Most air purifier boxes list a CADR number, but few explain what it actually measures or how to use it to pick the right size for a specific room. Get the sizing wrong and you either pay for airflow you don't need or end up with a unit that can't keep up with the room's air volume. The math behind proper sizing is simple once you know the standard behind the number.
CADR stands for Clean Air Delivery Rate, a testing standard developed by AHAM (the Association of Home Appliance Manufacturers) under the AC-1 protocol. It measures the volume of filtered air a purifier delivers per minute, expressed in cubic feet per minute (cfm), inside a sealed test chamber where a known quantity of particles is injected and the rate of decline is measured against a natural decay baseline. A unit isn't tested with one generic pollutant; AHAM certifies three separate CADR numbers, one each for dust, pollen, and tobacco smoke, because these particle sizes behave differently in air and are captured at different efficiencies by the same filter.
Smoke particles are the smallest of the three test categories, typically in the 0.1 to 1 micron range, which makes them the hardest for any filter media to trap and the slowest to settle out of the air on their own. Because of that, the smoke CADR number is almost always the lowest of the three listed figures for a given machine, and it's the number worth focusing on if your concern is general air quality, allergens, or wildfire smoke infiltration rather than only larger dust and pollen particles.
AHAM's own sizing guidance is often called the two-thirds rule: a purifier's CADR (using the lowest, i.e. smoke, rating for a conservative estimate) should be at least two-thirds of the room's floor area in square feet, assuming a standard 8-foot ceiling height. So for a 150 square foot bedroom, you'd want a smoke CADR of at least 100. For a 300 square foot open living area, you'd want at least 200.
This rule is calibrated to produce roughly 4 to 5 air changes per hour (ACH) in a room with typical ceiling height, which is the range most commonly cited for meaningfully reducing airborne particle concentration over the course of an hour. If you undersize below the two-thirds threshold, the unit can still run continuously and provide some benefit, but it will take proportionally longer to reduce particle counts after a pollution event like cooking, cleaning, or outdoor smoke infiltration.
The two-thirds rule assumes 8-foot ceilings, but the actual physical quantity a purifier has to clean is the room's air volume, not its floor area. For rooms with higher or lower ceilings, calculate volume directly: length × width × height in feet gives you cubic feet. From there, air changes per hour is ACH = (CADR × 60) ÷ room volume in cubic feet, since CADR is a per-minute rate and there are 60 minutes in an hour.
As an example, a 200 square foot room with a 10-foot ceiling has a volume of 2,000 cubic feet, not the 1,600 cubic feet a flat 8-foot assumption would suggest. A purifier with a 150 smoke CADR in that room delivers (150 × 60) ÷ 2,000 = 4.5 ACH. During events with elevated particle loads, such as wildfire smoke infiltration, guidance generally points toward the higher end of the ACH range, so rooms with tall ceilings or open floor plans may need a higher CADR than the flat square-footage rule alone would indicate.
A genuine AHAM Verifide label shows three separate numbers, one each for dust, pollen, and smoke, and a maximum recommended room size for each. That recommended room size on the label is often calculated using a different ACH assumption than the two-thirds rule (commonly around 2 ACH), so two purifiers with similar CADR numbers can list different "recommended room sizes" depending on which ACH target the manufacturer chose to advertise against.
The safest approach is to ignore the manufacturer's suggested room size claim and instead do your own calculation using the smoke CADR number and your room's actual square footage or volume. If a specific area of concern applies, such as smoke, pet dander, or general fine particulate matter, sizing against the lowest (smoke) CADR figure gives you a built-in margin of safety for the other two categories as well, since dust and pollen CADR numbers are typically higher for the same unit.