Room Acoustics Calculator

Two independent behaviours govern a room, and this calculation reports both. Above a transition frequency the sound field is statistically diffuse and decay is described by the Sabine equation, RT60 = 0.161 V / A in metric units, where V is volume in cubic metres and A is total absorption in square-metre sabins, each surface area multiplied by its absorption coefficient. Below that transition the room behaves as a resonator: axial modes occur wherever half wavelengths fit between parallel surfaces, at f = n c / 2L, so a 6 metre length resonates near 28.6 Hz and at multiples of it. The Schroeder frequency, roughly 2000 times the square root of RT60 divided by volume, marks the boundary between the two regimes. Practitioners target about 0.3 to 0.4 seconds RT60 for a small control room, 0.6 to 0.8 for a classroom or conference space, and 1.8 to 2.2 for a concert hall built for orchestral repertoire. Absorption coefficients supply the input: painted drywall is roughly 0.05 to 0.10 at mid frequencies, heavy carpet 0.3 to 0.5, and 100 mm mineral wool approaches 1.0. The main limitation is that the Sabine equation assumes absorption is modest and evenly distributed; in a heavily treated or lopsided room it overestimates reverberation time, and the Norris-Eyring formulation is the usual correction. It also says nothing about modal behaviour, which dominates below the Schroeder frequency and is why small rooms need corner bass absorption rather than more mid-frequency panels.

The field starts with a specific building. In 1895 Wallace Clement Sabine, then a young physics instructor at Harvard, was asked to fix the unusable lecture room of the new Fogg Art Museum. Working at night with organ pipes, a stopwatch and seat cushions borrowed from a nearby theatre, he measured decay times against varying quantities of absorbing material and found duration to be proportional to volume and inversely proportional to absorption. The constant he derived, 0.161 in metric units, underlies the equation, his name survives in the sabin unit, and his first major application was the acoustic design of Boston Symphony Hall, which opened in 1900. Later work refined the boundaries of his formula. Carl Eyring, publishing in 1930, derived an alternative decay expression that stays accurate in rooms with high absorption where the Sabine version breaks down. Richard Bolt at MIT examined how room proportions distribute low-frequency modes and in the 1940s published the range of length-to-width-to-height ratios still cited as the Bolt area. Manfred Schroeder, working at Bell Laboratories through the 1950s and 1960s, supplied the statistical criterion separating modal from diffuse behaviour and later designed the number-theoretic diffusers that carry his name, shifting room treatment from absorption alone toward controlled scattering.