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Duct Size Calculator

Find what size round or rectangular air duct you need for your airflow, at a target air speed or friction rate. It also converts between round and rectangular ducts with the Huebscher formula.

Level: Grade 12 to college

Printable worksheet

Duct Size Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Find
Units

The fastest you want the air to move. Slower air is quieter and loses less pressure, but it needs a bigger duct.

One side of the rectangular duct, often set by the joist or wall cavity depth.

Result

Minimum round diameter

10.24 in

400 CFM at 700 ft/min needs a round duct of about 10.236 in, or 8 × 11.03 in rectangular.

Friction rate at that size (galvanized steel)
0.0763 in. w.c./100 ft
Next common round size up
12 inStock sizes vary by supplier.
Velocity in that size
509 ft/min
Friction rate in that size
0.0352 in. w.c./100 ft
Rectangular width with a 8 in side
11.03 in

See the step-by-step solution ↓

Step-by-step solution

  1. Find the area the air needs: airflow ÷ air speed, because airflow is speed times area

    400700=0.571429 ft²

  2. Find the diameter of a circle with that area, then multiply by 12 to turn feet into inches

    12×4×0.571429π=10.235694 in

  3. Find the rectangle that loses the same pressure: with one side of 8 in, find the width whose Huebscher match is 10.2357 in

    b=11.029613 in

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find the right size air duct for the airflow it has to carry. Every supply and return duct must move its share of the air. Too small, and the air moves so fast it whistles. Too small also means it loses so much pressure that the far rooms get too little air.

Two numbers usually set the size. One is the air speed (velocity) you're willing to accept. The other is the friction rate, meaning the pressure the air loses over 100 ft of straight duct. Rectangular ducts come in when a round pipe won't fit in a joist bay or a wall.

This duct size calculator works four ways. It finds the round size for an airflow at a target speed, or estimates it at a friction rate. It also gives the round duct that equals a rectangle, or the rectangle that equals a round duct for a side you choose. When sizing, it suggests the next common round size and shows the speed and friction in that size. It also gives a rectangle with the same friction. You can work in CFM (cubic feet per minute) and inches, or in litres per second and millimetres.

Where it's used

Why this math matters outside the classroom:

  • Branch duct runs. An HVAC installer finds 400 CFM at 700 ft/min needs a 10.24 in round duct and runs 12 in pipe instead.
  • Fitting a joist bay. A remodeler swaps a 10 in round duct for a rectangle 8 in deep, which needs to be about 10.5 in wide.
  • Reading old drawings. A technician checks that an existing 12 × 8 in trunk is equal in friction to a 10.66 in round duct.
  • Classroom fluid mechanics. Engineering students solve the Colebrook equation for an air duct and compare the answer with a friction chart.
  • Quiet supply design. A designer upsizes a bedroom branch so the air moves more slowly and the grille makes less noise.

How to use it

  1. Choose what to find: a size for an air speed, a size for a friction rate, or a round or rectangular equivalent.
  2. Pick US or metric units.
  3. Enter the airflow and the target speed or friction rate. Or enter the duct sizes you already have.
  4. If you want a rectangular duct, enter one side of it. Then read the round size, the next common size and the rectangle's width.

What the inputs mean

Airflow
Use the airflow this one duct must carry, not the whole system's. A branch to one room carries only that room's share. That share often comes from the room's heating or cooling load.
Target air velocity
Slower air means a bigger, quieter duct. Design guides set speed limits by duct type. Branches near rooms get lower limits than main trunks.
Friction rate
In a full design, the friction rate comes from the pressure the blower has left after filters, coils and grilles. That pressure is spread over the longest run, fittings included. Entering a typical value only gives an estimate.
Duct surface roughness
Friction charts for sheet-metal duct are usually drawn for galvanized steel at 0.09 mm. Flexible duct is much rougher. Flex that sags or gets squashed loses far more.
Absolute roughness
Flexible duct is far rougher than sheet metal, and even more so when it isn't pulled straight.
Rectangular side (height)
The side of the rectangle you can't change, such as the depth between joists. The calculator works out the other side.

Formula and method

Velocity sizing: A = Q ÷ V,   d = √(4A ÷ π)
Huebscher: Dₑ = 1.30 × (a × b)^0.625 ÷ (a + b)^0.25
Friction: Δp ÷ L = f ÷ d × ρV² ÷ 2,  with 1/√f = −2 log₁₀(ε ÷ 3.7d + 2.51 ÷ (Re √f))
Standard air: ρ = 1.204 kg/m³, ν = 1.516 × 10⁻⁵ m²/s;  1 in. w.c. = 249.08891 Pa

In the first line, Q is the airflow, V is the air speed, A is the duct's cross-section area and d is its diameter. The rule is simple: airflow equals speed times area. With CFM and feet per minute, the area comes out in square feet. A circle with that area has a diameter of √(4A ÷ π), and the calculator multiplies by 12 to get inches.

In Huebscher's formula, a and b are the two sides of the rectangle and Dₑ is the round duct that matches it. Matching means both lose the same pressure from friction when they carry the same airflow. A rectangle has more wall for its area, so it always needs a little more area than its round match. You can't solve this formula straight for a missing side. So the calculator finds that side by halving its guess range over and over until it fits.

Friction sizing uses the Darcy–Weisbach equation for standard air. In it, Δp ÷ L is the pressure lost per length of duct, ρ (rho) is the air's density and ν (nu) is how thick, or viscous, the air is. The friction factor f comes from the Colebrook equation, where ε is the wall roughness and Re (the Reynolds number) describes how the air flows. Pressure loss drops steeply as the duct gets bigger. So the calculator searches for the diameter whose loss equals the rate you entered. 'In. w.c.' means inches of water column, a small unit of pressure.

Worked example

A branch must carry 400 CFM at no more than 700 ft/min, and it has to fit in a cavity 8 in deep.

  1. Area needed: 400 ÷ 700 = 0.571429 ft².
  2. Round diameter: 12 × √(4 × 0.571429 ÷ π) = 10.235694 in.
  3. The next common round size is 12 in. There the air moves at 509 ft/min and loses about 0.0352 in. w.c. per 100 ft.
  4. Rectangle with an 8 in side: the Huebscher formula reaches 10.24 in at a width of 11.03 in.

Result: Use at least a 10.24 in round duct (12 in from common stock), or an 8 × 11.03 in rectangle. Round up to the next size you can get.

Understanding the result

The minimum diameter is the smallest duct that meets your target, so round up to a size you can buy. Going bigger lowers the air speed and the friction rate. The calculator shows both for the suggested size, so you can see the effect.

Two ducts that are Huebscher equivalents lose the same pressure per foot at the same airflow. But the rectangle has more area than the round duct. So the average air speed in the rectangle is a little lower.

Assumptions and limitations

  • Standard air at about 20 °C and sea-level pressure.
  • Straight duct only. Fittings, grilles, filters and coils add their own losses.
  • Speed sizing assumes a full round duct and uses the average air speed.
  • Sizing by friction rate here is an estimate, not an ACCA Manual D design. Manual D is the US standard method for home duct design. It works out the pressure available and the full length of every run, fittings included, before choosing sizes.
  • Flexible duct, duct liner and badly installed flex can lose several times more than sheet metal. Use a realistic roughness or the maker's data.
  • Local mechanical codes and the equipment maker's requirements come first. A qualified HVAC designer should size or approve a system.

Frequently asked questions

What size duct do I need for 400 CFM?

It depends on the air speed or friction you allow. At 700 ft/min, 400 CFM needs at least a 10.24 in round duct. At a friction rate of 0.08 in. w.c. per 100 ft in galvanized steel, it needs about 10.1 in. A 12 in round duct carries it at about 509 ft/min.

How do I convert a rectangular duct to round?

Use Huebscher's equivalent diameter, 1.30 × (a × b)^0.625 ÷ (a + b)^0.25, where a and b are the two sides. A 12 × 8 in duct works out to about 10.66 in. Matching the area instead gives too small a size, because a rectangle has more wall friction for its area.

What friction rate should I use for duct sizing?

There's no single right value. It should come from the pressure your blower has available, spread over the full length of the longest run, fittings included. Rules of thumb exist, but they're only a starting point. A Manual D design works it out for your actual system.

Why is my rectangular duct bigger in area than the round one?

Air drags along the walls. A rectangle has more wall around the same area than a circle does, especially when it's flat. So to lose the same pressure, it needs more area. That's what the Huebscher formula accounts for.

Sources

How this calculator is checked

Method: Continuity A = Q/V; Huebscher (1948) equivalent diameter 1.30(ab)^0.625/(a+b)^0.25, checked against published equivalent-diameter tables; Darcy–Weisbach with the Colebrook friction factor (shared src/lib/fluids/friction.ts) for standard air, checked against an independent Swamee–Jain calculation and typical galvanized-duct friction chart readings. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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