers a bad outcome; NNH (or NNTH) is used when it raises one, for example a side effect. A treatment is attractive when its NNT for the main benefit is much smaller than its NNH for important harms.
What is a good number needed to treat?
There is no universal cut-off. An NNT of 2 to 5 is a large effect, typical of antibiotics for some infections, while preventive drugs often have NNTs of 50 to several hundred over years. Whether an NNT is worthwhile depends on how serious the outcome is, the cost, and the harms.
How do I calculate the NNT from events per patient-year?
Convert each rate into a risk over the time you care about with risk = 1 − e^(−rate × years), then take 1 ÷ the difference. For 12 versus 4 events per 1,000 patient-years over one year the risks are 1.19% and 0.40%, and the NNT is about 126. For rare events this is close to 1,000 ÷ 8 = 125.
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Educational statistics tool, not medical advice. An NNT summarises one study population; treatment decisions should be made with a clinician who knows the patient.