Air Purifier CADR and Indoor PM2.5 Calculator

For a constant-volume room, conservation of particle mass gives

Here $V=AH$, $Q$ is particle CADR, $\lambda$ is outdoor air exchange, $P$ is penetration, $k_d$ is deposition and $S$ is indoor emission. All rates use hours. Set $J=P\lambda C_o+S/V$ and $r=\lambda+k_d+Q/V$; then $C_\infty=J/r$ and $C(t)=C_\infty+(C_0-C_\infty)e^{-rt}$. The purifier-off curve uses $r=\lambda+k_d$, including linear accumulation when that rate is zero.

For $C_0>C_T>C_\infty$, first passage is $t=\ln[(C_0-C_\infty)/(C_T-C_\infty)]/r$. A target equal to the steady level is approached asymptotically. An initially satisfied target has first-passage time zero; a warning identifies a later rise above it. The steady CADR threshold is $Q_T=\max[0,V(J/C_T-\lambda-k_d)]$. When starting above the target, finite-time crossing requires $C_\infty<C_T$. Zero CADR can satisfy this when natural removal already keeps the steady concentration strictly below the target; a positive CADR threshold must be exceeded. The 95% settling time is $\ln(20)/r$.

The balance is derived here from conservation. EPA Guide (2018), attached PDF page 3, provides the room-sizing benchmark: 65 cfm per 100 ft² at 8 ft implies 4.875 equivalent clean air changes per hour. Multiplying by actual volume adjusts for ceiling height. Four and six changes per hour are comparison scenarios, not regulatory requirements. Particle CADR is the performance metric named in ANSI/AHAM AC-1-2020; no standard test or product certification is performed here. Shaughnessy and Sextro (2006) discuss CADR and competing removal processes.

US PM2.5 sub-index comparisons truncate concentration to 0.1 µg/m³, interpolate EPA breakpoints, then round the index; values above 500 continue the hazardous segment, per EPA May 2026 guidance, pp. 13–15. India comparisons use CPCB Table 3.11, printed p. 35 (attached page 37): successive upper concentration cutoffs 30, 60, 90, 120 and 250 µg/m³. Fractional concentrations move to the next band immediately above each cutoff. Only categories are shown for India; no numeric value is invented for its open-ended Severe band.

One uniformly mixed room; fixed volume, CADR, outdoor concentration and source strength. Equal incoming and outgoing outdoor airflow. Penetration applies only to incoming particles; outgoing air carries the full indoor concentration. Deposition is an independent first-order sink, with no resuspension. CADR already includes filter efficiency; do not multiply it by HEPA efficiency again.

The default exchange rate 0.5 h⁻¹, penetration 0.8 and deposition 0.2 h⁻¹ are illustrative inputs, not literature-derived estimates for Delhi, Lahore, Dhaka or any particular building. Set them from measurements or test a range. Animated dots represent relative concentration on a fixed scale and their motion is illustrative, not a flow simulation.

Health disclaimer: Educational screening estimate, not medical advice, exposure certification, a safe re-entry time or a guarantee of health protection. A chosen target or a Good category does not prove indoor air is safe. Follow local public-health advice and consult a qualified health professional for individual concerns.

Suitable for approximate particle behaviour in one mixed room with constant conditions. Poor mixing, obstructed purifier airflow, adjoining rooms, changing wind, open doors, filter loading, humidity effects on monitors and intermittent cooking can cause large departures. Verify with a suitable PM2.5 monitor. CADR addresses particles; it does not establish removal of gases, CO₂ or CO. Avoid ozone-generating cleaners and maintain necessary ventilation. Installation or changes to ventilation/HVAC belong to a qualified person.

AQI is an outdoor-air reporting system: these instantaneous and steady PM2.5 comparisons are not an official daily AQI, a NowCast, an indoor limit or a complete multi-pollutant index. Rules used: US EPA May 2026 guidance (2024 PM2.5 breakpoints) and CPCB 2014 scheme; verified 25 October 2026. For compliance, check against the standard and rules in force.