Attack Rate: Definition & Formula

Attack Rate

The attack rate is the proportion of an at-risk population that develops a defined outcome (illness, injury, or death) during a specified observation period bounded by a discrete exposure event -- such as a foodborne outbreak, a point-source chemical release, or a single gathering -- calculated as new cases divided by the population at risk at the start of that period, multiplied by 100. Despite the name, it is a cumulative incidence proportion, not a true rate: it carries no explicit time dimension in the denominator. A measure qualifies as an attack rate rather than a general incidence proportion specifically because the population and time window are bounded by an identifiable exposure episode, not an open-ended surveillance period. Two named variants extend the same logic: the food-specific attack rate restricts both numerator and denominator to people exposed to one candidate vehicle (a specific dish, water source, or lot), used to identify which exposure caused an outbreak; the secondary attack rate restricts both to susceptible close contacts of a known primary case, used to measure person-to-person transmissibility within a household, ward, or classroom.

ByCASRAI Editorial Board

· Last updated 1 Sept 2026

Formula

Attack rate (%) = (number of new cases ÷ total population at risk at the start of the period) × 100.

The numerator counts people who meet the case definition for the outbreak; the denominator is everyone at risk of developing the outcome, whether or not they were exposed.

Overall, food-specific, and secondary attack rates

Overall attack rate — total new cases divided by the whole population exposed to the outbreak setting, regardless of which specific exposure (if any) they had.
Food-specific attack rate — restricts numerator and denominator to people exposed to one candidate vehicle (a dish, a water source, a production lot). Comparing the attack rate among people who were exposed to a candidate item against the attack rate among people who were not is the standard first step in identifying the source of a foodborne outbreak.
Secondary attack rate — restricts numerator and denominator to susceptible close contacts of a known primary case (a household, ward, or classroom), used as a transmissibility measure rather than a source-identification tool.

Attack rate vs. incidence rate

An attack rate is a special case of a cumulative incidence proportion, not a separate statistic. What distinguishes it is the setting: the population and time window are both bounded by a discrete, identifiable exposure episode. A rate calculated over an open-ended surveillance period (a flu season, an annual case count per 100,000) is an ordinary incidence rate, not an attack rate, even though the arithmetic is similar. For measures that instead incorporate the varying length of time each subject was actually observed and at risk — rather than treating the period as a single fixed window — see person-time.

Related CASRAI terms

Outbreak investigation steps — the field-epidemiology sequence in which attack rates are calculated and compared across candidate exposures.
Epidemic curve — the companion visualization of case onset over time used alongside attack-rate tables during an outbreak investigation.
Case fatality rate — the analogous proportion for deaths among confirmed cases, not the population at risk.
Cohort study vs. case-control study — attack rates are typically calculated within a retrospective cohort design during outbreak investigation.
What is epidemiology? — broader context on the discipline and its measures of disease frequency.

Use in your systems

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