# Reverberation time and Sabine’s Formula

The most accurate method to define the Reverberation Time (T60) into a room, is the measurement on site with technical instruments.

Anyway, it is possible to estimate the T60 value using the empiric method based on the *Sabine’s Formula*, getting pretty accurate evaluations.

For example, for simple spaces, with regular shapes, the Sabine Formula let you get accurate evaluation and reliable results.

__Sabine’s Formula__

This method is based on the principle of diffuse acoustic field and let you evaluate the reverberation time thanks to the formula below:

*Sabine’s Formula : T60*** = 0,161 * (V/A)**

In this formula, the value of *T60* is expressed in seconds, *V* indicates the volume of the analyzed room (expressed in m^{3}), and* A* is the equivalent absorption surface (expressed in m^{2}).

The equivalent absorption surface (*A*) is calculated with the formula below:

*A*= ∑(*α**i*si)*

In this formula, *si* represents the absorbing areas and *α**i *is the sound absorbing coefficients of these surfaces, for specific frequencies (usually 500 or 1000 Hz).

The sound absorbing coefficient is a characteristic of any surface and generally it is specified in the technical sheets or certifications of construction materials.

**Case study: How to calculate the Reverberation Time (T60)**

** **

We have to intervene into a canteen where the reverberation is too high and generates confusion.

The dimensions of the space are 20 x 8 m and 4 m high: the total volume is 640 m^{3}, the floor surface is 160 m^{2}, the ceiling area is 160 m^{2} and the walls are 224 m^{2}.

The floor is made of porcelain tiles, a material generally used into public environment because its resistance qualities, but, from an acoustic point of view, very reflective: the sound absorption coefficient is about α = 0,02.

The walls and the ceiling are finished with painted plaster, then the sound absorption coefficient is about α = 0,05.

To simplify the calculation, we will not consider the glass surfaces of windows or doors.

We remind that it is possible to find the sound absorption coefficient (α) of a material, from the technical sheets or certifications of construction materials, considering as frequencies 1000 Hz.

- The first step is the definition of the starting Reverberation Time (T60) using the Sabine’s Formula:

T60 = 0,161 x (V/A)

V = 640 m^{3}

A = (floor: 160 m^{2} x 0,02) + (ceiling: 160 m^{2} x 0,05) + (walls: 224 m^{2} x 0,05) =22,4 m^{2}

According to these values the **T60** will be **4,6 seconds**.

- Considering the intended use of this place as a canteen, we know that the T60 has to be reduced, to get a good level of acoustic comfort, from 4,6 seconds to around 1/1,2 seconds.

Now we will consider to install on the ceiling and on the wall around 90 m^{2} of sound absorbing surface with a value of α (sound absorption coefficient) as 0,8:

A = 22,4 + (90 x 0,8) = 94,4

- Using this value of equivalent absorption surface (A) we will calculate the obtained Reverberation time using the Sabine’s Formula:

T60 =0,161 x 640 / 94,4 = **1,09 seconds**

Installing 90 m^{2 }of sound absorbing panels with α = o,8 it is possible to reduce the Reverberation time from 4,6 seconds to 1,09 seconds and in doing so, we have greatly improved the acoustic comfort of the diners in the canteen.