Carpet Pile Density to Acoustic Absorption & Reverberation

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 10 inputs are read from the form on every keystroke: Pile Weight, Pile Height, Underlay Thickness, Fitted NRC Coefficient (a), Underlay Factor (b), NRC Ceiling, Carpeted Floor Area, Room Volume, Absorption of Everything Else and Bare Floor Absorption.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Estimated NRC together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Pile Bulk Density, Absorption Added, Reverberation Time (carpeted), Reverberation Time (bare) and Steady-State Noise Reduction — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

The tool loads with this case already solved — the Estimated NRC shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.

How to use it

1. Work through the input groups in order — Carpet Construction and Room. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Estimated NRC in the dark results panel — that is the headline figure, expressed in α.
4. Check the supporting rows underneath (Pile Bulk Density, Absorption Added, Reverberation Time (carpeted), Reverberation Time (bare) and Steady-State Noise Reduction) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing Estimated NRC before a trial is booked, so machine time and material in Carpet & Floor Coverings are committed against a calculated figure rather than an estimate.
• Costing and quotation — Estimated NRC is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Pile Weight) shows how much of the gap in Estimated NRC each variable explains.
• Teaching and study — the accepted ranges bracket normal Carpet & Floor Coverings practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• The NRC half is a regression, not physics: it was fitted over ordinary cut-pile carpet between roughly 4 and 15 mm and will mislead outside that, and it says nothing about the frequency shape — carpet absorbs the top of the band well and does almost nothing below 250 Hz, which is exactly where most room complaints live. Sabine also assumes a diffuse field and breaks down in rooms that are very dead or very long. Specify from measured ASTM C423 data when the number has to hold up; use this to decide whether a test is worth running.
• Every input is bounded to the range normal practice occupies (Pile Weight 150 to 3000 g/m², Pile Height 2 to 30 mm and Underlay Thickness 0 to 25 mm, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Questions people ask