Quick answer: room volume is length × width × ceiling height. A 12 × 14 ft room with an 8 ft ceiling holds 1,344 ft³ (38.1 m³). To convert that into the airflow a fan or purifier needs: CFM = ft³ × ACH ÷ 60. At 6 air changes per hour that room needs 134 CFM. In metric it is simpler still — m³/h = m³ × ACH.
The formula, and the sloped-ceiling case
Single slope: V = L × W × (Hlow + Hhigh) ÷ 2
Vaulted / A-frame: V = L × W × (Hwall + Hridge rise ÷ 2)
The flat case needs no explanation. The sloped case is worth one sentence, because people assume averaging the heights is a rough approximation and it is not — it is exact. A single flat slope creates a wedge of extra space above the average line that is precisely the same size as the wedge of missing space below it. The two cancel. You can average with confidence.
Worked example — a loft room 12 ft × 14 ft, ceiling sloping from 7 ft at the eaves to 11 ft at the ridge wall:
- Average height: (7 + 11) ÷ 2 = 9 ft
- Volume: 12 × 14 × 9 = 1,512 ft³ (42.8 m³)
The vaulted case is the same trick applied to a symmetrical roof: take the wall height and add half the ridge rise. A room with 8 ft walls rising to a 12 ft ridge has an effective height of 8 + (4 ÷ 2) = 10 ft. If your ceiling is genuinely irregular, split it into a box plus a triangular prism and add the two.
Air changes per hour — what your room actually needs
This is where room volume stops being arithmetic and starts being useful. ACH is the number of times the room's entire air volume is replaced in an hour, and it is the number every ventilation specification is written in.
| Room type | Typical ACH | CFM for a 1,344 ft³ room | Notes |
|---|---|---|---|
| Bedroom / living room | 0.35–1 | 8–22 CFM | ASHRAE 62.2 sets 0.35 ACH as a residential floor |
| Whole house, general | 0.35 | 8 CFM | Below this, moisture and CO₂ accumulate |
| Home office | 2–4 | 45–90 CFM | Occupancy-driven; CO₂ is the limiting factor |
| Commercial office | 4–6 | 90–134 CFM | Standard for open-plan workspace |
| Classroom | 6–8 | 134–179 CFM | High occupant density per m³ |
| Bathroom | 6–10 | 134–224 CFM | Moisture removal, not comfort, drives this |
| Kitchen (domestic) | 6–12 | 134–269 CFM | Extract at source over the hob is far more effective |
| Commercial kitchen | 8–25 | 179–560 CFM | Grease and heat load dominate |
| Laboratory | 6–12 | 134–269 CFM | Fume hood extraction sits on top of this |
| Hospital operating room | 15–25 | 336–560 CFM | Largely HEPA-filtered recirculation |
| Smoke / allergen clean-up | 4–5 | 90–112 CFM | The figure air purifier CADR should meet |
ASHRAE Standards 62.1 (commercial) and 62.2 (residential) express requirements partly per person and per floor area rather than purely as ACH, so these are practical working ranges rather than code compliance. For a regulated installation, size against the standard itself.
More is not always better. In a home, every air change you add is air you have paid to heat being thrown outside. Going from 0.35 to 3 ACH in winter is a large heating bill and uncomfortably dry air. Bathrooms and kitchens are the exception because the goal there is removing moisture and grease fast, not comfort.
Turning volume into airflow
Metric: m³/h = Vm³ × ACH
Reverse: ACH = CFM × 60 ÷ Vft³
The ÷ 60 in the imperial version is the only thing that trips people up: CFM is per minute and ACH is per hour. Metric has no such conversion because m³/h and ACH share the same time base — one of the rare cases where metric is genuinely simpler rather than just different.
The reverse form is the more useful one in practice. You rarely get to choose a fan's airflow from scratch; you usually have a fan with a rating on the box and want to know what it will actually achieve. A 100 CFM bathroom fan in a 640 ft³ bathroom gives 100 × 60 ÷ 640 = 9.4 ACH — comfortably inside the 6–10 target. The same fan in a 1,400 ft³ bathroom gives 4.3 ACH, which is not enough, and is why the mirror still fogs.
| Room size (8 ft ceiling) | Volume | CFM at 8 ACH | m³/h at 8 ACH |
|---|---|---|---|
| 5 × 7 ft (small bathroom) | 280 ft³ | 37 CFM | 63 m³/h |
| 6 × 8 ft | 384 ft³ | 51 CFM | 87 m³/h |
| 8 × 10 ft | 640 ft³ | 85 CFM | 145 m³/h |
| 10 × 12 ft | 960 ft³ | 128 CFM | 217 m³/h |
| 12 × 14 ft | 1,344 ft³ | 179 CFM | 304 m³/h |
| 15 × 20 ft | 2,400 ft³ | 320 CFM | 544 m³/h |
Sizing an air purifier properly
Air purifiers are sold by CADR — Clean Air Delivery Rate, in CFM — and by a floor area in square feet. The floor area figure is where most bad purchases happen, because it silently assumes an 8-foot ceiling.
AHAM's long-standing "two-thirds rule" says CADR should be at least ⅔ of the room's floor area in ft². For a 12 × 14 ft room that is 168 ft² × ⅔ = 112 CFM. Check it against the volume method: 1,344 ft³ × 5 ACH ÷ 60 = 112 CFM. Identical — because the rule was derived for a 5 ACH target at an 8 ft ceiling.
Now put the same room under a 12 ft vaulted ceiling. Floor area has not changed, so the two-thirds rule still says 112 CFM. But the volume is now 2,016 ft³, and 112 CFM delivers only 3.3 ACH. The room needs 168 CFM. Anyone with high ceilings who sizes by floor area is buying a purifier a third too small — and this is exactly why the volume calculation matters more than the marketing number.
| Room volume | CADR at 3 ACH (light dust) | CADR at 5 ACH (allergy) | CADR at 8 ACH (smoke) |
|---|---|---|---|
| 800 ft³ | 40 CFM | 67 CFM | 107 CFM |
| 1,000 ft³ | 50 CFM | 83 CFM | 133 CFM |
| 1,344 ft³ | 67 CFM | 112 CFM | 179 CFM |
| 2,000 ft³ | 100 CFM | 167 CFM | 267 CFM |
| 2,500 ft³ | 125 CFM | 208 CFM | 333 CFM |
| 4,000 ft³ (open plan) | 200 CFM | 333 CFM | 533 CFM |
Manufacturers quote CADR at the highest fan speed, which is usually the loudest. If you intend to run it overnight on low, size for the CADR at the speed you will actually use — often half the headline number.
Other things room volume tells you
- Dehumidifier sizing. Rated in pints or litres per day against room area, but volume and the severity of the damp matter more. A rough starting point for a damp room is 10 pints per 500 ft³, adjusted up for standing water or a basement.
- Heating load, roughly. Volume-based rules of thumb — around 4–6 watts per cubic foot for a well-insulated room — get you in the right range for a radiator or heater, but a proper heat-loss calculation accounts for insulation, glazing and exposed walls, which volume alone cannot.
- CO₂ and occupancy. One adult at rest exhales roughly 0.005 m³ of CO₂ per hour. In an unventilated 38 m³ bedroom with two sleepers, CO₂ climbs from ambient to over 2,000 ppm overnight — measurable as poor sleep quality. This is the real reason bedrooms need a ventilation floor.
- Acoustics. Reverberation time follows the Sabine equation, RT₆₀ = 0.161 V ÷ A in metric, where V is room volume in m³ and A is total absorption. Volume is the numerator, which is why large rooms echo and small ones do not.
- Paint and plaster. These need surface area, not volume — a common mix-up. Use the surface area calculator instead.
Common mistakes & pro tips
- Forgetting the ÷ 60 in the CFM formula. Gives an answer 60× too large. If your bathroom fan needs 8,000 CFM, you multiplied instead of dividing.
- Sizing by floor area with a high ceiling. The single most expensive mistake on this page — see the purifier section.
- Using external building dimensions. Measure inside the room. Wall thickness can account for several percent of a small room.
- Treating a sloped-ceiling average as an approximation. It is exact for a single flat slope. Do not add a fudge factor.
- Ignoring where the air comes from. An extractor fan can only remove as much as can get back in. A tightly sealed bathroom with a 100 CFM fan and no door undercut will not achieve 100 CFM.
- Pro tip — measure the ceiling, do not assume 8 ft. Older houses, converted lofts and new-build apartments all vary. It scales the whole answer linearly.
- Pro tip — check what you have before buying. Use the reverse formula on your existing fan's rating. It often turns out the fan is fine and the problem is that it is never switched on long enough — moisture removal needs the fan running 15–20 minutes after the shower stops.
How to use this calculator
- Pick the ceiling type — flat, single slope, or vaulted/A-frame. The inputs change to match.
- Enter the internal length, width and height in any unit; mixed units are handled by the unit selectors.
- Set a target air change rate, or leave the default and read the airflow for several common ACH values.
- Read across the stats for CFM, m³/h, litres, and the CADR your air purifier would need.
Frequently asked questions
How do you calculate the volume of a room?
Multiply length by width by ceiling height, using internal measurements. A room 12 ft by 14 ft with an 8 ft ceiling has a volume of 12 × 14 × 8 = 1,344 cubic feet. In metric, a room 3.6 m by 4.3 m with a 2.4 m ceiling holds 37.2 cubic metres. For a sloped ceiling, average the low and high heights before multiplying — that average is exact for a simple single slope, not an approximation.
How many air changes per hour does a room need?
It depends entirely on the room. ASHRAE guidance puts residential bedrooms and living spaces around 0.35 to 1 air change per hour, offices at 4 to 6, classrooms at 6 to 8, bathrooms at 6 to 10, commercial kitchens at 8 to 25, and hospital operating rooms at 15 to 25. Higher is not automatically better in a home — excessive air change wastes heating energy and can dry the air uncomfortably.
How do you convert room volume to CFM?
CFM = room volume in cubic feet × air changes per hour ÷ 60. The ÷ 60 converts hourly to per-minute. A 1,344 cubic foot room at 6 ACH needs 1,344 × 6 ÷ 60 = 134 CFM. In metric there is no division: cubic metres per hour equals room volume in cubic metres times ACH.
How do I calculate the volume of a room with a sloped ceiling?
Average the two heights: volume = length × width × (low height + high height) ÷ 2. For a single flat slope this is exact rather than an estimate, because the wedge of space above the average line exactly fills the space below it. A room 12 by 14 feet sloping from 7 ft to 11 ft has an average height of 9 ft and a volume of 1,512 cubic feet. For a symmetrical vaulted or A-frame ceiling, use the wall height plus half the additional ridge height.
What size air purifier do I need for my room?
Match the purifier's CADR rating to the air changes you want. Required CADR in CFM equals room volume in cubic feet × target ACH ÷ 60. For a 1,344 cubic foot room at 5 ACH — the rate generally recommended for allergy or wildfire smoke — you need about 112 CFM of CADR. AHAM's older two-thirds rule, CADR of at least two-thirds the floor area in square feet, assumes an 8 foot ceiling and delivers roughly 5 ACH; it under-sizes badly in rooms with high ceilings.
Should I subtract furniture from room volume?
For ventilation and air purifier sizing, no — furniture displaces a small share of the air and ignoring it builds in a useful safety margin. For acoustics or for a sealed-volume calculation such as a gas suppression system, yes, and furnishings can occupy 10 to 20 percent of a furnished room. The general rule is that if you are sizing airflow, ignore it; if you are sizing something that fills the space, do not.
References & further reading
- ANSI/ASHRAE Standard 62.1 — Ventilation for Acceptable Indoor Air Quality (commercial and institutional).
- ANSI/ASHRAE Standard 62.2 — Ventilation and Acceptable Indoor Air Quality in Residential Buildings.
- AHAM AC-1 — the CADR test method behind air purifier ratings and the two-thirds rule.
- US EPA, "How much ventilation do I need in my home to improve indoor air quality?"
- Sabine, W. C. — reverberation time and its dependence on room volume.
ACH ranges are practical working figures drawn from published guidance, not a substitute for a code-compliant ventilation design. For regulated or life-safety installations, size against the applicable standard. See our accuracy policy.