224 purifier cells — why you should buy for a smaller room than the box claims
Only two scales and three constants are written down. Divide the clean air delivery rate by the room’s volume and you get how many times an hour the air is replaced; the widely used target is five. Dust falls off exponentially, so the time to halve it does not depend on where it started — at five changes an hour it is 8.3 minutes. The advertised coverage area is measured assuming natural ventilation alongside, so a closed room has less headroom than the box suggests.
Air changes per hour
Room size \ Clean air rate (CADR)
| 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 | 14 | 16 | 18 | 20 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 3pyeong | 8 | 10 | 13 | 15 | 18 | 20 | 23 | 25 | 30 | 35 | 40 | 45 | 50 | 61 |
| 4pyeong | 6 | 8 | 9 | 11 | 13 | 15 | 17 | 19 | 23 | 26 | 30 | 34 | 38 | 45 |
| 5pyeong | 5 | 6 | 8 | 9 | 11 | 12 | 14 | 15 | 18 | 21 | 24 | 27 | 30 | 36 |
| 6pyeong | 4 | 5 | 6 | 8 | 9 | 10 | 11 | 13 | 15 | 18 | 20 | 23 | 25 | 30 |
| 7pyeong | 3 | 4 | 5 | 6 | 8 | 9 | 10 | 11 | 13 | 15 | 17 | 19 | 22 | 26 |
| 8pyeong | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 9 | 11 | 13 | 15 | 17 | 19 | 23 |
| 10pyeong | 2 | 3 | 4 | 5 | 5 | 6 | 7 | 8 | 9 | 11 | 12 | 14 | 15 | 18 |
| 12pyeong | 2 | 3 | 3 | 4 | 4 | 5 | 6 | 6 | 8 | 9 | 10 | 11 | 13 | 15 |
| 14pyeong | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 | 6 | 8 | 9 | 10 | 11 | 13 |
| 16pyeong | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 6 | 7 | 8 | 9 | 9 | 11 |
| 18pyeong | 1 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 5 | 6 | 7 | 8 | 8 | 10 |
| 20pyeong | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 5 | 5 | 6 | 7 | 8 | 9 |
| 25pyeong | 1 | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 | 6 | 7 |
| 30pyeong | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 | 6 |
| 35pyeong | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 5 |
| 40pyeong | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 5 |
Clean air rate divided by room volume gives air changes per hour. The target is five, at which dust halves in 8.3 minutes.
Where the advertised area parts ways with reality
The Korean standard (KS C 9314) measures the coverage area in a chamber with a 2.4 m ceiling, and its definition assumes natural ventilation is happening alongside. A closed room does not get that help, so taking the printed area at face value leaves you short. That is why the usual advice is to buy with headroom over your actual room. This chart leaves ventilation out and counts the purifier alone.
The two-thirds rule lands exactly on five
The common American shorthand is “CADR in cfm should be at least two-thirds of the room’s square footage”. Work it out at an 8-foot ceiling: (2/3) × A × 60 ÷ (8 × A) = 5, exactly. It is not a rule of thumb at all, it is five air changes an hour written differently. Eight feet is 2.44 m, essentially the same room as the Korean chamber’s 2.4 m, which is why both countries land on the same target.
Dust falls off exponentially
Clean air removes what is left in proportion to how much is left, so the time to halve the dust does not depend on where it started — the same arithmetic as radioactive half-life. Multiply air changes per hour by the halving time and you always get 41.6 minutes. Getting down to a tenth takes 3.32 times as long.
What this calculation leaves out
This assumes a closed room with no new dust being made. In practice it seeps in around windows, gets stirred up when people move, and is created afresh by cooking. A clogged filter drops the CADR too. And the maths assumes the air mixes evenly through the room, which it does not if the purifier sits in a corner.
How to read it
- Air changes per hour = clean air rate (m³/min) × 60 ÷ room volume (m³).
- Room volume is area × a 2.4 m ceiling — the height the standard tests at.
- The widely used target is five changes an hour.
- Time to halve the dust = 60 × ln2 ÷ air changes. At five an hour, that is 8.3 minutes.
- Getting to a tenth takes 3.32 times as long as halving.
- The advertised coverage area includes natural ventilation — a closed room has less headroom.
Common questions
Q. Can I just buy for the area printed on the box?
That coverage figure is measured assuming natural ventilation is happening at the same time. If you are closing the windows because of fine dust, you do not get that help, so it is safer to buy with headroom over your actual room.
Q. Where does “five changes an hour” come from?
It is the figure widely used in allergy and indoor-air-quality guidance. The common American shorthand — CADR at two-thirds of the room’s square footage — works out to exactly five at an 8-foot ceiling. They are the same statement.
Q. Why is the air not clean the moment I switch it on?
Because dust falls exponentially. Even at five changes an hour it takes 8.3 minutes to halve and 27.6 minutes to reach a tenth. What is removed is proportional to what is left, so the tail is slow.
Q. One big unit or two small ones?
By air changes alone, the same total CADR gives the same number. But this maths assumes the air mixes evenly, and in practice two units spread apart reach the corners better. The noise is split up too.