Indoor Air Quality Calculator — mass-balance CO2 + PM2.5 + VOC + formaldehyde + radon + humidity

Why indoor air is typically 2-10× more polluted than outdoor

Quick answer: indoor sources (cooking, cleaning, furniture off-gassing, pets, occupant respiration) add contaminants continuously while modern tight building envelopes reduce the rate at which outdoor air dilutes them. Old leaky houses had 1-2 air changes per hour naturally; modern energy-efficient houses can be 0.2-0.3 ACH without mechanical ventilation. Lower dilution × same or higher source rate = higher steady-state concentration.

EPA has studied indoor air extensively: the TEAM (Total Exposure Assessment Methodology) studies found benzene, chloroform, formaldehyde, and several other pollutants at 2-10× outdoor levels in typical US homes. Newer tighter buildings amplify this further. The answer isn\u0027t "make houses leakier" — it\u0027s controlled mechanical ventilation (HRV/ERV) that brings filtered outdoor air in while recovering heat/moisture so the conditioning load stays low.

The mass-balance equation

Quick answer: indoor contaminant concentration follows dC/dt = S/V - (Q/V + k)×C where S is source rate (μg/hr or similar), V is room volume (m³), Q is ventilation rate (m³/hr), and k is contaminant-specific decay/deposition rate (1/hr). Setting dC/dt = 0 for steady-state gives C_ss = S / (Q + k×V). That\u0027s one equation that governs every contaminant with appropriate per-contaminant values for S and k.

The equation says three things simultaneously. First: doubling ventilation halves steady-state concentration (for contaminants where k is small compared to Q/V, which is most). Second: decay-prone contaminants (PM2.5 deposition k≈0.2/hr; formaldehyde degradation k≈0.1/hr) benefit extra from the V term — larger rooms also dilute via deposition-per-volume. Third: persistent contaminants (CO₂ with k≈0) reach concentrations determined solely by Q and S — no amount of "air cleaning" removes CO₂ because filters don\u0027t capture it.

CO₂ as a proxy for overall indoor air quality

Quick answer: CO₂ itself is not dangerous at normal indoor concentrations (elevated CO₂ effects start above ~1500 ppm; life-threatening only above ~40,000 ppm). But CO₂ is PERFECTLY CORRELATED with occupant-generated contaminants — the breath that adds CO₂ also adds moisture, bioaerosols, VOCs, and body-odor molecules. Measuring CO₂ is cheap (sub-$100 sensor) and tells you whether ventilation is keeping up with occupants. Above 1000 ppm = "stale"; above 1400 ppm = cognitive impairment documented (Satish et al. 2012; Allen et al. 2016).

Occupant CO₂ generation: ~4.8 L/min at rest per adult; scales with activity level ~1× sedentary, 2× moderate activity, 3× heavy exercise. For a bedroom (50 m³) with 2 sleeping occupants and 0.5 ACH, CO₂ accumulates to ~1400-1500 ppm by morning — moderately elevated, aligning with "bedroom feels stuffy when waking up" subjective reports. Opening the window 5 cm all night drops this to ~800-900 ppm.

Formaldehyde — new-furniture off-gassing

Quick answer: pressed-wood furniture (particleboard, MDF, plywood with urea-formaldehyde resin) off-gasses formaldehyde for months-to-years, peaking in the first 6 months. New flooring, carpets, and foam insulation also contribute. WHO guideline is 0.1 mg/m³ 30-minute average; California CARB standard limits emissions at the product level (CARB Phase 2). IKEA, HB, and most major manufacturers meet CARB Phase 2 which cuts off-gassing ~80% vs pre-regulatory particleboard.

Mitigations: ventilate the room with new furniture for 2-4 weeks heavily before long occupancy. Activated carbon helps moderately (~50% capture). Low-formaldehyde products (E0, NAF "no added formaldehyde") cost slightly more but drop exposure. Biological: asparagus fern, peace lily, snake plant have measurable but small formaldehyde-absorption effects (impact far less than ventilation).

VOCs — cleaning products, air fresheners, solvents

Quick answer: Volatile Organic Compounds cover hundreds of chemicals including benzene, toluene, xylene, limonene, α-pinene. Sources: cleaning products (ammonia-based + pine-fresh), air fresheners (synthetic fragrance), paints and solvents, dry-cleaned clothing (perchloroethylene), and scented candles. Total VOC target: LBNL recommends <0.3 mg/m³; WHO sets per-chemical limits rather than aggregate.

Mitigation: activated carbon filter captures 75% of VOCs on recirculation (does NOT capture particulate — pair with MERV/HEPA). "Low-VOC" labels on paint and cleaners reduce but don\u0027t eliminate. Air fresheners are a pure pollution source — they add VOCs to mask other odors. "Green" cleaning products (vinegar, bicarb, hydrogen peroxide) have much lower VOC emissions.

PM2.5 — cooking, infiltration, and HEPA sizing

Quick answer: particulate matter smaller than 2.5 μm diameter penetrates deep into lungs and is the most health-significant indoor air contaminant. Indoor sources: cooking (especially gas stoves, high-heat searing, baking), smoking/vaping, candles, fireplaces, some cleaning activities. Outdoor source: infiltration from polluted outdoor air (particularly wildfire smoke, urban pollution). Deposition k ≈ 0.2/hr (particles settle on surfaces over hours); ventilation + filtration accelerate removal.

HEPA filter sizing: CADR (Clean Air Delivery Rate) should be at least the room\u0027s volume × 5 (for 5 air changes per hour of filtered air). For a 40 m³ bedroom, CADR 200+ CFM (340+ m³/hr) is the minimum effective unit. Undersized HEPA units are common — they don\u0027t reduce PM2.5 noticeably at room scale because the filter throughput is too low relative to room volume. Cooking PM2.5 spikes require even more aggressive filtration OR range hood venting directly outdoors.

Radon — the soil-entry carcinogen

Quick answer: radon is radioactive decay gas from naturally-occurring uranium in soil. It enters buildings through foundation cracks, slab joints, and sump pits — strongest in basements and slab-on-grade homes. EPA action level: 4 pCi/L (mitigation required); WHO reference: 2.7 pCi/L. Radon is the second-leading cause of lung cancer after smoking (~21,000 US deaths/year per EPA). Risk is cumulative + multiplicative with smoking.

Detection: $15-30 short-term test kit (3-7 days passive charcoal canister) → if positive, confirm with long-term (90-day) alpha-track test. Mitigation: sub-slab depressurization system ($1000-3000) runs a pipe from under the slab through the roof, with a small fan creating negative pressure under the foundation. Radon enters via convection driven by indoor-to-outdoor pressure difference; the fan reverses this. Testing every 2 years (or after renovation that affects foundation) is the ongoing protocol.

Humidity — mold risk at 70%+ and dust-mite growth at 50%+

Quick answer: relative humidity 40-60% is the optimal range for human comfort AND low mold risk AND low dust-mite growth. Below 30% RH: respiratory irritation, increased viral-particle viability (flu/COVID transmission rises), static electricity. Above 70% RH sustained: mold growth accelerates; above 50%+ accelerates dust mites.

Sources of indoor moisture: occupant respiration (~20 g/hour per adult), showering (100-200 g/shower vented to interior), cooking (100-500 g/meal), unvented clothes dryer, aquarium, indoor plants at scale. Controls: exhaust fan in bath + kitchen (exhaust directly outdoors), dehumidifier in basement (target 50%), humidifier in winter when heating dries indoor air. Smart humidity sensors ($30-50) placed in 2-3 rooms provide early-warning.

What this model does not capture

The mass-balance equation assumes a well-mixed single zone. Real rooms have concentration gradients (cooking PM2.5 is higher near stove; occupant CO₂ higher at face height when sitting). For detailed work, multi-zone CFD modeling (CONTAM, CFD) is used. This tool gives room-average values — usually accurate to ±30% for planning purposes.

Also not modeled: re-emission from surfaces (furnishings can SORB contaminants during high-concentration periods and desorb later, delaying decay), transient events (spike-and-decay for brief cooking events), multi-room interactions (contaminant migration between rooms via doors + HVAC returns), chemistry between contaminants (ozone + terpenes → secondary organic aerosols = new contaminants; known issue with air "ionizers" + citrus air fresheners).

Filter efficacy is simplified to capture-on-recirculation. Real filter performance depends on flow rate through filter (higher flow = lower capture per pass), duration since replacement (capacity degrades), and specific particle size distribution. MERV ratings and HEPA specifications have test-condition dependencies. For design-grade analysis, consult ASHRAE Handbook: Applications Ch. 48.

For measurement-grade IAQ assessment: professional indoor air quality survey with real-time monitors (CO₂, PM2.5, VOC, formaldehyde, CO) over 48-72 hours is the gold standard. Kits cost $3000-8000 for professional-grade; consumer versions (Airthings, Awair, Aranet) cost $150-400 and give useful directional data.

Sources and further reading

ASHRAE, Standard 62.1-2022 Ventilation and Acceptable Indoor Air Quality — the canonical ventilation-rate standard for residential and commercial buildings; sold by ashrae.org. ASHRAE, Handbook: Fundamentals Ch.11 (Air Contaminants) + Ch.16 (Ventilation) — deeper treatment of contaminant-specific source/sink rates + ventilation engineering. World Health Organization, WHO Guidelines for Indoor Air Quality: Selected Pollutants (WHO Europe, 2010) — formaldehyde, benzene, CO, naphthalene, NO₂, PAHs, radon, trichloroethylene, tetrachloroethylene. US EPA, Indoor Air Quality (IAQ) Reference Documents at epa.gov/indoor-air-quality-iaq — US regulatory context plus the TEAM studies establishing indoor-vs-outdoor contaminant ratios. Persily, A. and de Jonge, L. Carbon dioxide generation rates for building occupants, NIST Indoor Air 27(5) 2017 — the occupant CO₂ source-rate values used in this tool. For radon specifically: EPA, A Citizen\u0027s Guide to Radon + Consumer\u0027s Guide to Radon Reduction. For filtration: ASHRAE Standard 52.2 (MERV rating test method) + NSF/ANSI 42/53 (filter certification). For CO₂ + cognition: Satish, U. et al. Environmental Health Perspectives 120(12) 2012; Allen, J.G. et al. Environmental Health Perspectives 124(6) 2016.