How This Calculator Works
This calculator uses a simplified probability model to estimate the relative risk of contracting a respiratory infection with and without a mask. It is designed as an educational tool to illustrate how mask filtration, infection prevalence, contact number, and exposure duration affect cumulative risk.
The model assumes each contact with an infected person represents an independent probability event. A mask reduces the per-contact transmission probability by its filtration efficiency. The calculator then computes the cumulative probability of at least one successful transmission over all contacts.
Probability Model
The per-contact transmission probability depends on whether an infected person is encountered and whether the pathogen passes through the mask (if worn):
The cumulative risk over multiple contacts uses the complement probability:
The duration factor scales linearly with exposure time, with 1 hour as the baseline (factor = 1.0). For example, 2 hours of exposure doubles the per-contact risk, capped at a maximum of 1.0 per contact.
Types of Masks and Filtration
| Mask Type | Filtration Efficiency | Particle Size Filtered | Best For |
|---|---|---|---|
| No Mask | 0% | N/A | N/A |
| Single-layer Cloth | 20–35% | > 10 μm | Low-risk settings, source control |
| Multi-layer Cloth | 40–60% | > 3 μm | Everyday public use |
| Surgical / Procedure Mask | 60–80% | > 1 μm | Healthcare, public transport, crowds |
| KN95 | ~95% | ≥ 0.3 μm | High-risk environments |
| N95 (NIOSH certified) | ≥ 95% | ≥ 0.3 μm | Healthcare workers, high-aerosol settings |
| P100 / Elastomeric | ≥ 99.97% | ≥ 0.3 μm | Industrial, very high-risk clinical |
Mask Filtration Comparison Diagram
How Airborne Transmission Works
Respiratory pathogens can spread through several mechanisms:
- Large droplets (> 5 μm): Produced by coughing, sneezing, and talking. Travel short distances (1-2 meters) before settling. Surgical masks are effective against these.
- Aerosols (< 5 μm): Tiny particles that can remain airborne for hours and travel longer distances. N95/KN95 masks provide significantly better protection against aerosols.
- Fomite transmission: Touching contaminated surfaces then touching face. Masks do not protect against this route — hand hygiene is essential.
The relative importance of each route varies by pathogen. For example, measles and tuberculosis are primarily aerosol-transmitted, while many respiratory viruses use a combination of all three routes.
Evidence for Mask Effectiveness
Multiple lines of evidence support the effectiveness of masks in reducing respiratory pathogen transmission:
- Laboratory studies: Well-fitted N95 respirators block ≥ 95% of aerosolized particles. Surgical masks block 60-80% of exhaled respiratory droplets.
- Epidemiological studies: Population-level analyses show mask mandates were associated with reduced transmission rates in multiple countries during respiratory disease outbreaks.
- Source control: Masks worn by infected individuals (source control) are even more effective than masks worn by uninfected individuals, as they capture droplets at the source before they become aerosols.
- Fit is critical: A poorly fitting N95 may perform no better than a surgical mask. Proper seal testing and fit checks are essential for maximum protection.
Worked Example
Scenario: 2% infection rate, 20 contacts, surgical mask (70% filtration), 1 hour exposure:
Per-contact risk (surgical mask) = 0.02 × (1 − 0.70) × 1.0 = 0.006
Risk with mask = 1 − (1 − 0.006)20 = 1 − 0.8869 = 11.31%
The surgical mask reduces the estimated risk by about 66% in this scenario.
Limitations of This Model
- This is a simplified probability model — actual transmission depends on ventilation, viral load, immune status, vaccination, and many other factors
- Assumes each contact is independent and equally likely to be infectious, which is not always true
- Does not account for the direction of masking (source control vs. wearer protection)
- Filtration efficiency values are approximate — real-world performance depends heavily on fit, facial hair, and proper usage
- Linear duration scaling is a simplification; actual risk accumulation is more complex
- This calculator is for educational purposes only and should not be used for clinical decision-making
Frequently Asked Questions
Does wearing a mask protect me or others?
Both. Masks provide source control (protecting others from your respiratory droplets) and personal protection (reducing the amount of pathogen you inhale). Source control is generally more effective because droplets are captured before they can aerosolize and spread.
How does mask fit affect protection?
Fit is critical. Studies show that gaps around the mask can reduce effective filtration by 50% or more. An N95 with poor fit may perform similarly to a well-fitted surgical mask. Key areas to check: nose bridge, cheeks, and chin. A proper seal check (feeling for air leaks during breathing) is essential.
Can I reuse disposable masks?
Surgical masks are designed for single use. N95s can be reused for a limited time if stored properly in a breathable paper bag between uses. Performance degrades with moisture, physical damage, or soiling. Follow manufacturer guidelines for maximum use duration.
Are two masks better than one?
Double masking (cloth mask over surgical mask) can improve fit and filtration to approximately 85-90% efficiency by closing gaps. However, wearing two N95s is not recommended as it can compromise the seal of the outer mask.