Duct Transition (Reducer) Length from Slope
The length a duct size change needs to hold a target transition slope.
Example
You enter
- Large end dimension (in) 20
- Small end dimension (in) 12
- Transition slope (deg per side) 15
You get
- Concentric length 14.93 in
- Eccentric (one flat side) length 29.86 in
Details, formula, and sources
Concentric length = ((large - small)/2) / tan(slope), eccentric (one flat side) = (large - small) / tan(slope). SMACNA keeps the slope near 15 degrees per side (about a 4:1 run-to-offset ratio) to limit turbulence and pressure loss. A 20 in to 12 in concentric transition at 15 degrees is 14.93 in long; the same change eccentric (all on one side) needs 29.86 in; a steeper slope is shorter but noisier and higher-drop. On a rectangular duct the larger of the width and height changes sets the piece length. The SMACNA duct-construction standards and the system pressure loss govern.
concentric length = ((large_dim_in - small_dim_in) / 2) / tan(slope_deg); eccentric (one flat side) length = (large_dim_in - small_dim_in) / tan(slope_deg); run-to-offset ratio = 1 / tan(slope_deg).
Duct transition (reducer) length geometry, first-principles; SMACNA HVAC Duct Construction Standards keep the slope shallow to limit turbulence.
The transition length is a first-principles trigonometric identity (offset / tan slope); the end dimensions and the target slope come from the layout and the SMACNA standard.
Estimate. AHJ and licensed professional govern.
Field names used by the API: large_dim_in, small_dim_in, slope_deg, length_concentric_in, length_eccentric_in
- Slope per side SMACNA ~15 degrees per side (about 4:1); steeper is shorter but higher pressure lossSMACNA HVAC Duct Construction Standards
- Concentric vs eccentric concentric splits the change both sides; eccentric takes it on one side and needs twice the lengthsheet-metal layout