Room Reverberation Time (Sabine Equation)
Room Reverberation Time (Sabine Equation)
Reverberation time — how long sound lingers and decays in a room after the source stops — is one of the most important numbers in architectural acoustics. Too short and a concert hall sounds dry and lifeless; too long and speech becomes unintelligible as syllables blur together. The Sabine equation, derived empirically over a century ago, remains the standard first-pass estimate.Acousticians use this relationship early in a room design to size the total absorptive treatment (carpet, acoustic panels, curtains) needed to hit a target reverberation time — a few seconds for a concert hall aiming for a rich, sustained sound, well under a second for a classroom or conference room where speech clarity is the priority.
The Sabine equation gives the reverberation time as T60 = k·V/A, where k is the Sabine constant (0.161 s/m in SI units). where k_sabine is the Sabine constant, V_room2 is the room volume, A_abs is the total absorption (area-equivalent) of the room surfaces, and T60_rev is the resulting reverberation time.
Inputs
k_sabine := 0.161 s/m=0.16 s/m
V_room2 := 500 m^3=500 m^3
A_abs := 45 m^2=45 m^2
Apply the Sabine equation directly: a larger room needs more absorption to hit the same reverberation time, since T60 scales with volume but inversely with absorption.
T60_rev := k_sabine·V_room2/A_abs=1.79 s
Results
A reverberation time of around 1.8 seconds is on the lively side — appropriate for a small performance space but longer than ideal for a room meant primarily for spoken word. Adding more absorptive material (carpet, acoustic panels, more seating) increases A_abs and shortens T60 proportionally, which is exactly the lever acousticians pull when a finished room turns out too echoey.
Assumptions & limitations
- Diffuse (uniformly distributed) sound field — the Sabine model assumes reflections are well mixed.
- Absorption is uniformly distributed around the room surfaces.
- Breaks down for very "dead" (highly absorptive) or unusually shaped rooms, where more advanced models are needed.