Treating a room for reverberation

RT60 calculationhow many acoustic panelsSabine equationroom absorption

Getting a room's reverberation time down to target: absorption from the panels you buy, and the two equations that turn sabins into seconds.

Noise Reduction Coefficient (NRC)

NRC=α250+α500+α1000+α20004\mathrm{NRC} = \frac{\alpha_{250} + \alpha_{500} + \alpha_{1000} + \alpha_{2000}}{4}

The single number on an acoustic panel's data sheet: the plain average of its absorption coefficients in the 250, 500, 1000 and 2000 Hz octave bands, rounded to the nearest 0.05. Convenient, widely quoted, and it hides everything that happens below 250 Hz.

Total Absorption (Sabins)

A=S1α1+S2α2+S3α3A = S_1\alpha_1 + S_2\alpha_2 + S_3\alpha_3

Add up the room: every surface contributes its area multiplied by how much of the sound striking it never comes back. The total, in metric sabins, is the A that Sabine's reverberation equation divides into the volume.

Sabine Reverberation Time (RT60)

T60=0.161VAT_{60} = \frac{0.161\,V}{A}

How long a sound takes to fade by 60 decibels after the source stops — the single number that decides whether a room is a concert hall, a classroom or a swimming pool. Big rooms ring; absorptive rooms do not.

Eyring Reverberation Time

T60=0.161VSln(1αˉ)T_{60} = \frac{0.161\,V}{-S\,\ln(1-\bar{\alpha})}

Sabine's equation, corrected for rooms that actually absorb. Once a room is treated, sound is lost on every reflection rather than continuously, and the logarithm in the denominator is what accounts for it — Sabine's form runs long in exactly the rooms people pay to have treated.

How they fit together

The job is always the same shape. A room rings, someone wants it to stop ringing, and the question is how many square metres of absorber to buy. Work it backwards: pick the reverberation time you want, get the total absorption that implies, subtract what the room already has, and the remainder is the order. NRC is where the material data comes from, because it is what the panel datasheet quotes — the average of the absorption coefficients at 250, 500, 1000 and 2000 Hz, rounded to the nearest 0.05.

That averaging is the first trap. NRC says nothing at all below 250 Hz, and low frequency is where rooms actually misbehave. A 25 mm panel with an NRC of 0.75 is doing almost nothing at 125 Hz, so a room treated to a perfect mid-band RT60 can still sound boomy and muddy, and the measurement that proved it was fine never looked where the problem was. If the complaint is about boom rather than harshness, the answer is thickness, an air gap behind the panel, or a bass trap, and no amount of NRC-rated surface will substitute.

Total absorption is then just Σ Sα across the surfaces, and Sabine turns sabins into seconds. Sabine is the famous one and the one to distrust in exactly the situation this set exists for. It was fitted in a lecture hall of modest absorption, and it does not converge: as a room approaches total absorption its reverberation time should go to zero, and Sabine's does not. Above an average absorption coefficient of about 0.2 it over-predicts noticeably, which is precisely where you land after buying panels. Eyring is the correction, and it is the one to quote for a treated studio, a broadcast booth or any small dead room. Use Sabine for a live space — a classroom, a church, an office — where ᾱ stays low and the two agree anyway. One more thing worth knowing before ordering: reverberation time is inversely proportional to absorption, so halving RT60 means doubling the absorption in the room, not adding a bit more.