One number decides everything: CADR
In a well-mixed room, every particle metric you care about — peak exposure, how fast the air clears, long-run concentration — moves together with a single quantity: the clean air delivery rate (CADR), the volume of genuinely particle-free air the machine produces per minute. So “which cleaner is better” is not a matter of taste; it is: which one delivers more CADR under the noise, energy, cost and space limits you actually have. Everything below follows from maximizing that one number.
CADR = capture × airflow. A filter only helps to the extent it (a) catches particles and (b) lets the fan move air. Push either to an extreme and the product collapses.
Why HEPA loses in a real room
HEPA captures ≥99.97% of particles in a single pass — but it is so dense that the fan can barely pull air through it. Enormous capture, tiny airflow. A MERV-13/14 filter captures a little less per pass, but its low resistance lets the same fan move far more air. When you multiply capture × airflow, the open filter wins:
- At 0.3 µm, a seven-fan flat-panel “slab” delivers ~234 CFM with MERV-14 versus ~185 CFM with HEPA — i.e. HEPA gives about 21% less clean air, at roughly 2.7× the filter cost.
- Delivered CADR versus filter grade is single-peaked: MERV-14 is optimal for fine submicron particles (0.3–1 µm — smoke and viral aerosol), MERV-13 for coarser 1–3 µm, with MERV-13 the robust all-round choice. HEPA sits below the peak.
- HEPA’s proper home is single-pass containment behind a strong, high-static fan — not the low-pressure recirculating cleaning most rooms need.
Why the round cartridge is the wrong shape
CADR rises with installed filter area, so the geometric question is: which enclosure packs the most filter face into a given footprint? The intake density of a regular prism falls as it gains sides — and the cylinder is the limiting worst case. A flat-panel box presents 2/√π ≈ 1.13, about 13% more filter area than an equal-volume cylinder. So the round cartridge in a typical tower purifier is, quite literally, the least area-efficient shape you could choose — and it usually pairs that with airflow-choking HEPA media.
Quiet and cheap fall out of the same maths
- Noise scales with clean air: ~3 dB per doubling of CADR. A distributed array of quiet PC fans is 8–12 dB quieter than a single box fan at the same CADR.
- Pick fans by airflow-per-decibel, not static pressure — high-airflow 140 mm fans beat “performance” high-static fans here.
- Deeper filters are quieter: 2-inch MERV-13 has roughly half the resistance of 1-inch, so the fans idle slower.
- Energy: a validated flat-panel slab runs at ~26 CFM/W — about 2.4× the best large ENERGY STAR-certified unit and ~4× the fleet median, meeting a classroom’s clean-air target under a 40 dB(A) ceiling at 2–4× less energy.
The upshot: clean air carries a constant marginal price in three currencies at once — decibels, watts and dollars — and the optimal machine is a large-area, low-velocity flat panel with many slow fans and MERV-13/14 media. Exactly the Corsi-Rosenthal / slab design, now with a proof.
Does it hold up? Validation
The method was checked against two independent devices spanning its regimes: a commercial slab cleaner (predicted CADR band 310–395 CFM; measured 323; noise predicted 38.5 vs measured 38.8 dB(A) — within 0.3 dB) and an independent peer-reviewed Corsi-Rosenthal box (predicted 9–18% airflow reduction, measured 12%; CADR 600–852 CFM). It is also consistent with the 153-unit ENERGY STAR certified fleet.
Watch the short version
We turn these results into two-minute, no-jargon explainers on the Clean Air Education channel.
Based on: R. A. Satnoianu, “Exact design optimization of flat-panel recirculating air cleaners: closed-form sizing and the marginal cost of clean air in noise, energy, and dollars” (preprint under review). Figures on this page summarise the paper’s results; the full preprint and DOI will be linked here once posted.