Introduction
The math behind ventilation sizing is refreshingly short: one formula converts a room’s volume and a target air-change rate into the required airflow, and two standard rules cover bathrooms and kitchens. The confusion usually isn’t the arithmetic — it’s knowing which formula applies to which situation and keeping the units straight when CFM, m³/h, cubic feet, and cubic meters all appear on the same fan nameplate.
The Ventilation Calculator runs these formulas for you: enter dimensions and a target ACH and it returns CFM and m³/h. This guide derives each formula from first principles, shows where the constants come from, and works through examples in both unit systems so you can verify any result by hand.
The Core Formula: ACH to Airflow
Air changes per hour (ACH) is defined as the volume of air moved through a space per hour, divided by the volume of the space itself. Rearranging that definition gives the working formula:
Imperial: CFM = ACH × Volume (ft³) ÷ 60
ACH is per hour; CFM is per minute. The ÷ 60 converts hours to minutes. Example: a 1,000 ft³ room at 6 ACH needs 6 × 1,000 ÷ 60 = 100 CFM.
Metric: m³/h = ACH × Volume (m³)
No conversion factor needed — both sides are per hour. Example: a 28.3 m³ room at 6 ACH needs 6 × 28.3 = 170 m³/h.
Why the 60 matters
Forgetting the ÷ 60 is the classic error: it turns a correct 100 CFM answer into 6,000 CFM. Any time a ventilation result looks absurd, check for the missing 60 first — the common mistakes guide lists the other usual suspects.
Volume: The Input Everything Depends On
Volume = Length × Width × Height, with all three dimensions in the same units. Two subtleties:
- Sloped or vaulted ceilings: use the average height. For a simple gable ceiling, average ≈ (wall height + peak height) ÷ 2, then multiply by floor area.
- Connected spaces: include alcoves and open archways that share air with the room; exclude closed closets and sealed storage.
Unit consistency is non-negotiable: 12 ft × 10 ft × 8 ft = 960 ft³, while 3.66 m × 3.05 m × 2.44 m = 27.2 m³. Mixing feet and meters in one calculation silently corrupts the result.
Unit Conversions, Derived
These factors come from the definitions of the units — 1 ft = 0.3048 m, 1 hour = 60 minutes:
| Conversion | Exact factor | Planning shortcut |
|---|---|---|
| CFM → m³/h | × 1.6990 | × 1.7 |
| m³/h → CFM | ÷ 1.6990 | ÷ 1.7 |
| ft³ → m³ | ÷ 35.3147 | ÷ 35.3 |
| m³ → ft³ | × 35.3147 | × 35.3 |
Worked both ways: 100 CFM × 1.699 = 169.9 m³/h (≈ 170); 170 m³/h ÷ 1.699 = 100.06 CFM (≈ 100). The shortcut × 1.7 introduces less than 0.1% error — fine for equipment selection, where fans come in discrete sizes anyway.
The Bathroom Rule
Bathrooms are sized by direct CFM minimums, not ACH, because the moisture load depends on the shower rather than the room size:
- 50 CFM for intermittent (switch- or timer-controlled) operation
- 20 CFM for continuous operation
The logic: a fan running 24 hours at 20 CFM moves 28,800 ft³ per day; a 50 CFM fan run 30 minutes per shower, twice a day, moves only 3,000 ft³. Continuous low-rate ventilation is far more total air — hence the lower rate qualifies. For very large bathrooms (over about 100 ft² / 9.3 m²), many designers add roughly 1 CFM per square foot of floor area as a planning check.
The Kitchen Rule: 100 CFM per 10,000 BTU
Range hoods are sized to the cooktop’s heat output, not the kitchen’s volume, because the pollutant load comes from the burners:
Hood CFM = (Total cooktop BTU ÷ 10,000) × 100
A gas range with four 10,000 BTU burners totals 40,000 BTU → 400 CFM. An electric or induction cooktop of similar size typically needs less — many designers use 100 CFM per linear foot of cooktop width as the electric planning rule (a 30-inch / 76 cm cooktop → ~250 CFM). Duct length and elbows then push the selection up: each 90° elbow adds meaningful resistance, so a long duct run argues for the next blower size.
The Whole-House Formula: ASHRAE 62.2
Whole-house ventilation follows ASHRAE Standard 62.2, which sizes continuous fresh air from floor area plus occupants rather than ACH:
Qtot = 0.03 × Afloor (ft²) + 7.5 × (Nbr + 1) — result in CFM
Where Afloor is the conditioned floor area and Nbr is the number of bedrooms. Example: a 2,000 ft² home with 3 bedrooms → 0.03 × 2,000 + 7.5 × 4 = 60 + 30 = 90 CFM continuous whole-house ventilation.
The 0.03 × area term covers building-related pollutants (materials, furnishings); the 7.5 × (bedrooms + 1) term covers occupants, assuming bedrooms + 1 people. Local codes may adopt this standard with modifications — or use their own — so the code-compliance guide explains how to confirm which version your jurisdiction enforces.
Putting It Together: A Full House Example
A 2,000 ft² (186 m²) home, 3 bedrooms, 2 baths, 8 ft (2.44 m) ceilings:
- Whole-house baseline: 0.03 × 2,000 + 7.5 × 4 = 90 CFM continuous (≈ 153 m³/h).
- Bathrooms: 2 × 50 CFM intermittent = 100 CFM spot capacity.
- Kitchen: 40,000 BTU gas range → 400 CFM hood.
- Bedrooms (check): 12 × 10 × 8 = 960 ft³ each; 5 ACH → 80 CFM each.
The spot systems (bath, kitchen) handle peak loads; the 90 CFM continuous system handles the baseline. Note the kitchen hood dominates — 400 CFM intermittent needs a make-up air path in a tight envelope, a design point the pro tips guide covers in detail.
Related Guides
- Ventilation Complete Guide — the full overview behind these formulas.
- Ventilation Estimating Guide — step-by-step room-by-room estimation workflow.
- Common Mistakes — the arithmetic and measurement traps to avoid.
- Ventilation Calculator FAQ — quick answers to the most asked questions.
- Case Study — these formulas applied to a hypothetical home.
Frequently Asked Questions
Why do I divide by 60 in the CFM formula?
ACH counts air changes per hour, but CFM counts cubic feet per minute. Dividing by 60 converts the hourly air volume into a per-minute flow rate. The metric formula (m³/h = ACH × volume in m³) needs no conversion because both sides are hourly.
Is 1 CFM really 1.7 m³/h?
The exact factor is 1.6990, derived from 1 ft³ = 0.0283168 m³ × 60 minutes. The 1.7 shortcut is accurate to within 0.1% — fine for selecting equipment, which comes in discrete sizes anyway.
How is ASHRAE 62.2 different from the ACH method?
The ACH method sizes ventilation per room from room volume. ASHRAE 62.2 sizes whole-house continuous ventilation from floor area plus bedroom count (Q = 0.03 × ft² + 7.5 × (bedrooms + 1)). Use ACH for spot ventilation and 62.2 for the whole-house baseline.
How do I size a fan for a sloped ceiling?
Compute the average ceiling height — for a simple gable, (wall height + peak height) ÷ 2 — multiply by floor area for volume, then apply the ACH formula normally.
Do I add the bathroom and kitchen CFM to the whole-house number?
No — they’re different operating modes. Whole-house CFM is continuous baseline ventilation; bath and kitchen fans are intermittent spot ventilation for peak loads. Size each separately, then verify the envelope can supply make-up air for the largest intermittent load.
Verify Your Numbers
The formulas are short enough to check by hand: volume from dimensions, CFM from ACH and volume with the ÷ 60, metric results cross-checked with the × 1.7 factor, and whole-house totals against the ASHRAE 62.2 area-plus-occupants equation. Run your rooms through the Ventilation Calculator, verify one room manually using the steps above, and you’ll catch any unit or input error before it becomes an equipment order.
Disclaimer: Formulas shown are standard planning methods; actual requirements are set by your local building code, which may modify or replace them. Verify targets with your local building authority (AHJ) and consult a licensed HVAC professional for system design decisions.
