Sabine Reverberation Time (RT60)

Wallace Clement Sabine did not set out to found a science. In 1895 he was a young physics instructor handed an administrative problem: the lecture hall of Harvard's new Fogg Art Museum was unusable, because speech in it smeared into an unintelligible wash. Over several years of night work — carrying seat cushions in and out of the room, using organ pipes and his own ear as the instrument, timing the decay with a stopwatch — he established that the persistence of sound depended on just two things about a room: how big it was, and how much absorbing material it contained.

The relation he published in 1900 is the one above. Reverberation time is proportional to volume and inversely proportional to total absorption, and the constant of proportionality is not arbitrary. Trace a sound ray around a room and its mean free path between surfaces works out to $4V/S$; a decay of 60 dB is a fall to one millionth of the energy; put the two together and the constant is $24\ln(10)/c \approx 55.26/c$. At room temperature, with $c \approx 343$ m/s, that is 0.161 with volume in cubic metres and absorption in square metres.

The constant is therefore unit-bound, and this is where most of the arithmetic errors in room acoustics come from. In cubic feet and square feet the same physics gives $0.161 \times 0.3048 = 0.0491$, universally quoted as 0.049 — because a cubic foot divided by a square foot is a foot, and the constant has to carry that length. A number from a North American handbook and a number from a European one will not match unless you know which constant was used. This calculator pins the volume to cubic metres and the absorption to square metres in both systems, converts your entry, and applies the one constant, so the reveal steps show exactly where the difference lives.

Sabine's equation has known limits and they matter. It assumes a diffuse field — sound arriving from all directions with absorption spread evenly — and it treats absorption as a continuous drain rather than a loss taken at each bounce. That holds well while the average absorption coefficient is below about 0.2 and runs increasingly long above it, which is why Eyring's correction exists. It also ignores absorption by the air itself, significant above 2 kHz in large halls, and it says nothing useful at low frequencies in a small room, where there are too few modes for any statistical description to mean anything. Below roughly the Schroeder frequency a room is not a statistical object but a collection of individual resonances, and a measurement — or a wave-based model — is the only honest answer.