Duct sizing and geometry

Duct Shape Converter

Convert round, rectangular, and flat-oval dimensions using the selected area or friction basis.

Calculation inputs

This calculator runs in your browser and requires JavaScript.

An example is loaded automatically. Replace it with your project values; the result updates as you edit.

Shape and conversion basis Equal-area geometry preserves cross-sectional area. The equal-friction correlations match straight-duct friction per length at equal airflow; these are different results.

Inside round diameter (in) Clear inside diameter.

Selected rectangle aspect ratio (:1) Width divided by height.

Loading example values…

Result

No result yet

Results appear automatically when inputs are valid.

Formula and source basis

Concepts behind this calculation

Convert round, rectangular and flat-oval duct dimensions on a selected equal-area or equal-friction basis, with the two equivalent diameters clearly distinguished.

Equal-area conversion preserves volume-flow velocity at a given CFM. Equal-friction conversion uses empirical shape relationships intended to compare straight-duct resistance at the same airflow.

Hydraulic diameter represents four times area divided by wetted perimeter. It is a different geometric quantity from the equal-friction round diameter and should not silently replace it in a sizing method.

How to use this calculator

Choose the direction and equal-area or equal-friction basis in the shape and conversion selector.
Enter inside round diameter for a round starting section, inside width and height for a rectangle, or full major and minor axes for an existing flat oval.
For conversion to a noncircular section set the selected rectangle aspect ratio or fixed flat-oval inside minor axis. Compare the reported actual area with the chosen equivalent diameter before selecting an available product.

Calculation method and applicability

Equal area: D = √(4A/π). Rectangular equal friction: De = 1.30(WH)^0.625/(W+H)^0.25. Flat-oval equal friction: De = 1.55A^0.625/P^0.25, A = πb²/4 + b(a−b), P = πb + 2(a−b). Hydraulic diameter: Dh = 4A/P.

D = equal-area round diameter; De = equal-friction round diameter; Dh = hydraulic diameter. W/H and a/b are the rectangular and oval full dimensions. A = section area and P = wetted perimeter. Use consistent length units within each shape relation; the form dimensions are inches.

Input definitions and units

Shape and conversion basis: Equal-area geometry preserves cross-sectional area. The equal-friction correlations match straight-duct friction per length at equal airflow; these are different results. Choices: Round → rectangular: equal area; Rectangular → round: equal area; Round → rectangular: equal friction; Rectangular → round: equal friction; Round → flat oval: equal area; Flat oval → round: equal area; Round → flat oval: equal friction; Flat oval → round: equal friction.
Inside round diameter (in): Clear inside diameter. Applies to Shape and conversion basis: Round → rectangular: equal area.
Selected rectangle aspect ratio (:1): Width divided by height. Applies to Shape and conversion basis: Round → rectangular: equal area.
Inside rectangular width (in): Clear inside width. Applies to Shape and conversion basis: Rectangular → round: equal area.
Inside rectangular height (in): Clear inside height. Applies to Shape and conversion basis: Rectangular → round: equal area.
Inside round diameter (in): Equivalent round diameter for the selected equal-friction relationship. Applies to Shape and conversion basis: Round → rectangular: equal friction.
Selected rectangle aspect ratio (:1): Width divided by height. The result is theoretical, not a nominal stock size. Applies to Shape and conversion basis: Round → rectangular: equal friction.
Inside rectangular width (in): Clear inside width, excluding liner thickness. Applies to Shape and conversion basis: Rectangular → round: equal friction.
Inside rectangular height (in): Clear inside height. Either side may be longer. Applies to Shape and conversion basis: Rectangular → round: equal friction.
Inside round diameter (in): The target round cross-sectional area will be preserved. Applies to Shape and conversion basis: Round → flat oval: equal area.
Fixed flat-oval inside minor axis (in): Diameter of the two semicircular ends. The calculated major axis must be at least this large. Applies to Shape and conversion basis: Round → flat oval: equal area.
Flat-oval inside major axis (in): Overall long dimension of two straight sides joined by semicircular ends, not an ellipse. Applies to Shape and conversion basis: Flat oval → round: equal area.
Flat-oval inside minor axis (in): Diameter of the semicircular ends; cannot exceed the major axis. Applies to Shape and conversion basis: Flat oval → round: equal area.
Equivalent round diameter (in): The flat-oval major axis is solved from the selected ASHRAE equal-friction correlation. Applies to Shape and conversion basis: Round → flat oval: equal friction.
Fixed flat-oval inside minor axis (in): A feasible major axis must be at least the minor axis. The empirical correlation has a small rounding difference at a circular section. Applies to Shape and conversion basis: Round → flat oval: equal friction.
Flat-oval inside major axis (in): Overall long inside dimension; two straight sides with semicircular ends. Applies to Shape and conversion basis: Flat oval → round: equal friction.
Flat-oval inside minor axis (in): Diameter of the semicircular ends; cannot exceed the major axis. Applies to Shape and conversion basis: Flat oval → round: equal friction.

How to interpret the result

Retain the selected conversion basis beside the dimensions. Equal-area, equal-friction and hydraulic diameters answer different questions and cannot be treated as interchangeable nominal sizes.

Worked examples

Round → rectangular: equal area

Inputs: 10 in round, selected rectangle aspect 2:1.

Calculation: Preserve the 78.54 in² circle area and apply the 2:1 ratio.

Result: About 12.5 × 6.3 in equal-area rectangle.

Rectangular → round: equal area

Inputs: 12 × 8 in rectangle.

Calculation: Equivalent circle diameter √(4×96/π).

Result: About 11.1 in equal-area round diameter.

Round → rectangular: equal friction

Inputs: 16 in equivalent round diameter; selected rectangular width:height ratio 1.5:1.

Calculation: With W=rH, invert Equation 25: H = De/[1.30r^0.625/(r+1)^0.25], then W=rH.

Result: 18.018 × 12.012 in theoretical rectangular section; De=16 in.

Rectangular → round: equal friction

Inputs: 28 × 14 in rectangular duct from ASHRAE Chapter 21 Table 9.

Calculation: Use Equation 25 with the clear inside dimensions.

Result: 21.327 in equivalent round diameter, matching the table’s rounded 21.3 in. Hydraulic diameter is a separate 18.667 in.

Round → flat oval: equal area

Inputs: 16 in round duct; fixed flat-oval minor axis 12 in.

Calculation: Set πD²/4 = πb²/4 + b(a−b), then solve a.

Result: Major axis 19.330 in; minor axis 12 in. This preserves area.

Flat oval → round: equal area

Inputs: 18 × 12 in flat oval with semicircular ends.

Calculation: A = π12²/4 + 12(18−12) = 185.097 in²; equal-area D = √(4A/π).

Result: Equal-area diameter 15.352 in; the separate equal-friction diameter is 15.254 in.

Round → flat oval: equal friction

Inputs: 16 in equivalent round diameter; fixed flat-oval minor axis 12 in.

Calculation: Solve Equation 26 for major axis using the flat-oval area and perimeter equations, keeping the major axis at least 12 in.

Result: Major axis 19.662 in; minor axis 12 in; equal-friction De=16 in.

Flat oval → round: equal friction

Inputs: 28 × 14 in flat-oval duct from ASHRAE Chapter 21 Table 9.

Calculation: Area 349.938 in² and perimeter 71.982 in give Equation 26 equivalent diameter.

Result: 20.702 in equivalent round diameter, matching the table’s rounded 20.7 in. Hydraulic diameter is a separate 19.446 in.

Assumptions and limits

Equal-area diameter, equal-friction equivalent diameter and hydraulic diameter serve different purposes. An equal-friction section generally has a different actual area and velocity at the same airflow.
ASHRAE Equations 25 and 26 describe straight-duct equivalence at equal airflow and friction per unit length. They do not model changes in material roughness, flexible-duct compression, fittings, transitions or a complete system.
Flat oval here means two parallel straight sides joined by semicircular ends, not an elliptical section. Major axis must be at least minor axis.
The flat-oval correlation’s rounded coefficient does not give exact geometric circle diameter at equal axes; a 12 × 12 in limiting section gives De≈12.013 in. The inverse checks feasibility against that correlation instead of silently changing its coefficient.
Theoretical outputs are not nominal fabrication sizes. Select an available size and recheck the actual area, velocity, pressure loss and installation constraints. No universal aspect-ratio maximum or material preset is assumed.

FAQs

Which conversion preserves velocity?

Equal area preserves average velocity when airflow is unchanged. Equal friction generally changes actual area, so its velocity needs a separate calculation.

Is a flat oval just a rectangle with rounded corners?

The model uses two semicircular ends joined by straight sides. Enter the full major and minor axes specified by the fields, not a corner radius or the straight-side length.

Sources

ASHRAE 2025 Fundamentals, Chapter 21: Duct DesignDirectly inspected: Equation 24 hydraulic diameter; Equation 25 rectangular equivalence; Equations 26–28 flat-oval equivalence, area and perimeter. Table 9 provides rounded 28 × 14 in comparison cases.
Eastern Sheet Metal: Equivalent Round User GuideManufacturer guide distinguishes equivalent round diameter, actual cross-sectional area and hydraulic diameter; documents rectangular and flat-oval relationships.
Free HVAC Calculators: Rectangular to Round Duct ConverterPeer tool directly observed with rectangular/flat-oval conversion and explicit straight-duct limitations; not the formula authority.

Related calculators

Duct Airflow and Velocity Checker Enter duct dimensions and CFM or air speed to solve for airflow, velocity, or capacity. Duct Size Calculator Use airflow with a velocity or friction target to calculate round or rectangular duct dimensions. Duct Pressure Drop Calculator Enter duct dimensions, airflow, and length to estimate friction and documented fitting pressure losses.

Find a tool.