Herd Immunity Threshold Calculator
Calculate the vaccination coverage needed to achieve herd immunity based on a disease's basic reproduction number (R₀) and vaccine efficacy.
What Is Herd Immunity? Herd immunity, also called population or community immunity, is reached when enough people are immune, through vaccination or prior infection, that transmission cannot sustain itself. When enough people are immune, the disease can no longer spread efficiently and dies out, even protecting those who cannot be vaccinated (newborns, immunocompromised individuals).
The Basic Reproduction Number (R₀) R₀ (pronounced “R-naught”) is the average number of people an infected person will infect in a completely susceptible population.
- R₀ < 1: The disease will die out on its own
- R₀ = 1: The disease is endemic (stable)
- R₀ > 1: The disease will spread
Well-known R₀ values (approximate):
- Seasonal influenza: 1.2–1.4
- SARS-CoV-1: 2–3
- COVID-19 (original strain): 2–3; Omicron: 8–15
- Polio: 5–7
- Mumps: 4–7
- Rubella: 5–7
- Smallpox: 5–7
- Measles: 12–18 (one of the highest known)
Herd Immunity Threshold (HIT) Formula HIT = 1 − (1 / R₀)
This gives the minimum proportion of the population that must be immune to stop transmission.
Vaccination Coverage Needed If the vaccine is not 100% effective, more people need to be vaccinated: Vaccination coverage needed = HIT ÷ (vaccine efficacy / 100)
Worked Examples COVID-19 (R₀ = 5, 90% vaccine efficacy): HIT = 1 − 1/5 = 80% Coverage needed = 80% ÷ 0.90 = 88.9%
Measles (R₀ = 15, 97% vaccine efficacy): HIT = 1 − 1/15 = 93.3% Coverage needed = 93.3% ÷ 0.97 = 96.2% (This is why 96%+ measles vaccination is required for herd immunity)
Why the real number is always higher than this This formula assumes a population that mixes at random and immunity that does not fade. Neither is true, so treat the result as a floor rather than a target:
- Immunity wanes over time for both vaccines and natural infection
- R₀ varies with behavior, population density, and variants
- Coverage has to be spread evenly. Clustered unvaccinated groups sustain local outbreaks even when the national figure looks fine, which is how measles keeps returning to countries that had eliminated it
- Some diseases have animal reservoirs, making true eradication impossible
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
SuperGlobalCalculator is independently built and maintained. See how we build and verify our calculators.