Reverberation Time Calculator

If you are interested in room acoustics, you should definitely give this reverberation time calculator a try. You can use it to define one of the most critical acoustical characteristics of any enclosed space: the reverberation time, which describes how sound is reflected and propagates in a room.

This article will give you an overview of how sound behaves in enclosed spaces and provide you with a handy RT60 equation (also known as the reverberation time formula). We will also give you examples of optimum reverberation times in rooms with various purposes.

To use the reverberation time calculator, follow these easy steps:

1. Enter the room's dimensions — length, width, and height.

2. Enter the dimensions and the number of any doors in the room.

3. Do the same for any windows in the room.

4. If you want to fine-tune the absorption coefficients of the room's surfaces (including the doors and windows), you can expand the reverberation time calculator's absorption coefficients section to do so.

5. The reverberation time calculator will show you the room's reverberation time.

Every sound is nothing but a wave propagating in space — either in the air or a different medium. When a sound wave is generated in a room, it travels forward until it reaches an obstacle. Every boundary of the room, such as the wall, the ceiling, or the window, is an obstacle to the sound wave.

Once the wave comes in contact with the obstacle, two things happen. Firstly, a part of the wave energy gets absorbed by the barrier, usually resulting in an exchange of heat. Secondly, the remaining portion of the wave gets reflected from the obstacle and begins to travel in an opposite direction.

After some time, the sound gets reflected so many times that most of the energy becomes absorbed. As this happens, the sound pressure level (SPL) decreases (see dB calculator). The time between sound emission and the moment when the drop in SPL reaches 60 dB is called the reverberation time.

There are two ways to measure the reverberation time. The first one is to use a dedicated device — a level recorder that can plot the SPL against time. The other way is to calculate it based on the parameters of the given room.

The RT60 equation is an empirically found formula that establishes the relation between the reverberation time and the absorptive properties of the room. It can be written as

where:

• $\text{RT60}$ – Reverberation time;
• $V$ – Total volume of the room, expressed in $\text{m}^3$; and
• $A$ – Effective absorbing area of the room, given in $\text{m}^2$.

As you probably noticed, the RT60 equation looks deceptively simple. All you have to do is divide the volume of the room by its area and multiply it by a known coefficient. If you give the formula another look, though, you will discover that, in reality, it is much more complicated.

The main idea behind the reverberation time formula is applying the effective absorbing area instead of the regular room surface area. This number can be calculated according to the following equation:

where:

• $S_i$ – Area of a specific part of the room's surface; and
• $\alpha_i$ – Absorption coefficient of that surface.

The absorption coefficient describes what fraction of a sound wave's energy gets absorbed by the obstacle. It can have a value between 0 and 1.

• $\alpha = 0$ means that no sound is absorbed, and it's all reflected — an acoustic equivalent of a mirror.
• $\alpha = 1$ means that no sound is reflected — this would happen if you opened the window, for example.

Our reverberation time calculator can determine the effective absorbing area of any room with a regular cuboid shape. If you expand the absorption coefficients section at the bottom, you will be able to customize the absorption coefficients of all room elements: walls, the ceiling, the floor, doors, and windows.

The optimum reverberation time depends on the room's intended use. If the reverberation time is too low, the sound will appear "flat" without the richness and fullness that music should have. On the other hand, higher reverberation times result in a perceived loss of articulation and increased difficulties when trying to understand speech.

You can use the formulas below to estimate the optimum reverberation time for different purposes. $V$ is again the room's volume.

• Communication:
  $T = 0.32 \log V - 0.17$

• Speech:
  $T = 0.37 \log V - 0.14$

• Music performance:
  $T = 0.45 \log V + 0.07$

• Music rehearsal:
  $T = 0.47 \log V - 0.37$

In general, high reverberation times are perfect for large music halls. Low times are preferable for lecture halls or recording studios. If there is no reverberation whatsoever, the sound levels are subject to the inverse square law (see distance attenuation calculator).