Acoustic Panel Calculator: Panels for a Target Reverberation Time

What it calculates

For a rectangular room, the calculator uses Sabine's formula to give:

• the room volume and surface area;
• the current reverberation time, estimated from an average absorption coefficient for the existing surfaces;
• the absorption needed to reach the target reverberation time, and the extra absorption beyond what the room already has;
• the number of acoustic panels of the size and coefficient entered;
• the reverberation time achieved with that many panels.

Reverberation time is the time for sound in a room to decay by 60 dB after the source stops, the quantity measured in finished rooms under ISO 3382-2.

Inputs

Room length, width and height are in metres. Height is to the ceiling, or to the soffit if there is no ceiling.

Target reverberation time is in seconds. It is your design input, taken from the project's acoustic brief. The calculator does not choose a target, and the 0.6 s it starts with is only the value used in the worked example.

Panel width and height are in metres.

Panel absorption coefficient or NRC comes from the panel data sheet, for the panel as it will be mounted. Absorption coefficients are measured under ISO 354 or ASTM C423; NRC, defined in ASTM C423, is the average of the coefficients at 250, 500, 1000 and 2000 Hz, rounded to the nearest 0.05.

The assumptions panel holds the average absorption coefficient of the existing room surfaces.

Method

1. Volume V = length × width × height; surface area S = 2 × (L × W + L × H + W × H).
2. Existing absorption A = S × average coefficient of the existing surfaces.
3. Current RT = 0.161 × V ÷ A (Sabine, metric units).
4. Absorption needed = 0.161 × V ÷ target RT; extra absorption = needed − existing, or zero if the room already meets the target.
5. Each panel covers a surface, so it adds (panel coefficient − room coefficient) × panel area.
6. Panels = extra absorption ÷ absorption per panel, rounded up.
7. RT with panels = 0.161 × V ÷ (existing absorption + panels × absorption per panel).

Assumptions

The defaults for the inputs are a 6 × 4 × 3 m room, a target of 0.6 s, and 1.2 × 0.6 m panels with a coefficient of 0.8. They are example values, not recommendations.

Limitations

• Sabine assumes a diffuse sound field. It treats sound as spread evenly through the room. Long, narrow, very low or very irregular rooms, and rooms with all the absorption on one surface, do not behave that way.
• It averages across frequency. One coefficient stands for all frequencies. Real reverberation time differs from band to band, and thin panels absorb little at low frequencies; check the data sheet band by band where low frequencies matter.
• It overstates RT in very absorbent rooms. Where the average coefficient is high, Sabine gives a longer reverberation time than the room will have, so the panel count is on the high side. The calculator warns above an average of 0.3.
• Position is not considered. Panels on parallel walls that face each other, or on the ceiling, behave differently from panels bunched in one place. Placement is part of the acoustic design.
• Air absorption, people and furniture are not modelled separately; fold them into the average coefficient if you include them.
• It says nothing about sound insulation. Panels inside a room do not stop sound passing to the next room; that depends on the partition, the ceiling void and flanking paths.

Worked example

A meeting room 6 × 4 × 3 m with an average existing coefficient of 0.1, a target of 0.6 s from the acoustic brief, and 1.2 × 0.6 m panels with a coefficient of 0.8:

The room needs 17 panels, 12.24 m² in all, which brings the estimated reverberation time from 1.07 s to 0.6 s.

How engineers use it

At design stage, an acoustic consultant or designer sets a reverberation time target for each room type in the acoustic brief, then calculates RT from the volume and the absorption of every proposed finish, using data sheet coefficients band by band. Panels, ceiling and floor finishes are adjusted until each band meets the target. A single-number Sabine check like this one is used earlier, to see whether a room is likely to need treatment and roughly how much panel area to allow on the layout.

When a professional design must replace it

Use the calculator to get a first view of how much absorption a room needs, or to check a panel quantity you have been given. Replace it with an acoustic design by a consultant wherever speech intelligibility or privacy matters, such as boardrooms, video conference rooms, training rooms and auditoria, wherever the room is large or irregular, and wherever the target has to be verified by measurement under ISO 3382-2 after completion.