Use termination geometry and sound speed to estimate octave reflection loss and optional outgoing sound power.
Concepts behind this calculation
Estimate uncapped octave-band end reflection for a documented long straight rigid duct termination. Distinguish flush and qualifying free-space conditions, reflected energy and optional outgoing sound power.
End reflection describes the part of incident acoustic power reflected back into a duct at its termination. The model relates frequency, sound speed, termination treatment and effective diameter. For a rectangle, effective diameter is based on equal opening area, not equal friction. Smaller openings and lower frequencies generally produce larger reflection loss in this relation, leaving a smaller fraction of incident power transmitted through the end.
The geometry qualifies the model as well as setting its numeric result. The implemented approach needs more than three effective diameters of straight rigid duct, and free-space treatment needs at least five effective diameters to every reflecting surface. Slots, flexible connections and short or curved approaches need different evidence. Optional outgoing sound power also requires an incident rating that has not already deducted this termination effect.
How to use this calculator
Choose Clear duct shape, complete Termination, sound-speed and model reference, and establish End-reflection model basis and Termination environment.
Enter Clear inside width and height or Clear inside diameter, Speed of sound for the stated air condition and Uninterrupted straight rigid approach length.
For free space, enter Minimum distance to any reflecting surface. Select Incident sound-power spectrum available and enter all eight incident bands only when the source basis supports a further end-reflection deduction.
Review effective diameter, approach and clearance ratios, octave losses and energy fractions; carry optional outgoing power forward without confusing it with receiver pressure.
Calculation method and applicability
De = √(4A/π) for a rectangle; De = clear diameter for a circle. Raw ERL(f) = 10 log10[1 + (a1 c/(π f De))²], with a1 = 0.7 flush or 1 free space. Derived transmitted fraction = 1/(1+x²); reflected fraction = x²/(1+x²). Optional Lw,out = Lw,in − ERL.
De = equal-area opening diameter (ft); c = sound speed (ft/s); f = octave center frequency (Hz); a1 = dimensionless termination factor. ERL is dB and optional Lw levels are dB re 1 pW.
Input definitions and units
Clear duct shape
Circle and area-equivalent rectangular geometry share this page. Use actual clear airway dimensions; do not substitute friction-equivalent diameter. Choices: Rectangular clear opening; Circular clear opening.
Termination, sound-speed and model reference
Identify actual rigid termination, surrounding surfaces, uninterrupted straight approach, source of air sound speed and model applicability. For optional Lw, record its rating basis to avoid deducting end reflection twice.
End-reflection model basis
This estimate excludes flexible connections, slot devices and short/curved approaches. Confirm applicable long straight rigid sheet-metal conditions and compatible source data. A confirmation does not certify an installation. Choices: Not established; Applicable rigid straight termination and source basis established.
Termination environment
Choose the actual ASHRAE application environment. Ordinary blade diffusers/grilles use the flush treatment only when its documented model applies. Do not infer free space from a ceiling-plenum location. Choices: Flush with reflecting surface / applicable blade-type termination; Open free space, at least 5 effective diameters from any surface.
Clear inside width (in)
Clear airway at termination, not outside sheet-metal or nominal fitting dimension. Slot/high-aspect terminal devices require a different model. Applies to Clear duct shape: Rectangular clear opening.
Clear inside height (in)
Clear airway at termination, not outside sheet-metal or nominal fitting dimension. Slot/high-aspect terminal devices require a different model. Applies to Clear duct shape: Rectangular clear opening.
Clear inside diameter (in)
Actual circular airway at termination, excluding any liner. Applies to Clear duct shape: Circular clear opening.
Speed of sound for the stated air condition (ft/s)
Enter the applicable speed from a documented air-state basis. This illustrative Titus value is not an automatic standard-air constant or a weather/temperature lookup.
Uninterrupted straight rigid approach length (ft)
Immediately before the termination; must exceed 3 effective diameters for this bounded long-straight model. Short or curved approaches are withheld.
Minimum distance to any reflecting surface (ft)
Include wall, floor, ceiling and other reflecting planes. The selected ASHRAE application gate requires at least 5 effective diameters; AMCA laboratory criteria are different and are not substituted. Applies to Termination environment: Open free space, at least 5 effective diameters from any surface.
Incident sound-power spectrum available?
Geometry alone gives ERL and derived energy fractions. Add only a complete compatible unweighted incident Lw spectrum to estimate power transmitted through this termination. Choices: No — calculate ERL and energy fractions only; Yes — add all eight compatible incident Lw bands.
Incident sound power at 63 Hz (dB re 1 pW)
One source at the same termination and operating state. Receiver Lp, NC and overall dBA are different quantities. Missing bands are not zero; numeric support −100 to 200 dB does not state instrument accuracy. Applies to Incident sound-power spectrum available?: Yes — add all eight compatible incident Lw bands.
Incident sound power at 125 Hz (dB re 1 pW)
One source at the same termination and operating state. Receiver Lp, NC and overall dBA are different quantities. Missing bands are not zero; numeric support −100 to 200 dB does not state instrument accuracy. Applies to Incident sound-power spectrum available?: Yes — add all eight compatible incident Lw bands.
Incident sound power at 250 Hz (dB re 1 pW)
One source at the same termination and operating state. Receiver Lp, NC and overall dBA are different quantities. Missing bands are not zero; numeric support −100 to 200 dB does not state instrument accuracy. Applies to Incident sound-power spectrum available?: Yes — add all eight compatible incident Lw bands.
Incident sound power at 500 Hz (dB re 1 pW)
One source at the same termination and operating state. Receiver Lp, NC and overall dBA are different quantities. Missing bands are not zero; numeric support −100 to 200 dB does not state instrument accuracy. Applies to Incident sound-power spectrum available?: Yes — add all eight compatible incident Lw bands.
Incident sound power at 1,000 Hz (dB re 1 pW)
One source at the same termination and operating state. Receiver Lp, NC and overall dBA are different quantities. Missing bands are not zero; numeric support −100 to 200 dB does not state instrument accuracy. Applies to Incident sound-power spectrum available?: Yes — add all eight compatible incident Lw bands.
Incident sound power at 2,000 Hz (dB re 1 pW)
One source at the same termination and operating state. Receiver Lp, NC and overall dBA are different quantities. Missing bands are not zero; numeric support −100 to 200 dB does not state instrument accuracy. Applies to Incident sound-power spectrum available?: Yes — add all eight compatible incident Lw bands.
Incident sound power at 4,000 Hz (dB re 1 pW)
One source at the same termination and operating state. Receiver Lp, NC and overall dBA are different quantities. Missing bands are not zero; numeric support −100 to 200 dB does not state instrument accuracy. Applies to Incident sound-power spectrum available?: Yes — add all eight compatible incident Lw bands.
Incident sound power at 8,000 Hz (dB re 1 pW)
One source at the same termination and operating state. Receiver Lp, NC and overall dBA are different quantities. Missing bands are not zero; numeric support −100 to 200 dB does not state instrument accuracy. Applies to Incident sound-power spectrum available?: Yes — add all eight compatible incident Lw bands.
How to interpret the result
Read reflection loss and transmitted/reflected percentages as model power quantities. Optional outgoing octave sound power is still a source-path quantity, not room sound pressure. Retain the qualification ratios and large-loss flags when continuing the acoustic analysis.
Worked examples
Rectangular clear opening
Inputs: Titus source geometry/speed: 15 × 12 in clear rectangle, air sound speed 1128 ft/s, flush treatment. A 10 ft straight approach and incident octave Lw of 80, 75, 70, 65, 60, 55, 50, 45 dB re 1 pW are constructed additions.
Calculation: Area = 1.25 ft²; De = √(5/π) = 1.261566261 ft. Use a1 = 0.7 and exponent 2. At 125 Hz, the uncapped formula gives 5.490324363 dB; transmitted power fraction is 1/[1 + (0.7 × 1128/(π × 125 × De))²].
Result: Raw ERL at 125 Hz is 5.490324363 dB, rounding to the Titus printed 5 dB. With constructed incident 75 dB, outgoing Lw is 69.509675637 dB re 1 pW. All eight model bands are shown; this is not room Lp.
Circular clear opening
Inputs: Constructed circular example: 12 in clear diameter, 1128 ft/s, flush treatment and 10 ft uninterrupted straight approach; the same complete incident teaching spectrum.
Calculation: De = 1 ft and area = π/4 ft². Apply the same model, with a1 = 0.7. At 125 Hz, ERL = 7.026815657 dB.
Result: 7.026815657 dB raw ERL at 125 Hz; outgoing teaching Lw = 67.973184343 dB re 1 pW. A switch to free space requires an actual entered clearance, not hidden example data.
Assumptions and limits
Named ASHRAE 2023 Chapter 49 Equation 12 simplified application model, not complete system or current-code certification. Pink-spectrum octave constants are used; this is not an exact broadband/tonal filter or arbitrary termination simulation.
This bounded implementation requires more than 3 effective diameters of uninterrupted straight rigid duct. Free-space selection additionally requires at least 5 effective diameters from any reflecting surface. AMCA 300-24 laboratory setup rules are different and are not mixed into the selected application gate.
Blade-type terminals follow flush treatment only where the documented source model applies. Slot/high-aspect devices, flexible connections, short/curved approaches and unknown configurations require separate data; no zero-loss default is inserted for them.
Raw ERL greater than 20 dB is flagged because it is difficult to confirm in practice. Results are not automatically capped at 14 dB or added to a laboratory rating; such correction depends on the actual applicable test/rating standard.
Effective diameter is equal-area acoustic geometry, not hydraulic or equal-friction diameter. Use actual clear airway and a documented speed of sound, not nominal outside sizes or an assumed universal air state.
The optional spectrum must be compatible incident unweighted Lw re 1 pW at this termination. Understand prior rating/measurement end corrections so this effect is not deducted twice. Missing bands cannot be replaced by 0 dB or overall dBA/NC/Lp.
Energy fractions and outgoing Lw are explicit model derivations, not measured coefficients or receiver sound pressure. Other duct/liner losses, regenerated noise, breakout, correlated sources and room transfer remain separate. Negative valid outgoing levels are preserved.
FAQs
Is an outlet in a ceiling plenum automatically a free-space termination?
No. Establish its minimum distance to all reflecting surfaces, including ceiling, floor and walls, and verify the actual termination model. A location label does not establish the required geometric clearance.
Should I cap a raw reflection loss above 20 dB or subtract it from a catalog rating automatically?
The tool preserves raw values and flags the difficulty of confirming large losses. A cap or rating correction depends on the actual source and rating method; first determine whether the supplied sound power already includes the outlet effect.
Sources
ASHRAE 2023 HVAC Applications, Chapter 49: Duct End Reflection LossEquations 11 and 12, flush/free-space coefficients, pink octave-band context, greater-than-20 dB caveat, long-straight and flexible/slot termination limits. This tool uses the application model, not the laboratory selection rules of another standard.
Titus Engineering: end-reflection example (2012)15 × 12 in and 1128 ft/s example prints six rounded ERLs at 125–4000 Hz. These rounded values are independently reproduced. Its printed De unit ft² is dimensionally a typo; this tool reports De in ft. The historical 14 dB rating-correction context is not automatically applied to raw application estimates.
Strutt: Duct End/Grille elementActual acoustic software documentation supports the separate end-reflection workflow and distinguishes open/blade/slot/flex conditions. No paid plugin execution or numeric parity claim.
AMCA 300-24, Annex EOriginal laboratory standard corroborates the equation form but uses its own surface-distance/wavelength conditions and add-back correction. It is context only; this tool does not implement or certify that test procedure.
