How to Calculate Number Needed to Treat and Number Needed to Harm

Number needed to treat (NNT) is calculated as the reciprocal of the absolute reduction in the risk of an undesirable outcome: NNT = 1 ÷ absolute risk reduction. Number needed to harm (NNH) is the reciprocal of the absolute increase in the risk of an adverse event: NNH = 1 ÷ absolute risk increase. Event rates must be entered as decimal proportions, and every result should be interpreted for a clearly defined outcome, comparison group, population, and follow-up period.

These measures translate differences between treatment and control groups into clinically understandable numbers. They can support evidence-based discussions about benefits and harms, but they do not determine whether a treatment is appropriate for an individual patient.

What Is Number Needed to Treat?

The number needed to treat is the estimated number of patients who would need to receive one intervention instead of a comparison intervention for one additional patient to experience the desired outcome during a specified period.

Depending on the study, the desired outcome may be:

• Prevention of an undesirable event, such as stroke, hospital admission, relapse, or death.
• Achievement of a beneficial event, such as symptom improvement, remission, healing, or treatment response.

A lower NNT generally represents a larger absolute treatment effect. However, whether an NNT is clinically favorable depends on the importance of the outcome, treatment burden, cost, safety profile, follow-up duration, and characteristics of the population.

What Is Number Needed to Harm?

The number needed to harm is the estimated number of patients who would need to receive an intervention instead of the comparison treatment for one additional patient to experience a specified adverse outcome during the study period.

Examples of harmful outcomes include major bleeding, treatment discontinuation, kidney injury, severe infection, symptomatic hypotension, or another clearly defined adverse event.

A higher NNH is usually preferable because it means that more patients would need to be treated before one additional harmful event is expected. Nevertheless, an apparently high NNH may still be concerning when the adverse outcome is severe or irreversible.

Information Required for NNT and NNH Calculation

For a binary outcome, obtain the following values from a clinical trial, cohort study, systematic review, or other comparative source:

• Experimental event rate (EER): the proportion of participants experiencing the event in the intervention group.
• Control event rate (CER): the proportion experiencing the same event in the control or comparison group.

Calculate each event rate using:

Event rate = number of participants with the event ÷ total number of participants in the group

The event must have the same definition and assessment period in both groups.

How to Calculate Number Needed to Treat

Method 1: Preventing an undesirable outcome

When the event is undesirable and occurs less frequently with treatment, calculate the absolute risk reduction:

Absolute risk reduction (ARR) = CER − EER

Then calculate:

NNT = 1 ÷ ARR

If percentages are used instead of decimal proportions:

NNT = 100 ÷ ARR expressed as a percentage

Worked NNT example

Suppose a study reports that an undesirable outcome occurred in 20% of the control group and 12% of the treatment group.

1. Convert the percentages to decimals: CER = 0.20 and EER = 0.12.
2. Calculate the absolute risk reduction: ARR = 0.20 − 0.12 = 0.08.
3. Calculate the NNT: NNT = 1 ÷ 0.08 = 12.5.
4. Round upward to the next whole patient: NNT = 13.

The result means that approximately 13 patients would need to receive the treatment instead of the control intervention for one additional undesirable outcome to be prevented over the study’s follow-up period.

Method 2: Producing a beneficial outcome

If the recorded event is beneficial, such as clinical response, calculate the absolute benefit increase:

Absolute benefit increase (ABI) = EER − CER

Then calculate:

NNT = 1 ÷ ABI

For example, if 60% of treated patients and 45% of control patients achieve a response:

1. ABI = 0.60 − 0.45 = 0.15.
2. NNT = 1 ÷ 0.15 = 6.67.
3. Round upward: NNT = 7.

Approximately seven patients would need to be treated for one additional patient to achieve the beneficial response during the stated follow-up period.

How to Calculate Number Needed to Harm

When an adverse event occurs more frequently in the treatment group, calculate the absolute risk increase:

Absolute risk increase (ARI) = EER − CER

Then calculate:

NNH = 1 ÷ ARI

If the absolute risk increase is expressed as a percentage:

NNH = 100 ÷ ARI expressed as a percentage

Worked NNH example

Suppose a treatment-related adverse event occurs in 10% of the intervention group and 4% of the control group.

1. Convert the percentages to decimals: EER = 0.10 and CER = 0.04.
2. Calculate the absolute risk increase: ARI = 0.10 − 0.04 = 0.06.
3. Calculate the NNH: NNH = 1 ÷ 0.06 = 16.67.

The unrounded result is an NNH of approximately 16.7. When a whole number is required, the rounding convention should be stated. A conservative safety convention rounds NNH downward, producing an NNH of 16, because it avoids overstating how many people can be treated before an additional harm occurs.

The interpretation is that treating approximately 16 patients instead of using the comparison intervention may result in one additional specified adverse event over the study period.

NNT and NNH Formula Summary

How to Interpret NNT and NNH Together

NNT and NNH describe separate outcomes and should not be compared mechanically. The severity, reversibility, timing, and patient importance of each outcome must be considered.

For example, a treatment might have:

• An NNT of 20 for preventing one stroke over five years.
• An NNH of 50 for causing one additional major bleeding event over five years.

These values may help structure a benefit–harm discussion, but they do not prove that the treatment is beneficial for every patient. Preventing a disabling stroke and causing a reversible minor adverse effect are not clinically equivalent. Conversely, a rare but fatal harm may carry substantial weight even when the NNH is high.

Interpretation should consider:

• The clinical importance of the beneficial and harmful outcomes.
• The probability of each outcome without treatment.
• The duration of treatment and follow-up.
• Patient preferences and treatment goals.
• Competing risks, comorbidities, and life expectancy.
• Cost, inconvenience, monitoring requirements, and treatment burden.

Why Baseline Risk Matters

NNT is based on an absolute risk difference, so it is strongly influenced by baseline risk. Patients at higher baseline risk may have a greater absolute benefit from an effective preventive treatment, even when the relative risk reduction is similar across risk groups.

Consider a treatment that reduces relative risk by 25%:

The relative reduction is 25% in both examples, but the NNT differs substantially because the baseline risks differ. An NNT from one study should therefore not be applied automatically to a population with a different underlying risk.

Always Include the Time Frame

An NNT or NNH is incomplete without a follow-up period. An NNT of 20 over three months is not equivalent to an NNT of 20 over ten years.

A complete statement should identify:

• The intervention and comparator.
• The beneficial or harmful outcome.
• The population studied.
• The follow-up period.

For example: “The five-year NNT was 20 for preventing one additional stroke among adults with the study’s eligibility characteristics.”

Confidence Intervals and Statistical Uncertainty

NNT and NNH are estimates derived from observed risk differences. They should ideally be reported with confidence intervals, particularly in research reports and evidence summaries.

The confidence interval is usually calculated for the absolute risk difference first, and its limits are then inverted. This process can produce unusual-looking intervals because a risk difference of zero corresponds to an infinite NNT.

If the confidence interval for the risk difference includes zero, the data may be compatible with benefit, no difference, or harm. In that situation, reporting only the point estimate can create a misleading impression of certainty. The interval may need to be expressed as separate ranges extending through infinity, such as a possible number needed to benefit on one side and a possible number needed to harm on the other.

Time-to-event outcomes, adjusted analyses, cluster-randomized trials, and studies with varying follow-up generally require appropriate statistical methods rather than simply applying the basic reciprocal formula to crude percentages.

Common Calculation Errors

Using relative risk reduction

NNT is the reciprocal of the absolute risk reduction, not the relative risk reduction. Using relative risk reduction usually produces an incorrect and overly favorable result.

Failing to convert percentages

When using the formula 1 ÷ ARR, enter 8% as 0.08, not 8. Alternatively, use 100 ÷ 8.

Reversing the event rates

First determine whether the recorded event is desirable or undesirable. The subtraction must reflect the direction of benefit or harm.

Ignoring the outcome definition

An NNT for reducing symptoms cannot be interpreted as an NNT for preventing death. Each result applies only to the measured outcome.

Ignoring follow-up duration

Comparing NNT values from studies with substantially different follow-up periods can be misleading.

Comparing different populations directly

Differences in age, disease severity, baseline risk, adherence, comorbidities, and co-interventions can change absolute treatment effects.

Assuming every treated patient has the same result

NNT is a population-level summary. It does not identify which particular patient will benefit or experience harm.

Reporting excessive precision

Values such as an NNT of 12.487 suggest more certainty than the data usually support. Report the unrounded calculation when useful, followed by a clearly defined whole-number convention and an appropriate confidence interval.

Practical Calculation Checklist

1. Define the outcome as beneficial or harmful.
2. Confirm that both groups use the same outcome definition and follow-up period.
3. Calculate the experimental and control event rates.
4. Calculate ARR, ABI, or ARI using the appropriate direction.
5. Convert percentages to decimal proportions before taking the reciprocal.
6. Calculate NNT or NNH.
7. Apply and state an appropriate rounding convention.
8. Report the intervention, comparator, outcome, population, and time frame.
9. Include confidence intervals when available.
10. Interpret the result alongside outcome severity, baseline risk, study quality, and patient preferences.

Clinical Limitations of NNT and NNH

NNT and NNH are useful communication tools, but they compress complex evidence into single values. They may obscure differences in the timing or severity of events, recurrent events, treatment adherence, competing risks, and variation in individual treatment effects.

The calculations are also only as reliable as the underlying evidence. Bias, imprecision, missing outcome data, selective reporting, short follow-up, or poor applicability can make a mathematically correct NNT clinically unreliable.

NNT and NNH should therefore be interpreted with relative and absolute effect estimates, confidence intervals, study design, certainty of evidence, and individual clinical circumstances.

About the Author

Dr. Taimoor Asghar writes evidence-aware medical and clinical-calculation resources for taimoorasghar.com.

Medical disclaimer: This article is for educational purposes and does not provide individual diagnosis or treatment advice. NNT and NNH values should not replace clinical judgment, a complete assessment of the evidence, or discussion with an appropriately qualified healthcare professional. Do not start, stop, or change a treatment solely on the basis of a calculated NNT or NNH.