Sabine vs Eyring: When to Use Each RT60 Formula and How Big the Error Can Be

Three formulas dominate reverberation time prediction in architectural acoustics. Wallace Clement Sabine published the first in 1898. Carl F. Eyring corrected it in 1930. Raymond Fitzroy extended both in 1959. All three predict the same physical quantity — RT60, the time for sound to decay by 60 dB — but they produce different numbers depending on how much absorption the room contains and how that absorption is distributed across its surfaces.

Choosing the wrong formula does not produce a subtle difference. In a treated meeting room with an average absorption coefficient of 0.31, Sabine overestimates RT60 by 20%. In a recording studio control room at 0.54, the overestimate reaches 43%. These are not rounding errors. They are systematic biases that push predictions across compliance thresholds, inflate construction budgets, and undermine the credibility of acoustic consultants who should know better.

This article presents all three formulas, runs them head-to-head across five room types, walks through a complete worked example with real numbers, and gives you a clear decision framework for choosing the right formula for any project.

The Three Formulas

Sabine (1898)

T60 = 0.161V / A

Where:

• V is room volume in cubic meters
• A is total absorption: A = sum of (alpha_i x S_i), the sum of each surface's absorption coefficient multiplied by its area
• 0.161 is derived from the speed of sound in air at 20 degrees C: 0.161 = 24 ln(10) / c

ISO reference: ISO 3382-2:2008 Annex A, Section A.1

Eyring (1930)

T60 = 0.161V / (-S x ln(1 - alpha_bar))

Where:

• S is total surface area in square meters
• alpha_bar is the mean absorption coefficient: alpha_bar = A / S
• ln is the natural logarithm

Eyring still assumes a diffuse sound field and uniform distribution of absorption. It corrects for the magnitude of absorption but not for its spatial distribution.

ISO reference: ISO 3382-2:2008 Annex A, Section A.2. Originally published in C. F. Eyring, "Reverberation Time in 'Dead' Rooms," Journal of the Acoustical Society of America, Vol. 1, No. 2, pp. 217-241, January 1930.

Fitzroy (1959)

T60 = 0.161V / S^2 x (Sx/(-Sx x ln(1 - alpha_x)) + Sy/(-Sy x ln(1 - alpha_y)) + Sz/(-Sz x ln(1 - alpha_z)))

Where:

• Sx, Sy, Sz are the total areas of surfaces in the x, y, and z axis pairs (floor/ceiling, front/back walls, side walls)
• alpha_x, alpha_y, alpha_z are the mean absorption coefficients for each axis pair

Literature reference: D. Fitzroy, "Reverberation Formula Which Seems to Be More Accurate with Nonuniform Distribution of Absorption," Journal of the Acoustical Society of America, Vol. 31, No. 7, pp. 893-897, July 1959.

Why the Formulas Diverge: The Mathematics

The relationship between Sabine and Eyring is precise. If you expand -ln(1 - alpha_bar) as a Taylor series:

-ln(1 - x) = x + x^2/2 + x^3/3 + x^4/4 + ...

Sabine uses only the first term (x). Eyring uses the complete infinite series via the logarithm. The higher-order terms are the error that Sabine introduces.

At alpha_bar = 0.05, the second-order term (x^2/2) adds only 0.00125 to the 0.05 — a 2.5% correction. Negligible. At alpha_bar = 0.30, the correction terms sum to 0.057 on top of the 0.30, an 19% difference. At alpha_bar = 0.50, the correction is 0.193 on top of 0.50, a 39% difference. The error is not random. It is always positive. Sabine always overestimates RT60, and the overestimate grows monotonically with alpha_bar.

There is also a boundary condition that exposes the fundamental flaw in Sabine's model. When alpha_bar = 1.0 (every surface is a perfect absorber), Sabine predicts T60 = 0.161V / S, which is a finite, positive number. This is physically absurd — a room with perfectly absorptive surfaces has zero reverberation. Eyring correctly predicts T60 = 0, because -ln(1 - 1.0) = -ln(0) = infinity, making the denominator infinite and T60 = 0. This limiting behavior confirms that Eyring is the more physically correct model.

Head-to-Head: Five Room Types Compared

The following table calculates Sabine, Eyring, and Fitzroy RT60 predictions for five rooms spanning the full range of acoustic conditions encountered in practice. Each room uses realistic dimensions, surface areas, and absorption coefficients drawn from published manufacturer data and ISO 354 test results.

Room Specifications

Room 1 — Untreated concrete warehouse: 10m x 8m x 2.5m = 200 m^3. All surfaces bare concrete (alpha = 0.02) except concrete floor (alpha = 0.02). Total S = 260 m^2. A = 260 x 0.02 = 5.2 m^2 Sabine. alpha_bar = 0.02.

Room 2 — Standard open-plan office: 10m x 6m x 2.5m = 150 m^3. Suspended ceiling tiles (alpha = 0.55, 60 m^2), carpet (alpha = 0.20, 60 m^2), plasterboard walls (alpha = 0.05, 80 m^2). Total S = 200 m^2. A = 33.0 + 12.0 + 4.0 = 49.0 m^2 Sabine. alpha_bar = 0.245 (but absorption is highly non-uniform — ceiling alpha = 0.55, walls alpha = 0.05).

Room 3 — Treated meeting room: 6m x 4m x 3m = 72 m^3. Acoustic ceiling tile (alpha = 0.85, 24 m^2), carpet (alpha = 0.30, 24 m^2), plasterboard walls with some fabric panels (alpha = 0.10 weighted average, 60 m^2). Total S = 108 m^2. A = 20.4 + 7.2 + 6.0 = 33.6 m^2 Sabine. alpha_bar = 0.311.

Room 4 — Recording studio control room: 5m x 4m x 3m = 60 m^3. Heavy absorptive treatment on all surfaces: ceiling broadband absorber (alpha = 0.90, 20 m^2), floor thick carpet on underlay (alpha = 0.40, 20 m^2), walls mixture of bass traps and absorptive panels (alpha = 0.45 weighted average, 54 m^2). Total S = 94 m^2. A = 18.0 + 8.0 + 24.3 = 50.3 m^2 Sabine. alpha_bar = 0.535.

Room 5 — Anechoic chamber: 6m x 5m x 4m = 120 m^3. All surfaces lined with deep wedge absorbers (alpha = 0.99). Total S = 148 m^2. A = 148 x 0.99 = 146.5 m^2 Sabine. alpha_bar = 0.99.

Results

*In an anechoic chamber with alpha_bar approaching 1.0, Eyring gives the mathematically correct answer (T60 approaching zero), but the measurement concept of RT60 itself becomes meaningless. There is no diffuse field. Sound does not reverberate. The concept of reverberation time does not apply, and neither formula is being used within its domain of validity.

The Calculations Behind Each Row

Concrete warehouse: Sabine: T60 = 0.161 x 200 / 5.2 = 32.2 / 5.2 = 6.19 s. Eyring: -ln(1 - 0.02) = 0.0202. Denominator = 260 x 0.0202 = 5.25. T60 = 32.2 / 5.25 = 6.13 s. Difference: 0.06 s, or +1%. At this level of absorption, the choice of formula is irrelevant.

Standard office: Sabine: T60 = 0.161 x 150 / 49.0 = 24.15 / 49.0 = 0.49 s. Eyring: alpha_bar = 49.0 / 200 = 0.245. -ln(1 - 0.245) = 0.281. Denominator = 200 x 0.281 = 56.2. T60 = 24.15 / 56.2 = 0.43 s. Difference: 0.06 s, or +15%. This is already above the threshold where the choice matters for compliance. However, note that this room has highly non-uniform absorption — the ceiling alpha is 11 times the wall alpha. Fitzroy would give a more accurate prediction here, likely longer than Eyring because of the flutter echo potential between the hard walls.

Treated meeting room: Full worked example below.

Recording studio: Sabine: T60 = 0.161 x 60 / 50.3 = 9.66 / 50.3 = 0.192 s. Eyring: -ln(1 - 0.535) = 0.766. Denominator = 94 x 0.766 = 72.0. T60 = 9.66 / 72.0 = 0.134 s. Difference: 0.058 s, or +43%. At this level of absorption, using Sabine is indefensible. The predicted RT60 is 43% higher than the Eyring prediction, and the Eyring prediction itself will likely be closer to what you measure.

Anechoic chamber: Sabine: T60 = 0.161 x 120 / 146.5 = 19.32 / 146.5 = 0.132 s. Eyring: -ln(1 - 0.99) = 4.605. Denominator = 148 x 4.605 = 681.5. T60 = 19.32 / 681.5 = 0.028 s. This extreme case illustrates why Sabine fundamentally cannot handle high absorption. It predicts a reverberation time of 0.132 seconds in a room specifically designed to have no reverberation at all.

Complete Worked Example: The Treated Meeting Room

This is the room type where the choice of formula most frequently affects real design decisions. Meeting rooms are where WELL v2 compliance, BB93 compliance, and client comfort expectations intersect, and where acoustic treatment budgets are scrutinized.

Room Definition

• Dimensions: 6 m (length) x 4 m (width) x 3 m (height)
• Volume: 6 x 4 x 3 = 72 m^3
• Total surface area: 2(6 x 4) + 2(6 x 3) + 2(4 x 3) = 48 + 36 + 24 = 108 m^2

Surface Schedule

The fabric panel on long wall 2 is a 2m x 3m wall-mounted absorber with an NRC of 0.85, which gives alpha = 0.45 at 500 Hz when area-weighted across the full wall. The furniture contribution is estimated at 0.6 m^2 Sabine based on standard allowances for a conference table and eight upholstered chairs (approximately 0.075 sabins per chair is typical).

Step 1: Calculate Mean Absorption Coefficient

alpha_bar = A_total / S_total = 33.6 / 108 = 0.311

This value — 0.311 — is well above the 0.15 threshold where Sabine begins to diverge from Eyring, and above the 0.20 threshold where the divergence becomes practically significant.

Step 2: Sabine Calculation

T60_sabine = 0.161 x V / A

T60_sabine = 0.161 x 72 / 33.6

T60_sabine = 11.592 / 33.6

T60_sabine = 0.345 s

Step 3: Eyring Calculation

First, calculate the logarithmic correction:

-ln(1 - alpha_bar) = -ln(1 - 0.311) = -ln(0.689) = 0.373

Then the Eyring denominator (effective absorption):

S x (-ln(1 - alpha_bar)) = 108 x 0.373 = 40.25

Finally, the reverberation time:

T60_eyring = 0.161 x V / (S x (-ln(1 - alpha_bar)))

T60_eyring = 0.161 x 72 / 40.25

T60_eyring = 11.592 / 40.25

T60_eyring = 0.288 s

Step 4: Quantify the Error

Sabine overestimate = (T60_sabine - T60_eyring) / T60_eyring x 100

= (0.345 - 0.288) / 0.288 x 100

= 0.057 / 0.288 x 100

= 19.8%

Sabine predicts a reverberation time that is nearly one-fifth longer than Eyring. In absolute terms, the difference is 0.057 seconds — which may sound small until you consider that WELL v2 limits and BB93 targets are specified to one decimal place (e.g., 0.6 s, 0.8 s, 1.0 s). A 0.057 s error can move a prediction from one side of a compliance boundary to the other.

Step 5: Fitzroy Check

This room has moderately non-uniform absorption. The ceiling/floor pair has a weighted alpha of (0.85 + 0.30) / 2 = 0.575. The wall pairs have a weighted alpha of approximately (0.18 + 0.05 + 0.05 + 0.05) / 4 = 0.083. The ratio of highest to lowest axis pair absorption is 0.575 / 0.083 = 6.9, which is significant but not extreme. Fitzroy would predict a somewhat longer RT60 than Eyring — approximately 0.32 s — because the hard walls sustain lateral reflections that neither Sabine nor Eyring accounts for. In practice, for rooms with this level of non-uniformity, Eyring is still considered the standard calculation method. Fitzroy becomes essential when the ratio exceeds 10:1.

The Decision Framework

When to Use Sabine

• alpha_bar below 0.15: Churches, concert halls, gymnasiums, atriums, untreated industrial spaces. In these rooms, Sabine and Eyring differ by less than 8%, which is within the measurement uncertainty of RT60 itself (ISO 3382-2 reports typical measurement uncertainty of plus or minus 5% for T20 and T30 extrapolations).

• Quick preliminary estimates: When you need an order-of-magnitude RT60 during early design, before surface materials have been specified. Sabine is simpler to calculate by hand, and the overestimate provides a built-in safety margin.

• Teaching and communication: Sabine is simpler to explain to non-specialist audiences. If you are presenting to an architect who does not have acoustic training, showing A = sum(alpha x S) and T60 = 0.161V/A is more accessible than introducing natural logarithms.

When to Use Eyring

• alpha_bar above 0.15: Any room with acoustic treatment — suspended ceilings, carpet, wall panels, acoustic plaster. This covers the vast majority of rooms that acoustic consultants are asked to assess: offices, classrooms, meeting rooms, hospitals, retail spaces, restaurants, and residential living areas.

• Compliance calculations: When the RT60 prediction will be compared against a regulatory or certification threshold (BB93, WELL v2 Feature S07, DIN 18041, ANSI S12.60), Eyring is the defensible choice. Using Sabine for a compliance calculation in a treated room is like using a ruler with the wrong scale — you will get a number, but it will be systematically wrong.

• Cost optimization: When you are trying to determine the minimum acoustic treatment needed to meet a target. Sabine overestimates RT60, which means it also overestimates the amount of treatment needed. Eyring gives a more accurate prediction, enabling tighter specification and lower material costs.

• Any room where alpha_bar exceeds 0.30: At this point, the Sabine overestimate exceeds 19%, and using it is no longer a matter of professional judgment — it is simply incorrect.

When to Use Fitzroy

• Non-uniform absorption distribution: When one surface pair has an average absorption coefficient more than 10 times higher than another pair. The classic case is a room with a highly absorptive ceiling (alpha = 0.70+) and bare concrete or glass walls (alpha = 0.03-0.06). In these rooms, sound decays quickly in the vertical direction but persists in the horizontal plane, creating a two-stage decay curve that neither Sabine nor Eyring captures.

• Rooms with one dominant absorptive surface: Open-plan offices with acoustic ceilings but hard floors and glass walls. Lecture theatres with absorptive seating but a hard stage enclosure. Restaurants with acoustic ceilings but stone or tile floors and glass facades.

• When Eyring and measured RT60 disagree: If you measure a room and find that RT60 is significantly longer than the Eyring prediction, non-uniform absorption distribution is the most common cause. Recalculating with Fitzroy will often resolve the discrepancy.

When to Use Ray Tracing

• Complex geometry: L-shaped rooms, rooms with balconies or mezzanines, rooms with significant obstructions (large columns, partial-height walls), coupled spaces (rooms connected by openings). Analytical formulas assume a shoebox geometry. When the room shape deviates significantly, ray tracing (Odeon, CATT-Acoustic, Ramsete) is the appropriate tool.

• Frequency-dependent analysis: All three formulas can be applied per octave band, but ray tracing provides spatial resolution — it can predict RT60 at specific receiver positions, not just a room average. This matters for performance spaces and any room where the listening position varies.

• Coupled spaces: When two volumes are connected by an opening (e.g., a stage house and auditorium, or an open-plan office connected to a corridor), the decay curve is typically double-sloped. None of the analytical formulas can predict coupled space behavior.

Why This Matters Commercially

The choice of formula has direct financial consequences in two directions.

Overspecification: Spending Money You Did Not Need to Spend

In the treated meeting room example above, Sabine predicts T60 = 0.345 s. Suppose the design target is 0.40 s (a common target for small meeting rooms under WELL v2). Both formulas say the room passes, but Sabine says you have only 0.055 s of margin while Eyring says you have 0.112 s. An architect reviewing the Sabine calculation might decide the margin is too thin and specify a more expensive ceiling tile — upgrading from a standard mineral fiber product at 8-12 USD per square meter to a premium product at 20-30 USD per square meter. For a 24 m^2 ceiling, that is an unnecessary cost increase of 288 to 432 USD.

Now multiply that across a 40-room office fitout. The unnecessary ceiling upgrade costs 11,500 to 17,300 USD across the project. That is money spent solving a problem that does not exist, caused entirely by using a formula published before the Titanic sailed.

Underspecification: Discovering the Problem After Handover

The more dangerous scenario runs in the other direction. Suppose the target is 0.50 s and an architect uses Sabine's formula for a larger meeting room where the calculation produces T60 = 0.48 s — apparently just below the target. Confident in the result, they do not specify any additional treatment. After construction, the room is measured and the actual RT60 turns out to be 0.41 s (closer to the Eyring prediction). The room passes easily, so no harm done in this case.

But consider the reverse: a room where Sabine predicts 0.58 s against a 0.60 s target. The architect believes the room passes. It is built. But the Sabine prediction was optimistic in terms of absorption effectiveness — Sabine always overestimates RT60, meaning it also overestimates how much the treatment is helping. In this scenario, the actual RT60 could be lower (if the absorption is genuinely what was specified) or the architect might have made compensating errors elsewhere. The real danger occurs when the Sabine prediction is used to justify reducing treatment to save cost, on the assumption that 0.58 s is close enough. If the room is actually at 0.48 s, it may be fine. But if specification errors, construction variance, or furniture changes push the real absorption lower than planned, the actual RT60 could end up above target.

The point is that using a formula with a known systematic bias introduces unnecessary uncertainty into every design decision. Eyring removes that bias. There is no professional reason to accept it.

What AcousPlan Does

AcousPlan calculates both Sabine and Eyring RT60 for every simulation, displaying both values side by side so you can see the difference directly. The default prediction uses Eyring for any room where the mean absorption coefficient exceeds 0.15, following ISO 3382-2:2008 Annex A guidance. For rooms below that threshold, both formulas produce effectively identical results and either is displayed as the primary value.

The platform also flags rooms where the absorption distribution is highly non-uniform — where the ratio of the highest to lowest axis-pair absorption coefficient exceeds 8:1 — and recommends reviewing the results with awareness that Fitzroy or ray-tracing methods may provide more accurate predictions.

Every calculation shows the mean absorption coefficient, allowing you to immediately see which regime you are in and judge how much confidence to place in the analytical prediction.

The Professional Standard

The acoustics profession has known since 1930 that Sabine's formula overestimates RT60 in treated rooms. The correction has been published for nearly a century. It is referenced in ISO 3382-2. It is taught in every graduate acoustics program. It requires one additional mathematical operation — a natural logarithm — that every calculator and spreadsheet can perform.

There is no technical barrier to using Eyring. There is no computational barrier. There is no standards barrier. The only barrier is habit — Sabine is simpler, it was learned first, and it has always been "close enough." But when compliance frameworks specify RT60 targets to one decimal place, and when acoustic treatment budgets run to tens of thousands of dollars per project, "close enough" is not a professional standard. It is a liability.

Use Sabine for quick estimates in hard rooms. Use Eyring for anything with treatment. Use Fitzroy when the ceiling is doing all the work and the walls are doing none. And use AcousPlan to calculate all of them simultaneously, so you never have to wonder which answer you are looking at.

Try the Comparison Yourself

AcousPlan's room acoustics calculator computes Sabine and Eyring RT60 in real time as you adjust room dimensions and surface materials. Enter your room, assign materials to each surface, and see both predictions instantly — along with the percentage difference and a recommendation for which formula to trust.

Open the RT60 Calculator and run your own head-to-head comparison. No account required for basic calculations.