Calculating reverberation time: the principle of the acoustically open window
8 min read
In our last article Improve room acoustics we looked at why rooms reverberate and what can be done about it. But one question remains, and it is crucial to every acoustic design: How much sound absorption does a room actually need to become quiet? And how can you know before the first bag of plaster is even mixed? The answer lies in a surprisingly simple concept: the acoustically open window. With this concept and a single equation, the reverberation time can be calculated.
The open window as the perfect sound absorber
When sound hits a surface, part of it is reflected and part of it is absorbed. The proportion that is absorbed is described by the sound absorption coefficient α:
- α = 0: All of the sound is reflected. Example: a closed window or a hard, smooth wall.
- α = 1: All of the sound is absorbed; nothing is reflected back. Example: an open window, where the sound simply escapes outside.
Real materials usually fall somewhere between 0.2 and 0.8, and the value depends on frequency. An open window therefore represents the theoretical ideal: one hundred percent absorption. That is exactly why it works so well as a reference for everything else.
Equivalent absorption area: converting everything into an open window
A real room contains many surfaces with very different α values: floor, walls, ceiling and furniture. Instead of looking at each surface individually, they are combined into one value: the equivalent sound absorption area A. Imagine that all of the room’s sound absorption is concentrated into a single, fully absorbing surface: an open window of a certain size, measured in square metres.
This is how the calculation works surface by surface (simplified example):
Important: These 15.6 m² A o.F. represent an “acoustically open window” – a theoretical calculation value, not a real window area. It simply means that the room as a whole absorbs as much sound as an open window measuring 15.6 m². (Here, the everyday term “absorption value” refers to the sound absorption coefficient α described above.)
Typical absorption values as a guide
The following figures are rounded reference values from specialist literature (mid frequencies, around 500 to 1000 Hz) and are provided without guarantee. The actual value depends on the material, thickness, construction, distance from the wall and frequency, and is measured in a reverberation chamber. Surfaces are described by their sound absorption coefficient α (per m²), while individual objects and people are assigned a fixed A o.F. area per item.
A single person therefore contributes roughly 0.3 to 0.5 m² A o.F. , so a fully occupied room is noticeably quieter than the same room when empty. (In the Sabine formula below, the same quantity is simply called A.)
The larger the A o.F., the more “open window” the room has – and the shorter the reverberation.
The Sabine formula: reverberation in one equation
The relationship between a room and its reverberation can be expressed in a surprisingly short formula:
Where T is the reverberation time in seconds (the time it takes for the sound level to fall by 60 dB), V is the room volume in cubic metres and A is the equivalent absorption area in square metres. The formula goes back to physicist Wallace Clement Sabine (1868–1919), who discovered the relationship around 1898 and determined the factor 0.163 experimentally. The reason was very practical: Sabine, then a young physicist at Harvard, was asked to solve the notorious reverberation problem in the lecture hall of the new Fogg Museum, where speakers were barely intelligible because of the excessive echo. That practical problem ultimately gave rise to the science of room acoustics.
What the formula tells us is intuitive: more volume means longer reverberation; more absorption area means shorter reverberation. To halve the reverberation time, the absorption area must be doubled. That is exactly what makes the formula so useful: the required area can be calculated instead of guessed.
Calculation example: an open-plan kitchen and living area
Take an open-plan kitchen and living area measuring 6 × 5 metres with a ceiling height of 2.7 metres. This gives a volume of around 81 m³. With hard finishes such as tiles, a glass façade and exposed concrete, the reverberation time can quickly climb above one second, making the room feel restless. A more comfortable target would be around 0.6 seconds.
How much absorption area is required to achieve that? We rearrange the formula to solve for A:
The room therefore needs around 22 m² A o.F. Translating that into acoustic plaster: if the surface achieves a broadband sound absorption coefficient of approximately α ≈ 0.7, the actual plaster area required is:
The ceiling of this open-plan kitchen and living area measures 6 m × 5 m = 30 m². If the entire ceiling is plastered, it practically covers the full required area and brings the reverberation time down to around 0.6 seconds. No visible technology, no panel grid – just the ceiling itself.
And what if there simply is not enough space for a thicker build-up? That is where DEKOZELL® Flexopanel comes in. It achieves “only” α ≈ 0.5, but requires a build-up of only around 1 cm – no other seamless acoustic system achieves this with so little thickness. A 30 m² ceiling therefore provides 30 m² × 0.5 = 15 m² A o.F., which is well over two thirds of the target. For the remaining 7 m² A o.F., simply include the wall: around 14 m² of wall area is enough. This is one of the advantages of DEKOZELL: because the system can be invisibly repaired and renovated, it can also be used on walls, unlike conventional acoustic plasters. The wall then becomes an additional sound absorber almost naturally.
What the formula does not tell you (yet)
As elegant as it is, the Sabine formula is an approximation. It assumes a uniformly mixed (diffuse) sound field. With very high or unevenly distributed absorption, it becomes less accurate; in such cases, the Eyring formula provides a more precise calculation. In addition, α is frequency-dependent, which is why professional acoustic design considers several frequency bands and, where necessary, includes on-site measurements.
Most importantly, however, it describes broadband reverberation in the mid and high frequencies – precisely the effect that makes speech sound blurred. It does not account for low-frequency booming caused by room modes. These low-frequency resonances depend on the proportions of the room and require genuine low-frequency absorption. How that works, and why thin layers are not enough here, is explained in Improve room acoustics.
From the calculated value to an invisible surface
This is where the calculation becomes practical: every square metre with a high α provides a large amount of “equivalent window area” and therefore directly reduces the reverberation time. The DEKOZELL® ACOUSTIC PLASTER SUPERSMOOTH provides this absorption across the speech, mid and high-frequency ranges as a smooth, velvety and completely invisible surface. Where very little build-up depth is available, the DEKOZELL® Flexopanel is only around 1 cm thick and can even be used on walls, allowing the wall area to contribute additional sound absorption where required. For low-frequency booming caused by room modes, the DEKOZELL® DISTANCE-Easy acoustic plaster system uses a deep mineral-wool backing. This turns the calculated target value into a surface that, in the end, is simply invisible.
Frequently asked questions
What does a sound absorption coefficient of 1 mean?
It means that the surface absorbs all incident sound and reflects nothing back – acoustically, it behaves like an open window. Real materials usually fall between 0.2 and 0.8. Good acoustic plasters achieve around 0.7 across a broad frequency range; a very thin system such as Flexopanel reaches around 0.5 and simply requires a little more surface area. Values around 0.9 are excellent.
How accurate is the Sabine formula?
It is a solid approximation for planning purposes as long as the sound field is reasonably diffuse. With very high or unevenly distributed absorption, it becomes less accurate, in which case the Eyring formula is used. Because α depends on frequency, demanding projects are calculated separately for each frequency band and verified with measurements at the end.
What reverberation time should I aim for?
That depends on how the room is used. For living spaces and open-plan kitchen and living areas, around 0.5 to 0.8 seconds generally feels calm while speech remains easy to understand. Concert halls may deliberately have a longer reverberation time. More important than the exact figure is the experience: conversations should feel effortless.
Does a large absorption area also help with bass booming?
Only to a limited extent. Broadband absorption reduces reverberation in the mid and high frequencies. Low-frequency room modes, on the other hand, are a bass issue and depend on the room geometry. They require sensible room proportions and targeted low-frequency absorption, such as a concealed bass absorber like DISTANCE-Easy.
AI tools were used to support the creation of these articles. Content, selection, contextualisation and final editorial review remain the responsibility of Thomas Neubauer.