Epidemiology & Public Health
Basic

Attack Rate

Proportion of an exposed population that develops the illness during an outbreak.

Formula

AR=Cases during outbreakPopulation exposed×100AR = \frac{\text{Cases during outbreak}}{\text{Population exposed}} \times 100

Variables

ARAttack rate (%)
\text{Cases during outbreak}People who fell ill
\text{Population exposed}Total people exposed

Example

30 ill at a 120-person event → AR = 25 %

How it works

Attack rate tells you what fraction of everyone who was exposed to a source of infection became sick during the outbreak. It works by comparing the number of new cases to the total number of exposed people, then converting that fraction into a percentage so it is easy to interpret and compare. This is especially useful when the group at risk is clearly defined, such as people who ate the same meal or attended the same event.

When to use it

Use this formula in outbreak investigations to measure how strongly a specific exposure is linked to illness. It is commonly used in foodborne outbreaks, school or workplace illness clusters, and other situations where investigators know exactly who was exposed.

Worked example, step by step

A company picnic had 80 attendees. After the picnic, 12 people developed the same stomach illness. Attack rate = (Cases during outbreak / Population exposed) × 100 Attack rate = (12 / 80) × 100 Attack rate = 0.15 × 100 Attack rate = 15% So, 15% of the exposed group became ill.

Common mistakes to avoid

  • Using the total community population instead of only the people who were exposed
  • Counting old cases that started before the outbreak instead of only new cases during the outbreak
  • Forgetting to multiply by 100, which leaves the answer as a decimal instead of a percentage

Did You Know?

Food-borne outbreaks are classic attack-rate investigations — the dish with the highest AR among eaters is usually the culprit.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026