Vaccine Immunity Calculator — Herd Immunity Threshold and Coverage

Formula

How this is calculated

When enough people in a population are immune, each infected person on average generates fewer than one new case, so the outbreak declines naturally. The herd immunity threshold (HIT) is the minimum immune fraction needed: HIT = 1 − 1/R₀, where R₀ is the basic reproduction number — the average number of secondary infections a single case generates in a fully susceptible population. A disease with R₀ = 3 requires at least 67% population immunity; measles with R₀ ≈ 15 requires over 93%.

Vaccine-derived immunity in the population = vaccine coverage × vaccine efficacy (VE). For example, 70% coverage with 90% VE contributes 63% immunity from vaccination alone. Adding natural immunity (from prior infection) gives total estimated population immunity. If this total meets or exceeds HIT, epidemic spread is theoretically suppressed.

Important limitations: R₀ is an average that varies by pathogen strain, social mixing patterns, and population density. Vaccine coverage and natural immunity estimates are always uncertain. The model assumes homogeneous mixing and that immunity is all-or-nothing — real populations have spatial clustering, waning immunity, and partial protection that make the actual threshold harder to pin down. Use these figures as illustrative estimates, not policy targets.