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Calculator · health

Mask Vs No Mask Infection Risk Calculator

Quantify how much masks reduce airborne infection risk indoors. Enter room size, ventilation, and mask type to compare masked vs unmasked risk using the Wells-Riley model.

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Inputs

Mask Worn by Infectious Person (Source)

Mask Worn by Susceptible Person (Receiver)

Activity Level (Quanta Generation)

Room Size

Ventilation Quality

Number of Infectious People

Exposure Time

Infection Risk Reduction

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Infection Risk Reduction—%

The formula

How the
result is
computed.

How the Mask vs No Mask Infection Risk Calculator Works

This calculator quantifies the percentage reduction in airborne infection probability when masks are worn, compared to an unmasked baseline under identical environmental conditions. It applies a modified Wells-Riley equation — the foundational model in airborne disease transmission science — extended to incorporate mask filtration efficiency for both the infectious source and the susceptible receiver.

The Core Formula

The risk reduction percentage is defined as:

Reduction (%) = [ 1 - (1 - e^{-Iq(1-E_s)p(1-E_r)t/Q}) / (1 - e^-Iqpt/Q) ] x 100

The numerator term computes infection probability when masks are worn by both parties. The denominator term computes infection probability in the fully unmasked scenario. Their ratio yields relative risk: a result of 87% means masking reduces infection probability to just 13% of what it would be without masks.

Variable Definitions

I — Number of Infectious Individuals: Each additional contagious person linearly increases quanta concentration in the shared space. One infectious person generates a baseline exposure; five infectious persons in the same room produce five times the quanta load under steady-state conditions.
q — Quanta Generation Rate (quanta/hour): The rate at which an infectious person emits viable viral particles via respiratory aerosols. Resting quietly generates roughly 2-10 quanta/hour; normal conversation generates 20-50 quanta/hour; loud singing or heavy exercise can exceed 100-500 quanta/hour. Empirical SARS-CoV-2 estimates are drawn from Buonanno et al. (2021) in Nature Scientific Reports, who back-calculated quanta emission rates from documented superspreader events.
E_s — Source Mask Efficiency: The outward filtration efficiency of the mask worn by the infectious person, representing source control. Per NIOSH N95 certification standards, a properly fitted N95 respirator filters at least 95% of 0.3-micron particles — the most penetrating size. Surgical masks provide approximately 50-80% source control; cloth masks approximately 20-50%.
E_r — Receiver Mask Efficiency: The inward filtration efficiency protecting the susceptible person. The same mask-type ratings apply, though real-world inward protection depends critically on face seal and fit. A poorly fitted N95 may perform no better than a surgical mask in practice.
p — Breathing Rate (m³/hour): An adult at rest inhales approximately 0.5 m³/hour. Light activity raises this to 0.8-1.2 m³/hour; vigorous exercise can reach 2.0-3.0 m³/hour. Higher breathing rates proportionally increase the inhaled quanta dose.
t — Exposure Time (hours): Total duration of shared indoor exposure. Risk accumulates continuously — a 4-hour indoor gathering carries roughly four times the quanta dose of a 1-hour meeting under identical ventilation and occupancy conditions.
Q — Room Ventilation Rate (m³/hour): Calculated as room volume multiplied by air changes per hour (ACH). Per ASHRAE ventilation guidelines, standard offices target 4-6 ACH while healthcare settings often exceed 12 ACH. Higher Q dilutes quanta concentration more rapidly, benefiting both masked and unmasked occupants.

Scientific Foundation

The Wells-Riley model (Riley et al., 1978) defines airborne infection probability as P = 1 - e^-(Iqpt/Q), where q represents infectious quanta — a dose unit defined so that inhaling exactly one quantum produces a 63% infection probability. This calculator extends that framework with the efficiency terms (1-E_s) and (1-E_r), a methodology validated in peer-reviewed airborne infection risk literature and consistent with findings in the CDC Science Brief on Community Use of Masks to Control SARS-CoV-2.

Worked Example

Consider a classroom with 1 infectious teacher speaking normally (q=30 quanta/hour), a 200 m³ room at 3 ACH (Q=600 m³/hour), a 1.5-hour class, and a student breathing at 0.6 m³/hour. Without masks, the infection probability is approximately 4.4%. With both parties wearing surgical masks (E_s=E_r=0.65), probability drops to roughly 0.55% — an 87% risk reduction. Upgrading both to N95 respirators (E_s=E_r=0.95) reduces probability to approximately 0.01%, achieving over 99.7% risk reduction relative to the unmasked baseline.

Model Limitations

This model assumes well-mixed room air and steady-state quanta concentration, which may overestimate risk at distance and underestimate it in close-contact near-field settings. It does not account for large-droplet transmission, surface contact routes, variable mask fit, humidity effects, or UV inactivation. Results should be interpreted as comparative guidance between scenarios rather than precise absolute infection probabilities for any specific individual exposure.

Reference

Frequently asked questions

What does the mask vs no mask calculator actually measure?

The calculator measures the percentage reduction in airborne infection probability when masks are worn, compared to an identical scenario without masks. It applies the Wells-Riley equation to model quanta accumulation in indoor air, then computes how much source-control and receiver-protection masks reduce the inhaled viral dose. For example, in a typical classroom scenario, two people wearing N95 respirators can reduce infection probability by over 99.7% compared to the unmasked baseline, while surgical masks may achieve an 80-90% reduction depending on room size and ventilation.

Which mask type provides the greatest risk reduction in the calculator?

N95 respirators provide the greatest risk reduction, filtering at least 95% of airborne particles at 0.3 microns when properly fitted, as certified under NIOSH standards. When both the infectious source and the susceptible receiver wear N95s, combined filtration can reduce quanta delivery by more than 99.75%. KN95 and KF94 masks offer comparable filtration. Surgical masks typically achieve 50-80% efficiency, while cloth masks range from 20-50%. Critically, fit matters as much as filtration rating — a well-sealed cloth mask can outperform a loosely worn N95 in real-world use.

How does room ventilation affect the mask infection risk calculation?

Ventilation quality, measured in air changes per hour (ACH), directly dilutes quanta concentration in the room. Higher ACH means infectious aerosol particles are removed faster, lowering infection probability in both the masked and unmasked scenarios. Doubling ACH from 3 to 6 roughly halves quanta concentration at steady state. ASHRAE recommends 6+ ACH for high-occupancy spaces. The calculator captures this interaction: excellent ventilation reduces the absolute benefit of masking because baseline risk is already lower, but masking still provides substantial additive protection regardless of ventilation level.

Does it matter more whether the infectious person or the susceptible person wears a mask?

Source control — masking the infectious person — is generally more impactful because it prevents quanta from entering the shared air supply, simultaneously protecting all occupants in the room. A single infectious source wearing an N95 reduces quanta output by 95%, benefiting everyone nearby. The susceptible person's mask, by contrast, protects only that individual. However, the CDC documents that masking provides additive protection, and both parties masking together offers substantially greater risk reduction than either alone. When the infectious person is unidentified or presymptomatic, receiver masking provides the only available layer of protection.

How accurate is the Wells-Riley model for real-world airborne infection risk?

The Wells-Riley model is validated for airborne pathogens in well-mixed indoor environments and has been applied to measles, tuberculosis, influenza, and SARS-CoV-2. Buonanno et al. (2021) in Nature Scientific Reports back-calculated COVID-19 quanta emission rates from documented superspreader events using this framework with reasonable accuracy. Its primary limitation is the well-mixed air assumption — real rooms have concentration gradients, especially close to the source. The model is most reliable for estimating relative risk differences between scenarios, such as masked versus unmasked, rather than predicting precise absolute infection probabilities for any specific exposure event.

What activity level should be selected for the most accurate infection risk calculation?

Select the activity level that best describes the infectious person's sustained behavior during the shared indoor exposure, since activity drives the quanta generation rate. Resting or sitting quietly generates roughly 2-10 quanta/hour; normal conversation generates 20-50 quanta/hour; loud talking, aerobics instruction, or singing can generate 100-500 quanta/hour. For mixed-activity settings such as a fitness class, choose the highest sustained activity level to obtain a conservative estimate. The susceptible person's activity affects their breathing rate and inhaled dose, but the source emission rate is typically the dominant factor in determining overall risk.