Duct Sizing Calculator Formula

Understand the math behind the duct sizing calculator. Each variable explained with a worked example.

Use the Duct Sizing Calculator

Formulas Used

Round Duct Diameter

round_diameter = max_velocity > 0 ? 2 * sqrt(area_sqft / pi) * 12 : 0

Cross-Section Area

area_sqin = area_sqft * 144

Actual Velocity at Next Size

actual_velocity = max_velocity > 0 ? cfm / (pi * pow(ceil(2 * sqrt(area_sqft / pi) * 12) / 2 / 12, 2)) : 0

Variables

VariableDescriptionDefault
cfmAirflow(CFM)400
max_velocityMax Velocity(ft/min)700
area_sqftDerived value= max_velocity > 0 ? cfm / max_velocity : 0calculated

How It Works

Duct Sizing by Velocity

A = CFM / Velocity

Diameter = 2 x sqrt(A / pi)

Convert the area to diameter for round ducts. For residential trunk lines, maximum velocity of 700 ft/min keeps noise low. Branch runs can go up to 600 ft/min. Round up to the next standard duct size.

Worked Example

400 CFM at a max velocity of 700 ft/min.

cfm = 400max_velocity = 700
  1. 01Area = 400 / 700 = 0.571 sq ft = 82.3 sq in
  2. 02Diameter = 2 x sqrt(0.571 / pi) x 12 = 10.2 in
  3. 03Use a 10-inch round duct (or 12-inch for lower velocity).

Ready to run the numbers?

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