Sabine Equation

A simple formula that estimates how long sound keeps echoing in a room based on the room size and how much soft, sound-soaking stuff is in it.

RT60 = 0.161 x V / A: room size fills the tub of sound, absorbers drain it, the curve shows the 60 dB decay.

What it is

A formula that estimates a room's reverb time from its volume and how much sound-absorbing material it holds.

Key facts

Formula: RT60 = 0.161 x V / A (metric). V = room volume in cubic metres (m3). A = total absorption in sabins (m2 of perfect absorber).
RT60 = the reverb time: seconds for sound to decay by 60 dB (drop to one millionth of its energy) after the source stops.
The 0.161 constant = 24 x ln(10) / speed of sound (343 m/s at 20C). Imperial version uses 0.049 with feet.
Speed of sound = 343 m/s in air at 20C (about 1235 km/h); rises ~0.6 m/s per 1C warmer.
Absorption A = sum of (each surface area S x its absorption coefficient alpha), in sabins. Bigger V = longer reverb, bigger A = shorter reverb.
Absorption coefficient alpha runs 0 (perfect reflector, e.g. polished concrete) to 1.0 (perfect absorber, e.g. open window); changes with frequency.
Typical alpha: painted concrete ~0.05, carpet on concrete ~0.3, heavy curtains ~0.5, 50mm acoustic foam ~0.8. One adult person adds ~0.4-0.5 sabins.
Target RT60: speech/conference ~0.4-0.6 s, multipurpose/live music ~0.8-1.2 s, concert hall ~1.8-2.2 s, cathedral 4-8 s. Boomy/muddy = too long.
Sabine assumes a diffuse field and only works well when average alpha is below ~0.2; above that use the Eyring formula. Named after Wallace Sabine (~1898).
RT60 is frequency-dependent (longer in bass, shorter in treble). Rule: double the absorption A = halve RT60 = drop reverberant level ~3 dB.

How it works

Measure the room: length x width x height = volume V in m3.
List every surface (walls, floor, ceiling) and its area in m2.
Look up each surface's absorption coefficient alpha for the band you care about (often 500 Hz or 1 kHz).
Multiply each area by its alpha and add them all up to get total absorption A in sabins.
Plug into RT60 = 0.161 x V / A and read the reverb time in seconds.
If RT60 is too long, add absorption (curtains, foam, bodies) to raise A and recalc.

Real examples

Empty 10x8x4 m hall (320 m3) with hard walls: A maybe 30 sabins, RT60 = 0.161 x 320 / 30 = ~1.7 s, boomy and muddy.
Same hall packed with 100 people adds ~45 sabins, A jumps to ~75, RT60 drops to ~0.7 s and tightens right up.
Add eight heavy stage curtains (40 m2 at alpha 0.5 = 20 sabins) before the gig to pre-drain the bass mud.
A tiled 5x4x2.5 m bathroom (50 m3, almost no absorption) has a long ringy RT60, which is why singing sounds huge in there.

How it helps in live sound

Recce the venue: empty rooms reverb far longer than the gig will (every body = ~0.45 sabins), so judge it expecting the crowd.
Hard, boomy room? Bring deployable absorption: heavy drapes, stage curtains, even gear cases, to raise A and shorten RT60.
Long RT60 kills speech intelligibility: pull back overall SPL and steer/array your tops at the audience, not the bare walls.
High-pass the system aggressively and tame low mids: reverb is worst in the bass, so cutting LF clears the mud fastest.
Use a measurement app (Smaart, REW, or an RT60 meter) to actually measure reverb per octave band instead of guessing.
More gain-before-feedback and clarity come from drier rooms, so absorption beats cranking the master fader.

Everyday analogy

It's a draining bathtub: the room is the tub of sound energy and every soft surface is another plughole, so more absorption drains the echo faster.

Watch out

Myth: a bigger PA fixes a boomy room. Wrong, RT60 depends on volume and absorption, not your amp, so more SPL just feeds the reverb and makes the mud worse, add absorption instead.

Fun fact

Wallace Sabine cracked the formula by lugging seat cushions from a nearby theatre into Harvard's awful Fogg lecture hall at night, measuring decay by ear with an organ pipe and a stopwatch, the birth of architectural acoustics.

Key takeaways

RT60 = 0.161 x V / A: reverb time scales UP with room size and DOWN with absorption.
RT60 = time for sound to fall 60 dB (a millionth of its energy) after the source stops.
Absorption A is summed sabins: each surface area times its alpha (0 = reflect, 1 = absorb).
People are absorbers: ~0.45 sabins each, so a packed room is much drier than an empty recce.
Double the absorption = halve the reverb and drop reverberant level ~3 dB.
Fix boom with absorption, not more volume: a bigger PA just feeds the echo.