Herd Immunity Threshold Calculator
HIT from basic reproduction number (R0).
About this calculator
The herd immunity threshold (HIT) is the share of a population that needs to be immune -- through vaccination or prior infection -- before an infectious disease can no longer sustain ongoing transmission. It follows directly from a pathogen's basic reproduction number, R0: the average number of secondary infections one case produces in a fully susceptible population. This calculator applies the standard epidemiological formula HIT = 1 - 1/R0, formalized in Paul Fine's widely cited 1993 review of herd immunity theory, so HIT depends on R0 alone -- vaccine efficacy and population size do not change the underlying threshold, only what it takes to reach it.
A pathogen with R0 = 2 (roughly seasonal flu's range) has a HIT of 50%; a highly contagious pathogen like measles, with R0 commonly cited around 12-18, needs on the order of 92-94% immunity, which is why measles requires such high vaccination coverage to stay controlled. Because no vaccine is perfectly effective, the required VACCINATION coverage is higher than the HIT itself -- this calculator divides HIT by the entered vaccine efficacy to estimate that gap, then scales it by population size to estimate how many people that represents. The formula assumes homogeneous mixing (everyone equally likely to contact everyone else) and random (not selective) immunity; real populations mix unevenly by geography and social network, so public-health guidance for a specific disease should come from a source like the CDC or WHO rather than this simplified model alone.
Medical Disclaimer
This calculator is for informational and educational purposes only. It is not a substitute for professional medical advice, diagnosis, or treatment. Always consult a qualified healthcare provider before making decisions about your health. Never disregard professional medical advice or delay seeking it because of results from this tool.
Inputs
Results
Herd immunity threshold (%)
66.7%
Figures current as of 1993. Source: Fine PEM. Herd immunity: history, theory, practice. Epidemiol Rev. 1993;15(2):265-302.
How to Use This Calculator
- Enter the pathogen's Basic reproduction number (R0), the Vaccine efficacy (%), and the Population size.
- Review the Herd immunity threshold (%) result — the share of the population that needs immunity to stop sustained transmission.
- Use Required vaccination coverage (%) and People to vaccinate to plan how many people actually need to be vaccinated, accounting for imperfect vaccine efficacy.
How the result changes with Basic reproduction number (R0)
| Basic reproduction number (R0) | Herd immunity threshold (%) |
|---|---|
| 1.5 | 33.3% |
| 2.25 | 55.6% |
| 4.5 | 77.8% |
| 7.5 | 86.7% |
What each input means
- Basic reproduction number (R0)
- Average number of secondary infections from one case in a fully susceptible population.
- Vaccine efficacy (%)
- Vaccine efficacy in preventing transmission.
- Population size
- Total population size for absolute calculations.
What each result means
- Herd immunity threshold (%)
- Minimum proportion immune to stop sustained transmission.
- Required vaccination coverage (%)
- Vaccination rate needed accounting for vaccine efficacy.
- People to vaccinate
- Absolute number needing vaccination in the population.
- Effective R at target coverage
- Effective reproduction number when coverage target is met.
- Susceptible remaining
- Number of susceptible individuals remaining at HIT.
How this is calculated
Worked example, using the default values
- Identify Input ParametersBasic reproduction number (R0) = 3, Vaccine efficacy (%) = 90, Population size = 330000000 = 3 input(s) provided
- Calculate Herd immunity thresholdHerd immunity threshold66.7 = 66.7%
- Calculate Required vaccination coverageRequired vaccination coverage74.1 = 74.1%
- Calculate People to vaccinatePeople to vaccinate244530000 = 244530000
Figures and sources
- Herd immunity threshold (HIT = 1 - 1/R0) (1993) — Fine PEM. Herd immunity: history, theory, practice. Epidemiol Rev. 1993;15(2):265-302.
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does raising vaccine efficacy not change the herd immunity threshold itself?
The herd immunity threshold (HIT) is a property of the pathogen's transmissibility alone -- it is derived purely from R0 via HIT = 1 - 1/R0. Vaccine efficacy determines how much VACCINATION coverage is needed to reach that fixed threshold (a less effective vaccine needs more people vaccinated to deliver the same amount of population immunity), but it does not move the threshold itself. That is why this calculator reports the herd immunity threshold and the required vaccination coverage as two separate numbers.
Why does measles require such a high vaccination rate compared to the flu?
It comes down to how contagious each pathogen is, measured by R0. Seasonal influenza's R0 is typically cited around 1-2, giving a herd immunity threshold near 0-50%. Measles is far more transmissible, with R0 commonly cited in the range of about 12-18, which plugs into HIT = 1 - 1/R0 to give a threshold around 92-94%. The more contagious a disease is, the larger the immune share of the population has to be before transmission chains can no longer sustain themselves.
Does reaching the herd immunity threshold mean a disease cannot infect anyone else?
No -- it means sustained community-wide transmission is expected to decline rather than grow, not that transmission stops instantly or that every susceptible person is protected. Above the threshold, each new case is expected to infect fewer than one other person on average, so outbreaks tend to shrink; pockets of unvaccinated or susceptible people can still experience local transmission, especially if mixing is uneven rather than the uniform mixing this formula assumes.
How much does population size change the herd immunity threshold?
Not at all -- population size only scales the absolute head-count outputs (how many people need to be vaccinated, how many remain susceptible at the threshold). The threshold itself, expressed as a percentage, is set entirely by R0 through HIT = 1 - 1/R0. A city of 50,000 and a country of 300 million with the same R0 have the identical percentage threshold; only the number of people that percentage represents differs.
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