Epidemiology & Public Health
Intermediate

Number Needed to Treat

Number of patients who must receive a treatment for one additional patient to benefit.

Formula

NNT=1ARRNNT = \frac{1}{ARR}

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Variables

NNTNumber needed to treat
ARRAbsolute risk reduction (control rate − treatment rate)

Example

Control event rate 20 %, treatment 15 % → ARR = 0.05, NNT = 20

How it works

Number Needed to Treat tells you how many people must receive an intervention for one extra person to have a good outcome compared with not receiving it. It comes from the absolute risk reduction because the benefit is the fraction of patients who are helped beyond what would have happened anyway; taking 1 divided by that fraction converts a per-patient difference into a "people needed" count. A smaller ARR means a rarer benefit, so more patients are needed to see one additional success.

When to use it

Use this when comparing a treatment or prevention strategy against a control in clinical trials, screening studies, or public health programs. It is especially useful for judging how practical or impactful an intervention is in real-world decision-making.

Worked example, step by step

Suppose a vaccine reduces disease risk from 12% in the control group to 7% in the vaccinated group. ARR = control rate − treatment rate = 0.12 − 0.07 = 0.05 NNT = 1 / ARR = 1 / 0.05 = 20 So, 20 people need to be vaccinated to prevent 1 additional case of disease.

Common mistakes to avoid

  • Using the treatment rate or control rate directly instead of the absolute risk reduction
  • Forgetting that ARR must be written as a decimal, not a percent
  • Rounding too early and getting an inaccurate NNT

Did You Know?

An NNT of 1 would be a perfect cure. In practice, aspirin for heart-attack prevention has an NNT around 100.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026