How to calculate the Reverberation Time (RT60)

(Copyright Arch. Silvano Spandre)
Tutorial with a practical case

Introduction
In other website pages, we have already defined the so-called Reverberation Time (or Reverb), also known as RT60 and expressed in seconds, as the parameter to determine the quality of the acoustic response in any environment.
In other terms, the reverb is partially comparable to the better-known concepts of echo and rumble, a sort of prolonged stay of sounds generated in a closed space.
If the sound length (RT60) is too long (let’s think about a space particularly rumbling), the result is a sense of confusion in which all sounds overlap and become incomprehensible; on the other hand, if the reverberation time is extremely short, sounds are too sharp or muffled, and don’t reach the listener’s ear (this last situation is almost infrequent). In other words, any environment has its own optimal reverberation time according to the specific intended use.
In order to proceed to the acoustic correction of a space, where there is an excessive reverberation time (thunderous space), the operative method is the following one:
A) Definition of the actual Reverberation Time (RT60).
B) Individuation of the optimal Reverberation Time valour according to the specific intended use.
C) Calculation of the quantity and type of sound-absorbing material to install on walls or to the ceiling in order to obtain the expected acoustic benefits.
In other pages of this website, we have already explained that the procedure methodologically most reliable to verify the actual values of the Reverberation Time in a space (previous point A) with a certain precision is the on-site measurement with phonometric tools.

Let’s describe a more empiric method, based on Sabine’s formula, that anyone can adopt for a first evaluation of the necessary acoustic interventions. In case of spaces with simple and uniform surfaces, this empirical calculation may lead to surprising accurate results.

Sabine’s formula
Sabine’s formula is based on the principle of the perfect sound diffusion, and defines the reverberation time according to the following formula:
Sabine’s formula:
T60 = 0,161 * (V/A) with RT60 expressed in seconds
Where (V) is the volume of analysed room expressed in cubic meters and (A) is the total square footage of absorption area expressed in square meters, calculated as follows:
A = ∑ (αi*si), where (si) is the boundary surface area expressed in square meters and (αi) is the absorption value for that boundary area at a specific frequency, generally 1000 Hz. The specific absorption value of a material is generally present in appropriate tables or derived from the certificates of the materials adopted to cover the surfaces of a space.

Practical calculation example on a case study
Let’s suppose to intervene in a space (for example a canteen or a gym), in which the excessive rumble causes a big sense of confusion.
The space is with plan sizes 20 x 8 m and height 4 m.
The analysed space has a volume of 640 cubic meters, a floor and ceiling surface of 160 square meters each, and total wall areas of 224 square meters.
Let’s suppose a floor made of porcelain stoneware (acoustically very reflecting) with a value of α – sound-absorbing coefficient – very low, for example α = 0,02; let’s also suppose walls and ceiling are made of painted plaster (so very reflecting), with a value of α = 0,05.
In order to simplify the calculation, we will not consider the eventual glazed areas (anyway, very reflecting).
The values of α (sound-absorbing coefficients at a specific frequency, generally of 1000 Hz) are available in certificates and technical tables about construction materials.
The first step is the determination of the actual Reverberation Time (RT60), with Sabine’s formula:
T60 = 0,161 * (V/A) with V= 640 cube meters
A = (floor 160 mq * 0,02) + (ceiling 160 mq * 0,05) + (walls 224 mq * 0,05) =22,4
We obtain a value of RT60 equal to 4,6 seconds.
Let’s suppose it is a canteen, so we want to reduce the value of RT60 from the actual 4,6 seconds to 1,8 seconds (for us, this last is a quality value).
We should obtain:
A = (V * 0,161) / T60 = (640 * 0,161) / 1,8 = 57,24
Therefore, we can think about the installation of a sound absorbing material to a ceiling surface of 160 square meters, with a minimum sound absorbing coefficient (at 1000 Hz) α = 0,27.
A = (floor 160 mq * 0,02) + (ceiling 160 mq * 0,27) + (walls 224 mq * 0,05) = 57,6
Appling Sabine’s formula again, we obtain the following result:
T60 = 0,161 * (640/57,6) = 1,78 seconds, as required.