Herd Immunity Threshold Calculator
The share of a population that must be immune to stop a pathogen spreading, from its basic reproduction number — with the vaccination coverage that reaches it at a given vaccine effectiveness, and the effective reproduction number at the immunity you have now.
Each case infects R₀ others in a fully susceptible population.
How the herd immunity threshold calculator works
Each case infects R₀ others in a fully susceptible population. If a fraction of people are immune, only the rest can be infected, so the effective number is R₀ times the susceptible share; when that falls below one, each case infects fewer than one other and the outbreak dies out. The threshold is 1 − 1/R₀: 67% for R₀ = 3, 94% for measles at 16.
A vaccine that is 90% effective protects only 90% of those who take it, so the coverage needed is the threshold divided by the effectiveness — and when that exceeds 100%, vaccination alone cannot get there.
Formula: HIT = 1 − 1/R₀; coverage = HIT / VE; R_eff = R₀ (1 − immune)
Worked examples
| Inputs | Herd immunity threshold | Note |
|---|---|---|
| R₀ of 3 | 66.67% | 67% immune, 74% coverage |
| Measles | 93.75% | 94% immune, 97% coverage |
| A weak vaccine | 80% | unreachable by vaccination alone |
FAQFrequently asked questions
What is herd immunity?
Protection of the unvaccinated by the immunity of those around them: when enough people cannot transmit, chains of infection break before they reach the susceptible.
What is R₀?
The average number of people one case infects in a population with no immunity. Seasonal flu is around 1.3, the original SARS-CoV-2 about 3, measles 12 to 18.
Why is the threshold so high for measles?
Because 1 − 1/16 is 94%. With a vaccine that is 97% effective, that means vaccinating essentially everyone — which is why measles returns wherever coverage slips.
Does immunity from infection count?
Yes — the threshold is about immunity, however acquired. Enter the share already immune from any source to see the effective R now.
What does the model leave out?
Uneven mixing, waning immunity, and variants with a higher R₀. Real thresholds are somewhat higher than this formula in clustered populations and lower in well-mixed ones.
Where these figures come from
- NCBI Bookshelf — Molecular Biology of the Cell — growth kinetics and molecular conventions
- CSIRO — Australia's national science agency
Last checked: September 2026. Formulas are the standard textbook forms; assumptions are stated on each page because they are where these models break.