How to Calculate Reverb Time and Required Surface Area Absorption

Managing reverb is essential in almost all spaces. From classrooms to boardrooms, offices to hospitals, echoes and noise can cause serious problems.

Very simply, reverberation is reflections of sound. When sound is emitted from a source it usually moves outwards omnidirectionally until it meets reflective surfaces. Where too many reflections occur, an uncomfortable environment is created. This is when acoustic treatment is needed to absorb some of the sound waves from the surfaces to reduce the number of waves being reflected.
Reverb is measured in Seconds: RT followed by a number (usually 60) shows the length of time in seconds for the measured sound to drop by x number of decibels. It is usually represented as RT60

To calculate reverb time we need to know the following facts about a space.

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Volume: The volume of the room (lwh) is used in the calculation

Absorbing surfaces and the areas of these: The contents of the room and what they are made of. This is important as different materials absorb different amounts of sound which affects reverb times. Carpet, for example, absorbs a lot more sound than a concrete floor.

Co-efficient values for the surface materials: Each material has a relating co-efficient (referred to as NRC), between 0 and 1. A coefficient of 1 shows that 100% of sound that hits the surface will be absorbed and 0% will be reflected. An NRC of 0.4 shows that 40% of sound will be absorbed and 60% reflected

We also need:

K- a constant for the formula. Where calculating the reverb time using measurements of metres, this value is 0.1611

The formula used to calculate the reverb time below is the end result of other formulas which do not need to be looked at here.

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Sabine’s Formula

 

 

 

 

 

 

 

 

 

An example of calculating reverb time.

Key pieces of information

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  • We have a room which measures 5 metres in length, 2.7m in height and has a width of 3.4m
  • The floor is carpet, the ceiling and walls are plasterboard. There is a wooden door which measures 1.5 x 2m and a glass window on one of the walls measuring 2x1m.
  • The room is going to be used for video conferencing

Once the required information is collated it is possible to input some of the numbers into the formula.

We know that K=0.1611 and we can calculate the volume of the room easily to be 45.90m3

To calculate the surface absorption we need to use an NRC (see appendix for a more detailed list). For this calculation we will use the following NRC ratings

For this calculation we will use the following NRC ratings

Plasterboard 0.02
Glass 0.03
Wood 0.04
Carpet 0.40

We need to calculate the area of each material:

Plasterboard* 57.36m2
Glass 2m2
Wood 3m2
Carpet 17m2

 

Ceiling 17m2
Wall 1 13.50m2
Wall 2 13.50m2
Wall 3 9.18m2
Wall 4 9.18m2
Minus Glass 2m2
Minus Door 3m2
57.36m2

 

Sa calculation:

Plasterboard = 57.36 x 0.02 1.15
Glass = 2 x 0.03 0.06
Wood = 3 x 0.04 0.12
Carpet = 17 x 0.40 6.80
Sum 8.13m2

 

We can now plug this number into the formula and complete the calculation:

 

 

 

 

 

 

 

 

This shows that the current reverb time in the room is 0.91 seconds.

The client’s acoustician has requested a reverb time of 0.5s to give extra protection against noise levels during video calls

To calculate how much treatment is needed for the space, we now need to work out Sa as the subject of the formula with the reverb time being a known number at 0.50s.

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The formula is therefore rearranged as follows:

 

 

 

 

 

 

 

 

This shows us the total absorption required for achieve a reverb time of 0.50s is 14.78m2. As we already have 8.13m2 in the room (used in the reverb time calculation) we can calculate that the required acoustic treatment would need to be 14.78-8.13=6.65m2 of absorption.

Treatment

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It is important to know that the square metre number for this calculation is used to describe the required amount of absorption area at an NRC of 1.

If an acoustic product has an NRC of 0.40 we need to increase the number of panels accordingly. To do this we would divide the required square meterage by the NRC of the product. For example, in this example we would divide 6.65 by 0.4 showing us that we would need 16.63m2 of this acoustic product

Acoustic treatments come in many shapes and sizes, are made from different materials and offer different levels of absorption. Below is a table with a brief overview of the standard types.

Treatment Area Materials NRC Product Examples
Walls PET 0.40 Autex Cube

AllSfär Panels

Walls Glass Wool 0.50 – 1 Ecophon Solo
Walls Fabric Wrapped Panels 0.50- 1 Autex Quietspace
Walls Wood Wool 0.40-0.75 BAUX
Ceiling Glass Wool 0.50 – 1 Ecophon Solo
Ceiling PET 0.40-0.75 Autex Frontier

Autex Horizon

 

Some acoustic products require specialist installation knowledge, whereas most fabric wrapped acoustic panels are relatively simple to install, are light weight and are often available with a peel-and-stick backing making DIY acoustic panel installation easy and efficient on time.

Appendix:

Material NRC.

The NRC (noise reduction co-efficient) is the average sound absorption across the frequency bands , 250, 500, 1000, 2000Hz.

This table provides a brief overview of the most commonly used materials we come across when dealing with interior acoustics.

Material NRC
Walls, hard surfaces average 0.03
(brick walls, plaster, hard floors, etc.)
Walls, rendered brickwork 0.03
Rough concrete 0.03
Smooth unpainted concrete 0.02
Rough lime wash 0.04
Smooth brickwork with flush pointing, 0.02
painted
Smooth brickwork, 10 mm deep 0.15
pointing, pit sand mortar
Brick wall, stuccoed with a rough finish 0.04
Ceramic tiles with a smooth surface 0.02
Limestone walls 0.04
Reverberation chamber walls 0.02
Concrete floor 0.03
Marble floor 0.02
Lightweight constructions and linings
Material
2 * 13 mm plasterboard on steel frame, 0.06
50 mm mineral wool in cavity, surface
painted
Wooden lining, 12 mm fixed on frame 0.18
Glazing
Material
Single pane of glass, 3 mm 0.03
Glass window, 0.68 kg/m2 0.04
Lead glazing 0.12
Double glazing, 2-3 mm glass, 0.03
> 30 mm gap
Double glazing, 2-3 mm glass, 0.04
10 mm gap
Double glazing, lead on the inside 0.16
Wood
Material
Wood, 1.6 cm thick, 0.10
on 4 cm wooden planks
Thin plywood panelling 0.11
16 mm wood on 40 mm studs 0.10
Audience floor, 2 layers, 0.05
33 mm on sleepers over concrete
Wood, stage floor, 2 layers, 0.06
27 mm over airspace
Solid wooden door 0.09
Floor coverings
Material
Linoleum, asphalt, rubber, 0.03
or cork tile on concrete
Cotton carpet 0.57
Loop pile tufted carpet, 1.4 kg/m2, 0.59
9.5 mm pile height: On hair pad,
3.0 kg/m2
Thin carpet, cemented to concrete 0.17
6 mm pile carpet bonded to 0.25
closed-cell foam underlay
306 Annex
Floor coverings (cont’d)
Material
6 mm pile carpet bonded to open-cell 0.38
foam underlay
9 mm tufted pile carpet on felt underlay 0.43
Needle felt 5 mm stuck to concrete 0.13
10 mm soft carpet on concrete 0.21
Hairy carpet on 3 mm felt 0.30
5 mm rubber carpet on concrete 0.09
Carpet 1.35 kg/m2, on hair felt 0.55
or foam rubber
Cocos fibre roll felt, 29 mm thick 0.29
(unstressed), reverse side clad
with paper, 2.2 kg/m2, 2 Rayl