Airborne Infection Risk Calculator

Context and Purpose

Respiratory illnesses spread through droplets and aerosols emitted when infected individuals breathe, speak, cough or sing. The COVID‑19 pandemic highlighted how airborne transmission can dominate in enclosed spaces with insufficient ventilation. Public health guidelines often express recommendations qualitatively—open windows, reduce occupancy, wear masks—but translating those actions into quantitative risk estimates remains challenging for laypersons. The Wells‑Riley model, developed in the 1970s for tuberculosis outbreaks, offers a straightforward way to approximate the probability that at least one susceptible person becomes infected in a shared environment. The calculator below implements a variant of this equation, allowing users to explore how ventilation, exposure time and activity level combine to shape risk.

The Wells-Riley Equation

The canonical form of the Wells‑Riley equation is $P = 1 - e^{- \frac{I}{Q} q p t}$ . Here $P$ represents the probability that a susceptible individual becomes infected; $I$ is the number of infectious people in the room; $q$ denotes the quanta emission rate, an abstract unit that captures the infectious dose of airborne particles; $p$ is the breathing rate of each susceptible person; $t$ is the exposure duration; and $Q$ is the room ventilation rate measured in volumetric flow per unit time. The quanta concept packages complex virology into a single parameter, enabling the model to accommodate different pathogens and activities. For example, singing emits far more quanta than quiet breathing, while a virus with high transmissibility has a larger quanta per particle. The exponential structure stems from a Poisson process: infection occurs when at least one infectious quantum is inhaled.

Model Implementation

Ventilation rate is commonly expressed as air changes per hour (ACH), the number of times per hour that room air is replaced with outside air or filtered through a system. To convert ACH to volumetric flow $Q$ , the calculator multiplies ACH by room volume: $Q = ACH \times V$ . Substituting into the Wells‑Riley equation yields the working formula:

$Risk = 100 \times 1 - e^{- \frac{I}{V} q p t}$

The result is multiplied by 100 to express risk as a percentage. Because the model predicts probability for an individual susceptible person, the calculator also multiplies this probability by the number of susceptible occupants to estimate the expected number of secondary infections. This expectation assumes independence between occupants, which holds when infection probability is low; at higher probabilities, the formula still offers a useful upper bound.

Parameter Guidance

Infectious Individuals. This value represents people actively shedding virus. Even one asymptomatic person can infect others, so conservative estimates often assume at least one. In known outbreaks, multiple infectious individuals can drastically amplify risk.

Susceptible Occupants. Everyone present who could become infected. Including this field helps scale results to gatherings of different sizes and informs decisions about limiting attendance.

Room Volume. The physical size of the space measured in cubic meters. Higher volume dilutes aerosols, lowering concentration. Ceilings and floor plans influence volume; large open areas are safer than cramped rooms for the same number of people.

Air Changes per Hour. ACH quantifies ventilation effectiveness. Natural ventilation might yield 1–2 ACH, while modern HVAC systems may provide 4–6 ACH or more. Increasing ACH dramatically reduces risk, as fresh air removes infectious quanta.

Exposure Duration. The amount of time people share the space. Risk accumulates with each passing minute as more quanta are inhaled. Shorter meetings or breaks between sessions allow aerosols to disperse.

Quanta Emission Rate. Measured in quanta per hour per infectious person, this variable captures the infectiousness of the activity and pathogen. Quiet breathing might correspond to 5–10 quanta/hour for an average respiratory virus, whereas shouting, singing or high‑intensity exercise can exceed 100 quanta/hour. Scientific studies provide reference values for specific diseases, but the calculator allows experimentation across a wide range.

Breathing Rate. The volumetric rate at which each susceptible person inhales air, typically 0.5–0.6 m³/hour at rest. Physical activity increases this rate, driving up risk because more air—and thus more quanta—is inhaled.

Risk Categories

Risk %	Interpretation
0–10	Low: transmission unlikely
11–30	Moderate: precautions advisable
31–60	High: strong mitigation needed
61–100	Severe: avoid or radically alter conditions

Understanding Results

The Wells‑Riley model assumes homogeneous mixing: infectious aerosols distribute evenly throughout the room. In reality, airflow patterns, thermal plumes from occupants and localized ventilation can create concentration gradients. Nonetheless, the model captures broad trends. A calculated risk of 5% suggests that, on average, one out of twenty susceptible people might become infected after the specified exposure. Doubling ventilation or halving time typically halves risk, illustrating the power of mitigation. Because the expected number of infections is simply the product of individual risk and susceptible count, organizers can compare scenarios: is it safer to host two smaller gatherings or one large event? The calculator supports such planning.

Mitigation Strategies

Several interventions reduce airborne transmission. Increasing ACH through mechanical ventilation, opening windows or using portable HEPA filters improves dilution. Limiting occupancy ensures each person has more air volume. Masking, particularly with well‑fitting respirators, decreases both emission and inhalation of quanta, effectively reducing $q$ and $p$ . Shortening exposure by holding briefer meetings or incorporating breaks lowers $t$ . Placing infectious individuals in isolation removes them from the calculation entirely. These strategies are multiplicative; combining them yields dramatic risk reduction. The calculator encourages experimentation: users can adjust parameters to evaluate which combination best fits their constraints.

Historical Examples

The Wells‑Riley model gained prominence after analysis of a 1970s tuberculosis outbreak in a university building. Investigators estimated quanta generation from the index case and calculated infection probability, finding strong agreement with observed infections. During the COVID‑19 pandemic, researchers applied the model to choir practices, call centers and restaurants where superspreading events occurred. In one widely studied choir case, a single symptomatic singer infected the majority of attendees during a two‑hour rehearsal with minimal ventilation. By plugging typical quanta values for singing into the model, the high attack rate becomes predictable, reinforcing the importance of ventilation and limiting high‑emission activities.

Limitations and Extensions

Despite its utility, the Wells‑Riley equation omits several nuances. It assumes constant emission and ventilation rates, yet real gatherings involve fluctuating activity and dynamic HVAC control. It also treats all quanta as equally infectious and assumes every susceptible individual responds identically, ignoring immunity and mask fit variability. At very high infection probabilities, the independence assumption breaks down; once one susceptible person becomes infected early in the gathering, they may contribute additional quanta. Advanced models incorporate time-varying parameters, deposition of aerosols on surfaces, viral decay and filtration efficiency. Nonetheless, the simplicity of Wells‑Riley allows rapid calculation and qualitative understanding without specialized software.

Another limitation is that quanta emission rates for many diseases remain uncertain. Researchers derive them from retrospective outbreak analyses or laboratory measurements, both of which carry wide error bars. Consequently, any risk estimate should be viewed as a range rather than a precise number. The calculator helps users explore sensitivity: doubling or halving $q$ shows how much uncertainty in quanta affects overall risk.

Broader Implications

Quantifying airborne infection risk informs decisions beyond immediate personal safety. Building owners can justify investments in ventilation upgrades by estimating reduced transmission in offices or classrooms. Event planners balance capacity against safety, choosing to hold smaller gatherings or mandate masks when calculated risk exceeds acceptable thresholds. Public health officials can simulate outbreak scenarios to prioritize interventions in settings like shelters, prisons or healthcare facilities. Even as pandemics fade from headlines, seasonal influenza and future pathogens make indoor transmission an evergreen concern. Tools that translate scientific equations into accessible interactive models empower individuals and institutions to act proactively rather than reactively.

Education is another domain where the calculator shines. Teachers can integrate it into STEM curricula, letting students investigate how diseases spread and how engineering controls mitigate risk. Such exercises bridge physics, biology and social responsibility. By tweaking variables, students witness the effects of ventilation design, occupancy limits and behavioral choices. This comprehension fosters community resilience when outbreaks emerge.

As research advances, future versions might incorporate mask filtration efficiencies, CO₂ monitoring as a proxy for ventilation, or stochastic simulations for small groups. The core message, however, remains: airborne transmission is a probabilistic process shaped by environmental and behavioral factors. Quantitative tools provide insight, guiding measures that keep communities healthier while preserving social and economic activity.