Reverberation Time: Sabine's Equation, and Why a Hall Sounds the Way It Does

Clap once in an empty school hall and the sound hangs for two seconds. Clap in a furnished bedroom and it is gone before your hand comes back. The difference is one number, RT₆₀, from one equation Sabine got out of the volume of a room and the absorption in it. This gives you that number, the decay drawn to your own figures, and how much absorption it would take to make speech intelligible.

Last updated 11 Nov 2026

Reverberation time from volume and absorption

Sabine, with the air term and an Eyring cross-check

Volume of the roomLength × width × height for a rectangular room. The default is a school hall 20 m × 15 m × 4 m. Volume is in the numerator, so a bigger room rings longer at the same absorption — a cathedral is reverberant because it is huge, not because stone is unusually reflective.

Total internal surface areaEvery surface facing into the room: four walls, floor and ceiling. For a box that is 2(LW + LH + WH), so 2(300 + 80 + 60) = 880 m² for the default hall. Using the floor area alone is the commonest mistake and roughly triples the answer. The least area a volume can have is a cube, 6V^2/3; the page says below when what you typed is smaller than that.

Average absorption coefficient at mid frequenciesThe fraction of the energy a surface swallows rather than returns, area-weighted over all the surfaces. The Illinois notes fix the ends: a = 0 is no absorption, a = 1 is total absorption, so an open window is nearly 1 and polished stone a few hundredths. A bare hall sits near 0.1, a carpeted and curtained room near 0.25. Published tables of material coefficients are everywhere and this batch could not trace one to a standards publication, so none is printed here. The coefficient is strongly frequency dependent, which is why sources quote it at six octave-band centres and why one number is a mid-frequency average and nothing more.

Extra absorption from people and furnitureAbsorption that is not a flat surface — an audience, upholstered seats, a bunched curtain. Measured in square metres of equivalent perfect absorber, so it adds straight into A rather than being multiplied by an area. Figures per seated person are widely quoted and this batch could not source one, so none is printed; if your question gives one, multiply by the number of people and type the total. The direction is the point: a full hall is far less reverberant than an empty one.

Air absorption coefficientThe air absorbs sound too, which matters in a large room at high frequency and nowhere else. Mateus and Pereira write Sabine as T = 0.161V/(A + 4mV), which is what this field drives; the Illinois notes give m rising from about 0.01 per metre at 2 kHz to 0.1 per metre at 8 kHz. Leave it at 0 for any school question — every textbook statement omits it. In the default hall m = 0.01 adds 48 m², nearly half as much again as all the surfaces together.

The sound dying away in your room. The solid red line is Sabine's prediction and its slope IS your reverberation time: steep means dry, shallow means reverberant, and it reaches 60 dB down exactly at RT60 where the red dot sits. The green dotted line is Norris–Eyring for the same room, so the gap between the two lines is how far the two conventions disagree. The blue dashed line is a fixed 0.6 second speech target. The time axis is always 0 to 2.5 seconds, so a room that rings longer runs off the right edge and the diagram says so.

1.83sExample

A bare school hall 20 m × 15 m × 4 m, average absorption 0.12, nobody in it, air absorption ignored

Sabine’s equation, the air term, and the Eyring form that replaces it when the room is absorbent

RT₆₀ = 0.161 V / A · A = Σ a_nS_n + A_extra + 4mV · imperial: RT₆₀ = 0.049 V / A · Norris–Eyring: RT₆₀ = 0.161 V / (−S ln(1 − a̅))

RT₆₀: HyperPhysics defines it as “the time for the sound to die away to a level 60 decibels below its original level”. 60 dB is a factor of a million in intensity, chosen because it is roughly the dynamic range of orchestral music
V: the volume in cubic metres, in the numerator, so bigger rooms ring longer. Hall acoustics is mostly a problem of large buildings
A: the total absorption, in square metres of equivalent perfect absorber (m² sabins): area times coefficient summed over the surfaces, plus people and furnishings, plus the air term. A is what you can change — you cannot alter the volume of a built hall
a_n: the coefficient of surface n, between 0 for no absorption and 1 for total absorption, and strongly frequency dependent. The UK and Portuguese school requirements both work in the 500, 1000 and 2000 Hz octave bands, which is what “mid frequencies” means
0.161: the Sabine constant, 0.161 s/m. Not arbitrary: it is 24 ln(10)/c, which for c = 343 m/s gives 0.1611. The imperial 0.049 s/ft is the same number — 0.049 × 3.2808 = 0.1608 — and the Illinois notes print both in one line
4mV: absorption by the air, which the school form omits. Negligible in a classroom, not negligible in a 20 000 m³ hall at 2 kHz
−S ln(1 − a̅): the Norris–Eyring denominator. Sabine adds the fractions removed at each reflection; Eyring multiplies the fractions that survive, which is what happens. They agree for small a̅, because −ln(1 − x) ≈ x, and part company as it rises

Worked example

A bare school hall 20 m × 15 m × 4 m, average absorption 0.12, nobody in it, air absorption ignored
VOLUME. V = 20 × 15 × 4 = 1200 m³.
NOW ALL SIX SURFACES, NOT FOUR. S = 2(LW + LH + WH) = 2(300 + 80 + 60) = 880 m². Floor and ceiling are 300 m² each and together are more than two thirds of the total — which is why a carpet does more for a hall than curtains do.
AREA INTO ABSORPTION. A = a̅S = 0.12 × 880 = 105.6 m² sabins. Nothing else is added: the hall is empty and we are ignoring the air. a is a bare ratio with no units, so A comes out in square metres.
SABINE. RT₆₀ = 0.161V/A = 193.2 / 105.6 = 1.83 s. Squarely in the concert-hall range — HyperPhysics gives 1.8 s for Boston Symphony Hall — which is a problem, because this is a room people have to be taught in.
HOW MUCH ABSORPTION WOULD FIX IT? For a 0.6 s target, A = 193.2/0.6 = 322 m² sabins. You have 105.6, so you need 216.4 m² more: an average coefficient of 322/880 = 0.366 over every surface. That is a carpeted floor and an absorbent ceiling, not a few wall panels, which is why retrofitting a hall is expensive.
AND THE LINE THAT MAKES IT INTUITIVE. The mean free path is 4V/S = 5.45 m, so a reflection every 15.9 ms and about 115 bounces in 1.83 s. Each removes 12% of what is left, and 0.88¹¹⁵ ≈ 10⁻⁶ — which is the 60 dB. That is the whole derivation in one line.

What reverberation time different rooms want, and where each figure comes from

**Read the fourth column before the second.** A measured value for a famous hall is not a target: nobody designed Carnegie Hall to 1.7 s, it came out at 1.7 s and turned out to be loved. The two genuine targets here are both for speech and they disagree by a factor of two — under 0.5 s against under 1 s — which is the honest state of the subject and not a defect in either source; the Illinois notes say outright that optimum reverberation time is subjective. **The last row carries no source and is marked as such.**
Room or purpose	RT60	Source	What it is
Lecture hall, classroom	under 0.5 s	Illinois PHYS 406	stated target, to avoid speech interference
Classroom	under 1 s	HyperPhysics (GSU)	stated as ‘much shorter’ than its 2 s auditorium figure
Medium general-purpose auditorium	about 2 s	HyperPhysics (GSU)	stated as desirable for both speech and music
New York Carnegie Hall	1.7 s	HyperPhysics (GSU)	measured value, not a target
Boston Symphony Hall	1.8 s	HyperPhysics (GSU)	measured value, not a target
Vienna Musikvereinsaal	about 2.05 s	HyperPhysics (GSU)	measured value, not a target
Cathedral, swimming pool	3 s and up	not sourced here	common knowledge; no primary source read

Why one number decides whether you can be understood in a room

Stand at the back of a bare school hall while someone talks at the front and you notice something before anything else: you can hear them perfectly well and you cannot tell what they are saying. The sound is loud and the words are gone. That is reverberation, and RT₆₀ is the time the sound takes to fall 60 decibels — a factor of a million in intensity — after the source stops.

What Sabine actually did. Asked in the 1890s why a new Harvard lecture theatre was unusable, Sabine measured the decay of an organ pipe in room after room while carrying seat cushions in and out. What came out is the equation here: the time goes as the volume and inversely as the total absorption. The constant is not a fudge. Sound bounces every 4V/S metres on average, losing a fraction of its energy each time, so the decay is exponential and the time to lose a factor of a million is 24 ln(10)V/(cA). Put c = 343 m/s in and you get 0.161.

Volume on top, absorption underneath. Those two placements explain nearly every complaint anyone has made about a building. A big room rings; a soft room does not. And because absorption is in the denominator, the first absorption you add does far more than the last: going from a̅ = 0.05 to 0.10 halves the time, while 0.30 to 0.35 changes it by a seventh.

Speech against music, which is the real question. A spoken syllable lasts about a fifth of a second. If the room is still ringing from the last syllable when the next arrives, the consonants — quiet, brief, and carrying most of the information — are buried under the vowel before them. So speech wants a short time: the Illinois notes put lecture halls and classrooms under 0.5 s. Music wants the opposite. A held note is supported by its own reflections and an orchestra blends; HyperPhysics names around 2 s as desirable for a general-purpose auditorium and gives 1.7 to 2.05 s as the measured values of three of the most admired concert halls in the world. No number satisfies both. A hall that must do both either compromises near 1 s and does neither well, or hangs curtains it can draw and furl.

What this page will not pretend. Sabine assumes a diffuse field — energy spread evenly, arriving equally from every direction — and real rooms are not like that, least of all when the absorption is all on the floor because that is where the people are. Mateus and Pereira report that across sixteen measured rooms Sabine came out below the measured value by a quarter to a third, and state the formula is not valid above a̅ = 0.2. The common textbook warning runs the other way, that Sabine over-predicts in absorbent rooms. This page gives you the Norris–Eyring figure alongside and does not tell you which direction the error goes, because the sources read here do not agree on it and an invented answer would be worse than none.

Where this goes wrong in an exam. Using the floor area instead of all six surfaces. Forgetting that a is a bare ratio, so A is in square metres and the 0.161 carries the seconds per metre. And quoting RT₆₀ to three figures from a coefficient known to one. For the companion pages, the inverse square law handles the sound that reaches you directly rather than by bouncing, the speed of sound is where the 343 m/s inside the constant comes from, and the Helmholtz resonator is how a cavity absorber tuned to one frequency works.

Frequently asked questions

Why 60 decibels? Why not until you cannot hear it any more?

Because 60 dB is roughly the dynamic range of orchestral music, and reverberation time was invented to describe concert halls — about the gap between a full fortissimo and the quietest sound still audible in a quiet hall. It is also practical: the decay is exponential, so the line on a decibel plot is straight and you can measure its slope over whatever range your equipment allows and extrapolate. Acousticians in fact measure the first 20 or 30 dB — T20 and T30 — and multiply up, because the last 30 dB vanishes into the room’s own background noise.

Does the shape of the room matter, or only the volume and the area?

Sabine says only volume and absorption, and that is both its strength and its weakness. Two rooms of the same volume and the same total absorption get the same answer whether one is a cube and the other a corridor, and real rooms disagree: a long narrow room, or one with all its absorption on the floor, has a field that is not diffuse and a measured decay that is not one straight line. Shape also decides faults reverberation time cannot describe — a slap echo off a flat rear wall, focusing from a curved ceiling, flutter between two parallel hard surfaces. Those make a hall unusable even when its RT₆₀ is perfect.

Why is a room so much less reverberant when it is full of people?

Because people are excellent absorbers — clothing, hair and soft tissue over a large, awkward surface. In a hall with a hard floor an audience can easily double or triple the total absorption, which halves or thirds the time. That is why a rehearsal in an empty auditorium sounds nothing like the concert, and why good halls use heavily upholstered seats: a seat absorbs about as much as the person who will sit in it, so the acoustics barely change between a full house and a thin one. You can add that absorption in the extra field. This page prints no figure per person, because the widely quoted ones could not be traced to a source here.

What is the Norris–Eyring equation and when should I use it instead?

Sabine adds up the energy removed at each reflection as though the losses were independent; Eyring multiplies the surviving fractions, which is what physically happens, so the denominator becomes −S ln(1 − a̅). For small a̅ they are the same thing — at 0.1 they differ by 5% — and they diverge fast above that: at a̅ = 0.5 Eyring gives 72% of Sabine, and as a̅ approaches 1 Eyring correctly goes to zero while Sabine does not. Mateus and Pereira put Sabine’s validity limit at a̅ = 0.2, so that is a defensible switching point. For a school answer use Sabine unless the question says otherwise — it is the one in every syllabus.

Is a short reverberation time always better in a classroom?

No, and this is worth knowing. Below about 0.3 s a room sounds dead: there is no support for a voice, so a teacher works harder to reach the back, and you lose the side-wall reflections that make a voice louder without being shouted. Some reverberation carries a voice; too much destroys the consonants. That is why the targets read as under half a second rather than as close to zero, and why the Illinois notes say outright that optimum reverberation time is subjective. The one case where shorter is always better is a recording studio, which wants the room contributing nothing.

Related calculators

References

University of Illinois at Urbana-Champaign, PHYS 406 Acoustical Physics of Music, Lecture 9 (S. Errede). Gives the Sabine constant in both systems in one line — K = 0.049 in secs/ft (= 0.161 secs/m) — and calls 0.049 a “universal number”. Defines the total absorption as A = Σ a_nS_n over the surfaces in the room, with a = 0 no sound absorption and a = 1 total sound absorption. Says that “T₆₀ reverberation times should also be < 0.5 seconds in lecture halls and/or classrooms” to avoid speech interference, and states plainly that “optimum reverberation time is subjective” — which is why this page gives ranges and not a single right answer. For air absorption it gives m varying from about 0.01/m at 2 kHz to 0.1/m at 8 kHz at 30–50% relative humidity. It does not mention the Eyring or Norris–Eyring equation at all, so the Eyring figure on this page is not attributed to it.
Montana State University, EELE 217 Introduction to Audio Engineering, Lecture 12 (R. Maher). States the Sabine equation as T₆₀ = 0.161 × V / A with V the volume of the room in cubic metres and A the total sound absorption, built as the sum of each surface area times its absorption coefficient. A second, independent statement of the same constant, which is why it is cited beside the Illinois notes rather than instead of them. It is careful about what the equation is worth: “The actual reverberation time may be more or less than the prediction”, while still showing which surfaces dominate the result.
HyperPhysics, Department of Physics and Astronomy, Georgia State University, Reverberation Time. Defines the quantity this page computes: “the time for the sound to die away to a level 60 decibels below its original level”. For targets it says “Around 2 seconds is desirable for a medium-sized, general purpose auditorium that is to be used for both speech and music” and that “A classroom should be much shorter, less than a second”. It gives measured halls rather than targets: Vienna Musikvereinsaal about 2.05 s, Boston Symphony Hall 1.8 s, New York Carnegie Hall 1.7 s. The page prints its Sabine formula as an image, so its own text never states the constant — the 0.161 on this page comes from the two sources above, not from here.
D. Mateus and A. Pereira, Proposal of a simplified methodology for reverberation time prediction in standard medium size rooms with non-uniformly distributed sound absorption, Acta Acustica 7, 31 (2023), DOI 10.1051/aacus/2023025. Writes Sabine with the air-absorption term as T = 0.161V/(A + 4mV), which is the form the air field on this page implements. States that Sabine’s formula “is not valid for spaces with high sound absorption (in particular for sound absorption coefficients greater than 0.2)” — the single most useful limit on this page, and one almost no school treatment mentions. Reports that across sixteen real rooms the Sabine prediction came out below the measured value, by average deviations of −24% at 500 Hz and −36% at 1000 and 2000 Hz. That is the opposite direction from the usual textbook warning that Sabine over-predicts, so this page does not claim a direction of error. It also records that the Portuguese RRAE and the UK’s Building Bulletin 93 both work in the 500, 1000 and 2000 Hz octave bands, which is what “mid frequencies” means in a school acoustics requirement.