Fluid Mechanics

CFM Calculator

Airflow calculator covering duct CFM (CFM = A v for rectangular and round ducts) and room air-change CFM (CFM = Volume × ACH / 60), with duct velocity, duct diameter, and ACH as solvable targets.

Formula CFM = A v; A = W H or π d² / 4Reviewed Sep 8, 2026

CFM (cubic feet per minute) is the standard measure of airflow in HVAC work, and it comes from one of two relationships depending on what you're sizing. For a duct, CFM = A v - the internal cross-sectional area times the average duct velocity. For a room, CFM = Volume × ACH / 60 - the room's volume times the target air changes per hour, divided by 60. This page covers both: duct geometry (rectangular width × height, or round diameter) with feet-per-minute as the native velocity unit, and room geometry (length × width × height) with air changes per hour, so you can go from either a duct or a room straight to CFM, or back-solve for duct velocity, duct diameter, or required ACH.

Calculation Bench

What Are You Sizing?

Solve for

01Duct Width

W · Internal width of the rectangular duct cross-section.

02Duct Height

H · Internal height of the rectangular duct cross-section.

03Duct Velocity

v · Average air velocity through the duct cross-section, not a local peak velocity.

Rectangular mode uses internal duct width and height together - it does not solve for a single missing dimension, since a required area doesn't split uniquely into two sides.

Solution

Enter the required values to calculate airflow.

CFM = (W × H) v

Formula Sheet

\text{CFM} = (W \times H)\,v

v = \dfrac{\text{CFM}}{W \times H}

\text{CFM} = \left(\dfrac{\pi d^2}{4}\right) v

d = \sqrt{\dfrac{4\,\text{CFM}}{\pi v}}

v = \dfrac{4\,\text{CFM}}{\pi d^2}

\text{CFM} = \dfrac{(L \times W \times H) \times \text{ACH}}{60}

\text{ACH} = \dfrac{\text{CFM} \times 60}{L \times W \times H}

QAirflow
WDuct Width
HDuct Height
dDuct Diameter
vDuct Velocity
L, W, HRoom Dimensions
ACHAir Changes per Hour

Variables & Units

Symbol	Variable	Description	Common Units
Q	Airflow	Volumetric airflow rate through the duct, most commonly reported in CFM (cubic feet per minute).	CFM, m³/h, L/s
W	Duct Width	Internal width of a rectangular duct cross-section.	in, mm, ft
H	Duct Height	Internal height of a rectangular duct cross-section.	in, mm, ft
d	Duct Diameter	Internal diameter of a round duct, used to derive its cross-sectional area.	in, mm, ft
v	Duct Velocity	Average air velocity through the duct cross-section, not a local peak velocity.	ft/min, m/s, ft/s
L, W, H	Room Dimensions	Internal room length, width, and height, multiplied together to get room volume.	ft, m
ACH	Air Changes per Hour	How many times per hour the room's full air volume needs to be replaced - a dimensionless count, not a physical unit.

How to Use This Calculator

01Choose what you're sizing first: Rectangular Duct, Round Duct, or Room / ACH.
02For duct modes, select which quantity to solve for: airflow (CFM), duct velocity, or - for round ducts only - the duct diameter. For Room / ACH mode, solve for either airflow (CFM) or the air changes per hour a known airflow delivers.
03Enter the remaining values with any supported units. Duct dimensions default to inches and velocity to feet per minute (FPM); room dimensions default to feet. Metric units are supported throughout.
04For rectangular ducts, enter the internal (not insulated or nominal) width and height - this page does not solve for a single missing rectangular dimension, since area alone doesn't split uniquely into two sides.
05For Room / ACH mode, air changes per hour is a plain count. If you do not know what ACH to use, start with the typical-range table below, then verify the final target against the code, standard, or project specification that applies to the space.

How the Formula Works

Duct airflow is defined as CFM = A v: the duct's internal cross-sectional area times the average air velocity through that section. For a rectangular duct, A = W H. For a round duct, A = π d² / 4.

Room airflow is defined by air changes per hour instead of velocity: CFM = (L × W × H) × ACH / 60, where L × W × H is the room's volume and ACH is how many times per hour that volume needs to be fully replaced. Rearranging that relationship also solves for the ACH a given supply or exhaust CFM actually delivers to a room of known size.

The practical result is not just a CFM number. Compare the calculated airflow with the fan, diffuser, or duct branch capacity, then check whether the implied duct velocity and static pressure are still reasonable for the system.

Worked Example 01

Airflow through a rectangular supply duct

Known

Duct Width (W): 12 in
Duct Height (H): 8 in
Duct Velocity (v): 700 ft/min

Formula

CFM = (W × H) v

Substitution

CFM = (12 × 8 / 144) × 700

Result

CFM ≈ 466.7

A 12 by 8 inch rectangular duct (0.667 ft²) carrying air at an average velocity of 700 feet per minute delivers about 466.7 cubic feet per minute.

Worked Example 02

Airflow through a round duct

Known

Duct Diameter (d): 10 in
Duct Velocity (v): 900 ft/min

Formula

CFM = (π d² / 4) v

Substitution

CFM = (π × 10² / 4 / 144) × 900

Result

CFM ≈ 490.9

A 10 inch inside-diameter round duct (about 0.545 ft²) at 900 feet per minute average velocity delivers roughly 490.9 cubic feet per minute.

Worked Example 03

Required round-duct diameter for a target airflow

Known

Airflow (CFM): 800 CFM
Duct Velocity (v): 1000 ft/min

Formula

d = √(4 CFM / (π v))

Substitution

d = √(4 × (800/1000) × 144 / π)

Result

d ≈ 12.1 in

To move 800 CFM at a target velocity of 1000 feet per minute, a round duct needs an inside diameter of about 12.1 inches.

Worked Example 04

Required airflow for a target room air-change rate

Known

Room Length (L): 10 ft
Room Width (W): 12 ft
Room Height (H): 8 ft
Air Changes per Hour (ACH): 4

Formula

CFM = (L × W × H) × ACH / 60

Substitution

CFM = (10 × 12 × 8) × 4 / 60

Result

CFM = 64

A 10 by 12 by 8 foot room (960 ft³) needs 64 CFM of supply airflow to achieve 4 complete air changes per hour.

Worked Example 05

Checking the air-change rate an exhaust fan delivers

Known

Room Length (L): 8 ft
Room Width (W): 6 ft
Room Height (H): 8 ft
Airflow (CFM): 80 CFM

Formula

ACH = CFM × 60 / (L × W × H)

Substitution

ACH = 80 × 60 / (8 × 6 × 8)

Result

ACH = 12.5

An 80 CFM exhaust fan in an 8 by 6 by 8 foot bathroom (384 ft³) delivers 12.5 air changes per hour - useful for checking that fan against a required minimum ACH.

Applications

01Sizing rectangular or round supply and return duct dimensions for a target CFM at a chosen duct velocity
02Checking the average velocity an existing duct run is running at for a known or measured airflow
03Sizing a bathroom, kitchen, or general ventilation fan's required CFM for a target air-change rate
04Checking whether an installed or spec'd exhaust fan meets a required air-change rate (e.g. a building-code ACH minimum) for a given room size

Typical ACH Starting Points

Space / Use	Typical ACH Range	Use this as
Bedroom / living room	1-3 ACH	Low-intensity comfort or circulation check
Office / classroom	2-6 ACH	General ventilation screening before code lookup
Bathroom exhaust	8-12 ACH	Fan sizing sanity check for small rooms
Kitchen / laundry	8-15 ACH	Moisture, odor, or heat removal starting point
Workshop / garage	6-12 ACH	Dust, fumes, or heat screening only

Assumptions

01Entered duct velocity is the average velocity across the full duct cross-section, consistent with CFM = A v.
02Duct dimensions are internal (clear) dimensions - not nominal sheet-metal size, and not outside dimensions including insulation or lining.
03Room mode assumes fully mixed air and a simple rectangular room volume (L × W × H) - it does not account for furniture, fixtures, or irregular room shapes that reduce free air volume.
04The tool evaluates a single straight duct section, or a single room, and does not model fittings, transitions, branch losses, or multi-room duct systems.

Where This Model Stops

01Does not calculate static pressure drop or friction loss. Use a duct friction chart or a Darcy-Weisbach-based tool when pressure loss, not just airflow, is what you need.
02Rectangular duct mode does not solve for a single missing duct dimension - width and height are both required inputs whenever airflow or velocity is being solved, since area alone can't be split uniquely into two sides.
03Room / ACH mode does not solve for a missing room dimension either, for the same reason - it only solves for airflow or air changes per hour, both of which use all three room dimensions as known inputs.
04The typical ACH ranges on this page are screening hints, not universal requirements. Healthcare, laboratory, industrial exhaust, and code-governed ventilation designs need the governing standard and professional review.

References

[1]
14.5 Fluid Dynamics
OpenStax University Physics Volume 1
Defines volumetric flow rate and derives Q = A v, the same area-velocity relationship duct airflow (CFM) is built from.
[2]
Duct System Design
ASHRAE (American Society of Heating, Refrigerating and Air-Conditioning Engineers)
Professional-society reference for duct sizing, airflow, and velocity practice used throughout commercial and residential HVAC design.
[3]
HVAC Duct Construction Standards
SMACNA (Sheet Metal and Air Conditioning Contractors' National Association)
Industry reference for rectangular and round duct fabrication and sizing conventions.

Frequently Asked Questions

How is this different from the Flow Rate Calculator?

The underlying relationship is the same area-velocity flow equation, but this page is built specifically around HVAC duct geometry: rectangular ducts by width and height, round ducts by inside diameter, feet per minute as the default velocity unit, and CFM as the default airflow unit. The Flow Rate Calculator is the general-purpose version for pipes and generic flow sections in mixed metric/imperial units.

Why is duct velocity in feet per minute (FPM) instead of feet per second?

Feet per minute is the unit HVAC ductwork is conventionally designed and specified in. This calculator defaults to ft/min for that reason, but you can switch the velocity field to m/s or ft/s if that's what your source data uses.

Can I calculate CFM from a room size and air changes per hour?

Yes - switch to Room / ACH mode. Enter the room's length, width, and height plus a target air changes per hour, and it solves CFM = (L × W × H) × ACH / 60. You can also go the other way: enter a known airflow and room size to solve for the air changes per hour that airflow actually delivers.

Why can't I solve for duct width, duct height, or a room dimension directly?

Because a required area or volume doesn't split into unique dimensions on its own - many different width/height or length/width/height combinations give the same area or volume. Fix all but one dimension based on your actual space or ductwork constraints, then divide the required area or volume by the known dimensions to get the missing one.

What air-change rate should I target?

Use the typical ACH table on this page only as a starting point. Bedrooms and living spaces are often lower, while bathrooms, kitchens, workshops, and exhaust-heavy spaces are higher. The final value should come from the applicable code, standard, design spec, or licensed HVAC professional.

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