Number Needed to Harm (NNH) Calculator

Compute the Number Needed to Harm (NNH) from treatment and control event rates or from an absolute risk increase (ARI). Includes automatic interpretation and confidence interval support.

1. NNH from 2×2 trial data

Enter the number of patients with the adverse event and the total number of patients in each group.

Treatment group

Control group

Optional: confidence interval for NNH
CI is computed on the absolute risk increase using a normal approximation, then inverted to obtain the NNH interval.

What is Number Needed to Harm (NNH)?

Number Needed to Harm (NNH) is a measure used in clinical epidemiology to express how many patients need to be exposed to a treatment or risk factor for one additional adverse event to occur, compared with a control or baseline condition.

It is the counterpart of the Number Needed to Treat (NNT), which expresses how many patients must be treated for one additional beneficial outcome. While NNT is based on an absolute risk reduction, NNH is based on an absolute risk increase.

Formulas used by this NNH calculator

1. Event risks in treatment and control groups

Let:
  • \(E_T\) = number of adverse events in the treatment group
  • \(N_T\) = total number of patients in the treatment group
  • \(E_C\) = number of adverse events in the control group
  • \(N_C\) = total number of patients in the control group
Then the event risks are:

\[ R_T = \frac{E_T}{N_T}, \quad R_C = \frac{E_C}{N_C} \]

The absolute risk increase (ARI) is:

\[ ARI = R_T - R_C \]

Finally, the Number Needed to Harm is:

\[ NNH = \frac{1}{ARI} \]

In practice, NNH is usually rounded up to the next whole number:

\[ NNH_{\text{reported}} = \lceil NNH \rceil \]

2. From risks or absolute risk increase

If you already know the event risks (as proportions or percentages), the same formulas apply:

\[ ARI = R_T - R_C, \quad NNH = \frac{1}{ARI} \]

If you know the absolute risk increase directly:

\[ NNH = \frac{1}{ARI} \]

3. Confidence interval for NNH (approximate)

The calculator can optionally compute an approximate confidence interval (CI) for the NNH by first calculating a CI for the absolute risk increase and then inverting it.

Standard error (SE) of the risk difference:

\[ SE(ARI) = \sqrt{\frac{R_T(1 - R_T)}{N_T} + \frac{R_C(1 - R_C)}{N_C}} \]

For a two-sided confidence level \(1 - \alpha\), with critical value \(z_{1-\alpha/2}\):

\[ ARI_{\text{low}} = ARI - z_{1-\alpha/2} \cdot SE(ARI) \] \[ ARI_{\text{high}} = ARI + z_{1-\alpha/2} \cdot SE(ARI) \]

The corresponding NNH interval is:

\[ NNH_{\text{low}} = \frac{1}{ARI_{\text{high}}}, \quad NNH_{\text{high}} = \frac{1}{ARI_{\text{low}}} \]

(assuming \(ARI_{\text{low}} > 0\); if the CI for ARI crosses zero, the NNH CI is not well defined and the calculator will warn you.)

How to interpret NNH

  • Smaller NNH (e.g. 5–20): relatively frequent harm; strong safety signal.
  • Larger NNH (e.g. > 100): rare harm; may be acceptable depending on the benefit.
  • Negative ARI: the treatment reduces the adverse event; interpret as NNT for benefit.
  • ARI ≈ 0: little or no difference between groups; NNH tends to infinity.

Always interpret NNH together with the clinical importance of the adverse event, the Number Needed to Treat (NNT) for benefit, and the quality of the underlying evidence.

Worked example

Suppose a randomized trial reports:

  • Treatment group: 25 serious bleeding events among 500 patients.
  • Control group: 10 serious bleeding events among 500 patients.

Step 1 – Compute risks:

\[ R_T = 25 / 500 = 0.05 \quad (5\%) \] \[ R_C = 10 / 500 = 0.02 \quad (2\%) \]

Step 2 – Absolute risk increase:

\[ ARI = 0.05 - 0.02 = 0.03 \quad (3\% \text{ absolute increase}) \]

Step 3 – NNH:

\[ NNH = \frac{1}{0.03} \approx 33.3 \Rightarrow NNH_{\text{reported}} = 34 \]

Interpretation: for every 34 patients treated, one additional serious bleeding event is expected compared with control.

Limitations and good practice

  • NNH assumes a constant risk difference across patient subgroups and time, which may not hold.
  • It is sensitive to baseline risk: the same relative risk can produce very different NNH values in different populations.
  • Confidence intervals are essential; a point estimate alone can be misleading.
  • Always report the time horizon (e.g. 1-year NNH vs. 5-year NNH).

This calculator is intended for educational and research support only and does not replace clinical judgment or local statistical guidance.

NNH Calculator – Frequently Asked Questions

What is Number Needed to Harm (NNH)?

Number Needed to Harm (NNH) is the number of patients who must be exposed to a treatment or risk factor for one additional adverse event to occur, compared with a control group. It is the inverse of the absolute risk increase (ARI) between treatment and control.

How do I choose between NNH and NNT?

If the treatment increases the risk of an adverse outcome (ARI > 0), you report NNH. If it reduces the risk of a bad outcome or increases the chance of a good outcome (absolute risk reduction > 0), you report NNT. This calculator automatically flags when ARI is negative and suggests interpreting the result as NNT instead.

Why does the calculator sometimes say “NNH not defined”?

When the absolute risk increase is zero or extremely close to zero, the NNH tends to infinity and cannot be meaningfully reported. This usually reflects no detectable difference in harm between treatment and control within the sample size of the study.

Should I always round NNH up?

Yes. By convention, NNH is rounded up to the next whole number (ceiling), because you cannot treat a fraction of a patient and rounding down would overstate the frequency of harm. The calculator shows both the exact value and the rounded NNH.

Can I use this NNH calculator for observational studies?

Mathematically, yes: you can compute NNH from any pair of risks. However, in observational studies the association may be confounded and not causal. In such cases, NNH should be interpreted as an association measure rather than a causal effect, and reported with appropriate caveats.