Room Volume and Ventilation Calculator (Air Changes per Hour, CFM)

Choose what to find, then enter the room size (length × width or floor area) and the ceiling height. If air changes per hour is left blank, 0.35 ACH, a common guideline for living spaces, is used. Enter the fan airflow (m³/h) to also see the actual ACH and how well it covers the need.

Units

What to find How to enter the room size

Room length (m)

Room width (m)

Ceiling height (m)

Room use (fills in a typical ACH)

Air changes per hour (ACH)

Fan airflow (m³/h, optional; shows the coverage ratio)

Fan 1 m³/h

Fan 2 m³/h

Fan 3 m³/h

Measure the inside dimensions (wall surface to wall surface). Air change guidelines vary with the room use and the building, so check your building code or designer for requirements. The coverage ratio and verdict only compare with the ACH (or number of people) you entered; they do not check code compliance. A fan's rated airflow drops in real use because of duct and air inlet resistance (pressure loss), so leave some margin.

Result and figure

Enter the room size (or floor area), the ceiling height and the air changes per hour (or the fan airflow or the number of people) on the left and press "Calculate". The result and a figure will appear here.

[ CLOSE ]

What you can do on this page
What is this calculation used for?
How to Use
Formulas and figures
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Find the room volume \(V\) (ft³) from the room length, width and ceiling height, or from the floor area and ceiling height
Multiply by the air changes per hour \(n\) (how many times the room air is replaced in one hour, such as 0.35 ACH for living spaces) and divide by 60 to get the required airflow \(Q\) in CFM, ready to compare with a fan's CFM rating
Work backward from the fan airflow (up to 3 fans added together) to the actual air changes per hour and the minutes it takes to replace the room air once
For meeting rooms, classrooms and shops, find the occupant-based airflow (number of people × CFM per person), compare it with the volume-based airflow and use the larger one
The result comes with a figure of the room and the air flowing in and out, plus a plain explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python

The room is treated as a box with a flat ceiling. The default air changes per hour and CFM per person are common guidelines. If a fan maker's sizing chart, your designer or your local building code gives a value, use that instead. This page does not calculate CO₂ levels or heat loss. Switch "Units" above the calculator to Metric to work in meters and m³/h.

What is this calculation used for?

Choosing a bathroom, toilet room or kitchen fan

When you replace an exhaust fan, you can tell whether its CFM rating is enough for the room from volume × ACH ÷ 60. For example, a 5 ft × 6 ft half bath with an 8 ft ceiling holds 240 ft³. At a guideline of 8 ACH, it needs 240 × 8 ÷ 60 = 32 CFM, so a 50 CFM fan (the common minimum for bathroom fans that run only when needed) has room to spare.
Kitchens often use a higher guideline, about 15 ACH while cooking. Duct length and air inlet size lower the real airflow, so people usually choose a fan with some margin. Range hoods over gas cooktops are sized by a different method, so follow the maker's sizing guide.

Checking continuous whole-house ventilation

For continuous ventilation of living spaces, 0.35 ACH is a common guideline. A 12 × 9 ft bedroom with an 8 ft ceiling (864 ft³) needs about 5.04 CFM, which you can compare with the share of the ventilation system's airflow for that room. For the whole home, ASHRAE Standard 62.2 gives 0.03 CFM per ft² plus 7.5 CFM × (bedrooms + 1): 90 CFM for a 2,000 ft² home with 3 bedrooms.
The other way around, fan CFM × 60 ÷ volume shows the actual ACH. It is a useful check that dirty filters or closed air inlets are not weakening the ventilation. For code requirements on home ventilation, check your building code or designer.

Sizing ventilation for meeting rooms, classrooms and shops by the number of people

In rooms where people gather, the number of people sets the airflow more than the room size does. For example, a meeting room of 20 × 15 ft with a 9 ft ceiling (2,700 ft³) used by 12 people at 15 CFM per person needs 180 CFM by the occupant-based rate. That is far more than the volume-based 2,700 × 0.35 ÷ 60 ≈ 15.75 CFM.
Using the larger value gives an airflow that keeps indoor CO₂ from rising too high. If a restaurant, classroom or office has its own per-person rate in your code, enter that value in the per-person field.

Ventilating while you paint or glue in a DIY project

When you use solvent-based paint or adhesives, the usual living space rate (0.35 ACH) is not enough. Open the windows and run a fan while you work. If you know the volume of the room, the CFM of your fan or box fan tells you how many minutes one full air change takes (60 ÷ actual ACH, or volume ÷ CFM). This helps you plan breaks and stopping points.
Each product needs a different level of ventilation, so always follow the label and the maker's instructions.

Thinking about humidifiers, air purifiers and air conditioners by the amount of air

Air purifiers and air conditioners are often labeled with a room size in square feet, but what they actually process is the amount of air, the room volume. Rooms with high or vaulted ceilings have more volume for the same floor area, so a size up may be a better fit.
An air purifier's clean air delivery rate (CADR) is in CFM. CADR × 60 ÷ volume shows how many times per hour the room air passes through it, which helps you compare models. (Unlike ventilation, this does not replace indoor air with outdoor air.)

Formulas and figures

Room volume

Figure

Standard notation (the usual math form)

\(V\) \(=\) \(L\) \(\times\) \(W\) \(\times\) \(H\)

\(V\) \(=\) \(S_f\) \(\times\) \(H\)

In words (symbols replaced with words)

④ \(V\): room volume \(=\) ① \(L\): room length \(\times\) ② \(W\): room width \(\times\) ③ \(H\): ceiling height

\(V\): room volume \(=\) ⑤ \(S_f\): floor area \(\times\) \(H\): ceiling height

The formula in words

① Multiply the \(L\): room length

② by the \(W\): room width to get the floor area,

③ then multiply by the \(H\): ceiling height

④ and you get the \(V\): room volume

⑤ If you already know the \(S_f\): floor area from a floor plan, multiplying it by the ceiling height gives the same value

Quick example

The volume of a 12 ft × 9 ft bedroom with an 8 ft ceiling is

volume \(V\) \(=\) length (12 ft) \(\times\) width (9 ft) \(\times\) ceiling height (8 ft)

\(12 \times 9 \times 8 = 108 \times 8 = 864\,\mathrm{ft^3}\)

Key idea

The room volume is the amount of air inside the room when you treat it as a box. In the US it is given in cubic feet (ft³). One cubic foot is a cube 1 ft on each side. A 12 × 9 ft bedroom with an 8 ft ceiling holds 864 ft³, and a 20 × 15 ft living room with the same ceiling holds 2,400 ft³. Measure the inside dimensions (wall surface to wall surface). For a sloped or vaulted ceiling, use the average height or split the room into boxes and add them up. If you also want the wall area or perimeter, use the wall, ceiling and floor area page. For unit conversions such as gallons, the rectangular prism volume page is the better fit.

Required airflow (from air changes per hour)

Figure

Standard notation (the usual math form)

\(Q\) \(=\) \(V\) \(\times\) \(n\) \(\div\) \(60\)

In words (symbols replaced with words)

③ \(Q\): required airflow (CFM) \(=\) ① \(V\): room volume (ft³) \(\times\) ② \(n\): air changes per hour \(\div\) \(60\)

The formula in words

① Multiply the \(V\): room volume (ft³)

② by the \(n\): air changes per hour (how many times the air is replaced in one hour) and divide by 60 (minutes in an hour)

③ and you get the \(Q\): required airflow in CFM (the air to move each minute)

Quick example

The airflow needed to ventilate an 864 ft³ room at 0.35 ACH (the room air is replaced about once every 2.9 hours) is

required airflow \(Q\) \(=\) volume (864 ft³) \(\times\) ACH (0.35) \(\div\) \(60\)

\(864 \times 0.35 \div 60 = 302.4 \div 60 = 5.04\,\mathrm{CFM}\)

Key idea

At "0.35 ACH", 35% of the room air is replaced every hour, so one full air change takes 60 ÷ 0.35 ≈ 171 minutes (about 2.9 hours). Volume × ACH gives cubic feet per hour. US fans are rated in cubic feet per minute (CFM), so divide by 60. If the fan's CFM rating is at least this value, it meets the target ACH. (In metric, volume in m³ × ACH gives m³/h directly, with no ÷ 60.) Air change guidelines differ a lot by room use. Common US guidelines are 0.35 ACH for living spaces (from ASHRAE Standard 62-1989), about 8 ACH for bathrooms and about 15 ACH for kitchens while cooking (from the Home Ventilating Institute, HVI). Rooms with local exhaust for moisture and odors need higher values. ASHRAE Standard 62.2 also sets minimum fan sizes: for example, a bathroom fan of 50 CFM if it runs only when needed, or 20 CFM if it runs all the time. These are general guidelines. If a fan maker's sizing chart, your designer or your building code gives a value, use that. Range hoods over gas cooktops are usually sized by a different method, based on the burners and the width of the range, not by ACH. The "Kitchen 15 ACH" in this calculator is a guideline for moisture and odors while cooking. Follow the maker's sizing guide when you choose a range hood.

Actual air changes per hour and air change time from the fan airflow

Standard notation (the usual math form)

\(n'\) \(=\) \(Q_f\) \(\div\) \(V\) \(\times\) \(60\)

\(T\) \(=\) \(60\) \(\div\) \(n'\)

In words (symbols replaced with words)

③ \(n'\): actual ACH \(=\) ① \(Q_f\): total fan airflow (CFM) \(\div\) ② \(V\): room volume (ft³) \(\times\) \(60\)

⑤ \(T\): time for one air change (min) \(=\) ④ 1 hour \(= 60\) min \(\div\) \(n'\): actual ACH

The formula in words

① Divide the \(Q_f\): total fan airflow (CFM)

② by the \(V\): room volume (ft³) and multiply by 60 (minutes in an hour)

③ and you get the \(n'\): actual ACH

④ Then divide 1 hour \(= 60\) min by the actual ACH \(n'\)

⑤ and you get the \(T\): time for one air change (min)

Quick example

For an 864 ft³ room with a 60 CFM fan, the actual ACH and the time for one full air change are

actual ACH \(n'\) \(=\) fan airflow (60 CFM) \(\div\) volume (864 ft³) \(\times\) \(60\)

\(60 \div 864 \times 60 = 3600 \div 864 \approx 4.17\)

\(T = 60 \div 4.1667 \approx 14.4\)

Key idea

This is the required airflow formula \(Q = V \times n \div 60\) solved for \(n\). Divide the airflow of the fan you have (or plan to buy) per hour by the room volume, and you see how many times per hour the room air is replaced. You can then compare it with the target ACH. If several fans run at the same time, add their CFM first. Divide 60 by that number and you get the minutes for one full air change (at 4.17 ACH, 60 ÷ 4.17 ≈ 14.4 minutes). In CFM you can also divide the volume by the airflow directly: 864 ÷ 60 = 14.4 minutes. In real use, the airflow is lower than the rated value because of the size of the air inlets, the duct length and dirty filters, so people usually leave some margin. A fan's rated CFM is usually measured with little or no duct resistance (for bathroom fans, HVI ratings are often given at 0.1 in. w.c. of static pressure). Long ducts, many bends or small air inlets add resistance (pressure loss), and the real airflow drops. For a ducted fan, the practical check is to read the maker's airflow and static pressure chart (fan curve) and make sure the CFM at your expected static pressure is above the required airflow.

Airflow from the number of people, compared with the volume-based airflow

Standard notation (the usual math form)

\(Q_p\) \(=\) \(N\) \(\times\) \(q\)

\(Q\) \(=\) \(\max(\) \(Q_v\) \(,\) \(Q_p\) \()\)

In words (symbols replaced with words)

③ \(Q_p\): occupant-based airflow \(=\) ① \(N\): number of people \(\times\) ② \(q\): airflow per person

⑤ \(Q\): required airflow used \(=\) \(\max(\) ④ volume-based \(Q_v = V \times n \div 60\) \(,\) occupant-based \(Q_p\) \()\)

The formula in words

① Multiply the \(N\): number of people

② by the \(q\): airflow per person

③ and you get the \(Q_p\): occupant-based airflow

④ Compare it with the \(Q_v\): volume-based airflow (volume × ACH ÷ 60) and take the larger one (\(\max\) stands for "take the larger value")

⑤ to get the \(Q\): required airflow used

Quick example

For an 864 ft³ room (volume-based airflow 5.04 CFM at 0.35 ACH) used by 3 people at 15 CFM per person, the required airflow is

occupant-based \(Q_p\) \(=\) people (3) \(\times\) per person (15 CFM)

\(3 \times 15 = 45\,\mathrm{CFM}\)

\(Q = \max(5.04,\ 45) = 45\,\mathrm{CFM}\)

Key idea

In rooms where many people gather, such as meeting rooms, classrooms and shops, the airflow you need depends less on the room size and more on how much the carbon dioxide (CO₂) people breathe out must be diluted. The idea is "how much outdoor air per person keeps indoor CO₂ below a set level", so the airflow is the number of people × the airflow per person. In the US, 15 CFM per person is a long-used guideline (ASHRAE Standard 62-1989 used 15 CFM for many spaces and 20 CFM for offices), and it is this calculator's default. Values differ by use and code, so use your designer's or your code's value if you have one. Calculate both the volume-based value (volume × ACH ÷ 60) and the occupant-based value, and use the larger one. Then the airflow is enough by either measure. In the example above, the occupant-based 45 CFM is much larger. As ACH, it equals 45 × 60 ÷ 864 ≈ 3.13 ACH. In homes with few people, the volume-based value is often larger. The more crowded the room, the more the occupant-based value matters.

Whole-house ventilation rate (ASHRAE 62.2 guideline)

Standard notation (the usual math form)

\(Q_{tot}\) \(=\) \(S_f\) \(\times 0.03 + 7.5 \times (\) \(N_{br}\) \(+ 1)\)

In words (symbols replaced with words)

③ \(Q_{tot}\): whole-house airflow (CFM) \(=\) ① \(S_f\): floor area of the home (ft²) \(\times 0.03 + 7.5 \times (\) ② \(N_{br}\): number of bedrooms \(+ 1)\)

The formula in words

① Take 0.03 CFM for each square foot of the \(S_f\): floor area of the home (ft²)

② and add 7.5 CFM for each person, counting the \(N_{br}\): number of bedrooms plus 1 as the number of people,

③ and you get the \(Q_{tot}\): whole-house airflow (CFM) , a guideline for continuous ventilation of the whole home

Quick example

For a 2,000 ft² home with 3 bedrooms, the whole-house airflow is

whole-house airflow \(Q_{tot}\) \(=\) floor area (2,000 ft²) \(\times 0.03 + 7.5 \times (\) bedrooms (3) \(+ 1)\)

\(2000 \times 0.03 + 7.5 \times (3 + 1) = 60 + 30 = 90\,\mathrm{CFM}\)

\(n = 90 \times 60 \div 16000 \approx 0.34\)

Key idea

For the whole home, ASHRAE Standard 62.2 (the US standard for residential ventilation) gives a guideline rate from the floor area and the number of bedrooms. In the 2016 and later editions, it is 0.03 CFM per square foot plus 7.5 CFM per person, where the number of people is taken as bedrooms + 1. Older editions used smaller numbers, and local codes may differ, so check which rule applies to you. In the example, the home has 8 ft ceilings, so its volume is 2,000 × 8 = 16,000 ft³. Converting 90 CFM to ACH gives 90 × 60 ÷ 16,000 ≈ 0.34 ACH, close to the 0.35 ACH guideline this calculator uses for living spaces. You can check a single room the same way: enter its size and 0.35 ACH to see the CFM share for that room.

The room volume is length × width × ceiling height (= floor area × ceiling height). The required airflow in CFM is the volume times the air changes per hour divided by 60, \(Q = V \times n \div 60\) (0.35 ACH is a common guideline for living spaces). Multiply the fan CFM by 60 and divide by the volume to get the actual ACH; divide 60 by that number to get the minutes for one full air change. In rooms where many people gather, also find people × airflow per person and use the larger of the two.

Symbols and terms

Symbols

\(V\)	vee	The room volume (ft³), from "volume". It is found with \(V = L \times W \times H = S_f \times H\).
\(L\)	ell	The room length (ft), from "length". Use the inside dimensions (wall surface to wall surface).
\(W\)	double-u	The room width (ft), from "width". It does not matter which side you call the length and which the width.
\(H\)	aitch	The ceiling height (ft), from "height" - the height from the floor to the ceiling.
\(S_f\)	ess sub eff	The floor area (ft²). \(S\) is often said to come from "surface" or "square", and the subscript f stands for "floor".
\(Q\)	cue	The required airflow (CFM). In physics and building services, \(Q\) is the usual symbol for a flow rate. It is found with \(Q = V \times n \div 60\).
\(n\)	en	The air changes per hour (ACH), from "number". It shows how many times the room air is replaced in one hour. At 0.35, one full air change takes about 2.9 hours.
\(Q_f\)	cue sub eff	The total fan airflow (CFM). The subscript f stands for "fan". With several fans, it is the sum of their airflows.
\(n'\)	en prime	The actual air changes per hour worked out from the fan airflow. The prime (') tells it apart from the target \(n\). It is found with \(n' = Q_f \times 60 \div V\).
\(T\)	tee	The time (min) for one full air change, from "time". It is found with \(T = 60 \div n'\).
\(N\)	capital en	The number of people in the room, from "number". It is a capital letter to tell it apart from the lowercase \(n\) (ACH).
\(q\)	lowercase cue	The airflow per person (CFM). It is a small flow for one person, so it is lowercase to tell it apart from \(Q\) for the whole room. A common US guideline is 15 to 20, and this calculator's default is 15.
\(Q_p\)	cue sub pee	The occupant-based airflow (CFM). The subscript p stands for "person". It is found with \(Q_p = N \times q\).
\(Q_v\)	cue sub vee	The volume-based airflow (CFM). The subscript v stands for "volume", and \(Q_v = V \times n \div 60\). Compare it with the occupant-based \(Q_p\) and use the larger one.
\(\max\)	max	Short for "maximum". It takes the largest of the values in the parentheses, as in \(\max(5.04,\ 45) = 45\).
\(Q_{tot}\)	cue sub tot	The whole-house airflow (CFM) in the ASHRAE 62.2 guideline, \(Q_{tot} = 0.03 \times S_f + 7.5 \times (N_{br} + 1)\). The subscript tot stands for "total".
\(N_{br}\)	en sub b r	The number of bedrooms in the ASHRAE 62.2 guideline. The number of people is taken as bedrooms + 1.
\(\mathrm{ft^3}\)	cubic feet	A unit of volume. One cubic foot is a cube 1 ft on each side, about 7.48 US gallons (1 m³ ≈ 35.31 ft³).
\(\mathrm{CFM}\)	C F M (cubic feet per minute)	The unit for how much air moves each minute, used for fan ratings in the US. 1 CFM ≈ 1.699 m³/h. Multiply by 60 to get cubic feet per hour.

Terms

Room volume	The size of the space inside a container. For a room it is floor area × ceiling height, in cubic feet (ft³). It is the basis for ventilation and air conditioning sizing.
Air changes per hour (ACH)	How many times the room air is replaced in one hour. At 0.35 ACH, one full air change takes about 2.9 hours. Living spaces use small values like 0.35 ACH, and local exhaust in kitchens, bathrooms and toilet rooms uses larger values.
Required airflow	The airflow needed to replace the air as much as the target ACH (or number of people) calls for, in CFM. If the fan airflow is at least this value, the target is met.
CFM (fan airflow)	How much air a fan can move each minute, shown in the catalog and on the fan label. The rated CFM is usually measured with little duct resistance. Duct length and small air inlets cause pressure loss, so the real airflow is lower. Leave some margin when you choose.
Static pressure	The pressure a fan must push against to move air through ducts, in the US usually in inches of water column (in. w.c.). The maker's fan curve shows how the airflow drops as the static pressure rises.
Pressure loss	Pressure lost because duct length, bends, small air inlets or filters get in the way of the airflow. The higher the pressure loss, the lower the real airflow of the same fan compared with its rating.
Exhaust fan	An electric fan that moves room air outdoors (or brings outdoor air in). Types include wall fans, ceiling fans with ducts and range hoods. Performance is shown as airflow in CFM.
Whole-house ventilation	A system of fans and air inlets that slowly and continuously replaces the air of the home. ASHRAE Standard 62.2 gives a guideline rate. For requirements, check your building code or designer.
Local exhaust	Strong ventilation for a short time only where odors, moisture or smoke come from, such as kitchens, bathrooms and toilet rooms. Its ACH guideline (about 8 to 15) is much higher than for living spaces (0.35).
General ventilation	Ventilation that replaces the air of the whole room little by little. Whole-house ventilation works this way, with a small ACH (such as 0.35).
Supply air (air in)	Outdoor air brought into the room. An exhaust fan alone cannot move much air if no air can come in, so the same amount must enter through air inlets or gaps around windows and doors.
Exhaust (air out)	Room air moved outdoors. A fan's airflow rating usually refers to this exhaust.
Occupants	The number of people in the room at the same time. In meeting rooms and classrooms, the airflow you need is often set by the number of people rather than the room size, as people × airflow per person.
CO₂ level	The share of CO₂ in the air (in ppm). It rises as people breathe out and falls with ventilation. The airflow per person is based on keeping this level below a set value (this calculator does not calculate the level itself).
Coverage ratio	The total fan airflow as a percentage of the required airflow. At 100% or more, the required airflow is met.
Inside dimensions	Measurements from wall surface to wall surface - the space you can actually use. The volume is calculated with these. They are a little smaller than measurements to the center of the walls on some plans.
Converting CFM and ACH	ACH = CFM × 60 ÷ volume (ft³), and CFM = volume × ACH ÷ 60. The 60 turns minutes into hours.
Ceiling height	The height from the finished floor to the finished ceiling. 8 ft is standard in US homes, and 9 ft or more is common in newer homes.

Good to know before you start

Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.

Volume of a rectangular prism (Grade 5)	The volume of a box is length × width × height = base area × height The difference between the volume unit \(\text{ft}^3\) (cubic feet) and the area unit \(\text{ft}^2\) (square feet)
Unit rates (Grade 6)	A per-unit amount, such as "cubic feet per minute", times a time or a number of people gives the total (airflow = volume × ACH ÷ 60, people × per person) The other way around, dividing a total amount by the volume tells you "how many times per hour"
Multiplying and dividing decimals (Grades 5–6)	What calculations like \(864 \times 0.35\) and \(3600 \div 864\) stand for (a calculator is fine for the arithmetic)
Percents (Grade 6)	"What percent of the need is covered" = part ÷ whole × 100 gives the coverage ratio
Units of time (Grade 3)	1 hour = 60 minutes, so "3 times an hour" is the same as "once every 60 ÷ 3 = 20 minutes"
Converting units of length (Grade 4)	1 ft = 12 in, so a 96 in ceiling is 8 ft

How to calculate it in Excel

Copy the whole table below and paste it into cell A1 in Excel. It works as is.

Table to find the room volume

Room length (ft)	12
Room width (ft)	9
Ceiling height (ft)	8
Volume (ft³)	=B1B2B3

Table to find the required airflow

Volume (ft³)	864
Air changes per hour (ACH)	0.35
Required airflow (CFM)	=B1*B2/60

Table to find the actual ACH and air change time from the fan airflow

Total fan airflow (CFM)	60
Volume (ft³)	864
Actual ACH	=B1*60/B2
Time for one air change (min)	=60/B3

Table to compare the occupant-based and volume-based airflow

Number of people	3
Airflow per person (CFM)	15
Volume-based airflow (CFM)	5.04
Occupant-based airflow (CFM)	=B1*B2
Required airflow used (larger) (CFM)	=MAX(B3,B4)

Table to find the whole-house airflow (ASHRAE 62.2 guideline)

Floor area of the home (ft²)	2000
Number of bedrooms	3
Ceiling height (ft)	8
Whole-house airflow (CFM)	=0.03B1+7.5(B2+1)
As ACH	=B460/(B1B3)

After pasting, the upper rows of column B are the inputs and the last rows are calculated automatically.
The first table gives a volume of 864 ft³, and the second a required airflow of 5.04 CFM. The third gives the actual ACH with a 60 CFM fan, about 4.1667 ACH, and a time for one air change of 14.4 minutes.
The fourth table compares the occupant-based 45 CFM with the volume-based 5.04 CFM using the MAX function, and the larger value, 45, is the required airflow used. The fifth gives a whole-house airflow of 90 CFM for a 2,000 ft² home with 3 bedrooms, about 0.3375 ACH.

How to calculate it in Google Sheets

Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.

Table to find the room volume

Room length (ft)	12
Room width (ft)	9
Ceiling height (ft)	8
Volume (ft³)	=B1B2B3

Table to find the required airflow

Volume (ft³)	864
Air changes per hour (ACH)	0.35
Required airflow (CFM)	=B1*B2/60

Table to find the actual ACH and air change time from the fan airflow

Total fan airflow (CFM)	60
Volume (ft³)	864
Actual ACH	=B1*60/B2
Time for one air change (min)	=60/B3

Table to compare the occupant-based and volume-based airflow

Number of people	3
Airflow per person (CFM)	15
Volume-based airflow (CFM)	5.04
Occupant-based airflow (CFM)	=B1*B2
Required airflow used (larger) (CFM)	=MAX(B3,B4)

Table to find the whole-house airflow (ASHRAE 62.2 guideline)

Floor area of the home (ft²)	2000
Number of bedrooms	3
Ceiling height (ft)	8
Whole-house airflow (CFM)	=0.03B1+7.5(B2+1)
As ACH	=B460/(B1B3)

The same formulas as Excel (basic arithmetic and the MAX function) work as is. Copy the whole table, paste it into cell A1 and change column B to your own numbers. To use metric instead, enter meters and m³/h and remove the "/60" and "*60" (m³ × ACH gives m³/h directly).

How to calculate it in Python

room_length_ft = 12          # room length (ft)
room_width_ft = 9            # room width (ft)
ceiling_height_ft = 8        # ceiling height (ft)
air_changes_per_hour = 0.35  # air changes per hour (ACH). A common guideline for living spaces
fan_flows = [60]             # fan airflow (CFM) list. For several fans, list them like [60, 50]
persons = 3                  # number of people. Use 0 if you do not need the occupant-based rate
flow_per_person = 15         # airflow per person (CFM). A common US guideline

volume = room_length_ft * room_width_ft * ceiling_height_ft   # volume (ft³)
required_by_volume = volume * air_changes_per_hour / 60        # volume-based airflow (CFM)
required_by_persons = persons * flow_per_person                # occupant-based airflow (CFM)
required = max(required_by_volume, required_by_persons)        # use the larger one

fan_total = sum(fan_flows)                                     # total fan airflow (CFM)
actual_air_changes = fan_total * 60 / volume                   # actual ACH
turnover_minutes = 60 / actual_air_changes                     # time for one air change (min)
sufficiency = fan_total / required * 100                       # coverage of the required airflow (%)

print(f"Volume: {volume:.5g} ft³")
print(f"Volume-based airflow: {required_by_volume:.5g} CFM")
print(f"Occupant-based airflow: {required_by_persons:.5g} CFM")
print(f"Required airflow used: {required:.5g} CFM")
print(f"Total fan airflow: {fan_total:.5g} CFM")
print(f"Actual ACH: {actual_air_changes:.3g}")
print(f"Time for one air change: {turnover_minutes:.3g} min")
print(f"Coverage: {sufficiency:.4g} %")

It runs with the standard library only. Change the sizes, ACH, fan airflow and number of people at the top to your own numbers and run it. If you do not need the occupant-based rate, set persons to 0 and the required airflow used becomes the volume-based value. Put the airflow of at least one fan in fan_flows (an empty list [] makes the total 0 and the division fails). For metric, use meters and m³/h and remove "/ 60" and "* 60".

How to write it in LaTeX and other math languages (copy and paste)

Room volume

V = L × W × H = S_f × H

V = L \times W \times H = S_f \times H

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>V</mi>
    <mo>=</mo>
    <mi>L</mi><mo>&#xD7;</mo><mi>W</mi><mo>&#xD7;</mo><mi>H</mi>
    <mo>=</mo>
    <msub><mi>S</mi><mi>f</mi></msub>
    <mo>&#xD7;</mo>
    <mi>H</mi>
  </mrow>
</math>

V = L xx W xx H = S_f xx H

V = L*W*H

V := L*W*H;

V = L*W*H;

V = L × W × H = S_f × H

Required airflow (from air changes per hour)

Q = V × n ÷ 60

Q = \dfrac{V \times n}{60}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>Q</mi>
    <mo>=</mo>
    <mfrac><mrow><mi>V</mi><mo>&#xD7;</mo><mi>n</mi></mrow><mn>60</mn></mfrac>
  </mrow>
</math>

Q = (V xx n) / 60

Q = V*n/60

Q := V*n/60;

Q = V*n/60;

Q = (V × n)/60

Actual air changes per hour and air change time from the fan airflow

n' = Q_f ÷ V × 60,  T = 60 ÷ n'

n' = \dfrac{60\,Q_f}{V},\quad T = \dfrac{60}{n'}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msup><mi>n</mi><mo>&#x2032;</mo></msup>
    <mo>=</mo>
    <mfrac><mrow><mn>60</mn><msub><mi>Q</mi><mi>f</mi></msub></mrow><mi>V</mi></mfrac>
    <mo>,</mo>
    <mi>T</mi>
    <mo>=</mo>
    <mfrac><mn>60</mn><msup><mi>n</mi><mo>&#x2032;</mo></msup></mfrac>
  </mrow>
</math>

n' = (60 Q_f) / V,  T = 60 / n'

nActual = 60*Qf/V; T = 60/nActual

nActual := 60*Qf/V;  T := 60/nActual;

nActual = 60*Qf/V; T = 60/nActual;

n' = 60Q_f/V, T = 60/n'

Airflow from the number of people, compared with the volume-based airflow

Q_p = N × q,  Q = max(Q_v, Q_p)

Q_p = N \times q,\quad Q = \max(Q_v,\ Q_p)

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>Q</mi><mi>p</mi></msub>
    <mo>=</mo>
    <mi>N</mi><mo>&#xD7;</mo><mi>q</mi>
    <mo>,</mo>
    <mi>Q</mi>
    <mo>=</mo>
    <mi>max</mi>
    <mo>(</mo>
    <msub><mi>Q</mi><mi>v</mi></msub>
    <mo>,</mo>
    <msub><mi>Q</mi><mi>p</mi></msub>
    <mo>)</mo>
  </mrow>
</math>

Q_p = N xx q,  Q = max(Q_v, Q_p)

Qp = nPersons*q; Q = Max[Qv, Qp]  (* N is a reserved word in Mathematica (numeric evaluation), so the number of people is nPersons *)

Qp := N*q;  Q := max(Qv, Qp);

Qp = N*q; Q = max(Qv, Qp);

Q_p = N × q, Q = max(Q_v, Q_p)

Whole-house ventilation rate (ASHRAE 62.2 guideline)

Q_tot = 0.03 × S_f + 7.5 × (N_br + 1)

Q_{tot} = 0.03\,S_f + 7.5\,(N_{br} + 1)

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>Q</mi><mi>tot</mi></msub>
    <mo>=</mo>
    <mn>0.03</mn><msub><mi>S</mi><mi>f</mi></msub>
    <mo>+</mo>
    <mn>7.5</mn>
    <mo>(</mo>
    <msub><mi>N</mi><mi>br</mi></msub>
    <mo>+</mo>
    <mn>1</mn>
    <mo>)</mo>
  </mrow>
</math>

Q_(tot) = 0.03 S_f + 7.5 (N_(br) + 1)

Qtot = 0.03*Sf + 7.5*(Nbr + 1)

Qtot := 0.03*Sf + 7.5*(Nbr + 1);

Qtot = 0.03*Sf + 7.5*(Nbr + 1);

Q_tot = 0.03S_f + 7.5(N_br + 1)

How to have ChatGPT do the calculation

You are an assistant for building ventilation calculations. Do the calculations below by actually running Python code, and base your answer only on the numbers from the output (do not calculate in your head or guess).

A room is a box 12 ft long, 9 ft wide, with an 8 ft ceiling.
1. Find the room volume (ft³).
2. Find the required airflow (CFM) at 0.35 air changes per hour.
3. With one 60 CFM exhaust fan in the room, find the actual air changes per hour and the minutes for one full air change.
4. Three people use the room, at 15 CFM per person. Find the occupant-based airflow (CFM), compare it with the volume-based value from step 2 and use the larger one.

Show the formulas you used and the numbers from the output. Also note that the ACH and the per-person value are general guidelines and not necessarily code requirements.

How to Use

1

Enter your numbers

Type the numbers you want to calculate with into the input fields
2

Calculate

Press the "Calculate" button
3

Check the result

The result appears on the spot. The same page also explains the idea behind the calculation and the formula