Most architects calculate RT60 using Sabine's formula. In rooms with average absorption above 20%, this overestimates reverberation time by 15–40%. Your WELL F74 assessment could pass on paper and fail on site. Here is the correction your acoustic consultant should be using.
What RT60 Measures and Why It Matters
Reverberation time (T60 or RT60) is the time it takes for sound pressure level in a room to decay by 60 dB after a source stops. It is the single most important metric in architectural acoustics. Every compliance framework — WELL v2, BB93, ANSI S12.60, DIN 18041 — uses RT60 as the primary criterion for evaluating whether a room is acoustically fit for its intended purpose.
Get the RT60 prediction wrong at the design stage, and one of two things happens. Either you specify more acoustic treatment than necessary, inflating the construction budget by thousands of dollars per room, or you specify too little and discover the problem after handover, when remediation costs four to ten times what it would have cost during fitout.
The formula you choose to predict RT60 determines which outcome you get.
Sabine's Equation: The Default That Should Not Be
The Formula
Wallace Clement Sabine published his reverberation formula in 1898, based on measurements in Harvard lecture halls and the Boston Music Hall. It remains the most widely taught equation in architectural acoustics:
T60 = 0.161 V / A
Where:
- T60 is reverberation time in seconds
- V is the room volume in cubic meters
- A is the total sound absorption in the room, measured in square meters Sabine (m² Sabine or metric sabins)
- 0.161 is a constant derived from the speed of sound in air at 20°C: 0.161 = 24 ln(10) / c = 24 (2.303) / 343 = 0.161
A = sum of (alpha_i x S_i)
Where alpha_i is the absorption coefficient of the i-th surface (ranging from 0.00 for a perfect reflector to 1.00 for a perfect absorber) and S_i is the area of that surface in square meters.
The ISO Reference
ISO 3382-2:2008, Annex A, Section A.1 formalizes Sabine's equation as the standard method for estimating reverberation time in ordinary rooms. The standard notes that this formula assumes a diffuse sound field — meaning sound energy is uniformly distributed throughout the room and arrives at any point from all directions with equal probability.
Where Sabine Breaks Down
Sabine's equation rests on two assumptions that are rarely satisfied in modern buildings:
Assumption 1: Low average absorption. Sabine derived his formula under conditions where room surfaces had absorption coefficients well below 0.20. In 1898, rooms had plaster walls, hardwood floors, and plaster ceilings. The average absorption coefficient was typically 0.03 to 0.10. Under these conditions, sound reflects many times before decaying, creating the diffuse field the equation requires.
Assumption 2: Uniform distribution. The formula assumes that absorption is spread relatively evenly across all room surfaces. When one surface (typically the ceiling) has a much higher absorption coefficient than the others, the sound field becomes directionally biased, and the diffuse field assumption fails.
In a modern treated room — one with acoustic ceiling tiles (alpha = 0.50 to 0.90), carpet (alpha = 0.15 to 0.35), and absorptive wall panels — the average absorption coefficient routinely exceeds 0.20. At this point, Sabine's formula begins to overestimate RT60 systematically. The higher the average absorption, the larger the error.
The mathematical reason is straightforward. Sabine's equation is a first-order approximation that assumes each sound wave loses a small fraction of its energy on each reflection. When that fraction becomes large, the linear approximation diverges from reality. Sound decays faster than Sabine predicts because each reflection removes proportionally more energy than the linear model accounts for.
Eyring's Correction: What You Should Be Using Instead
The Formula
In 1930, Carl F. Eyring published a corrected reverberation formula that accounts for the logarithmic relationship between absorption coefficient and energy loss per reflection:
T60 = 0.161 V / ( -S ln(1 - alpha_bar) )
Where:
- V is room volume in cubic meters
- S is total surface area in square meters
- alpha_bar is the mean absorption coefficient: alpha_bar = A / S
- ln is the natural logarithm
Why the Logarithm Matters
Consider what happens when alpha_bar = 0.30. Sabine assumes each reflection removes 30% of the energy linearly. Eyring recognizes that if a surface absorbs 30% of incident energy, the reflected energy is 70%, and the natural logarithm captures the compounding effect: -ln(1 - 0.30) = -ln(0.70) = 0.357. That 0.357 is 19% larger than 0.30, which means the effective absorption is higher than Sabine's linear model predicts, and the room decays faster.
As alpha_bar increases, the divergence grows. At alpha_bar = 0.50, the Eyring correction factor is 0.693 versus Sabine's 0.50 — a 39% difference. At alpha_bar = 0.60, it is 0.916 versus 0.60 — a 53% difference.
The Mathematical Relationship
It is instructive to understand exactly how the two formulas relate to each other. If you expand -ln(1 - alpha_bar) as a Taylor series, you get:
-ln(1 - x) = x + x²/2 + x³/3 + ...
The Sabine formula uses only the first term (x = alpha_bar), while Eyring uses the complete logarithmic expression. For small values of alpha_bar, the higher-order terms are negligible, and both formulas converge to the same result. This is why Sabine works well in reverberant churches and concert halls where alpha_bar is typically 0.05 to 0.12. For treated rooms where alpha_bar exceeds 0.20, the higher-order terms become significant, and ignoring them introduces the systematic overestimate.
The ISO and Literature References
Eyring's correction is referenced in ISO 11654:1997 Annex A.3, and in the foundational paper: C. F. Eyring, "Reverberation Time in 'Dead' Rooms," Journal of the Acoustical Society of America, Vol. 1, No. 2, pp. 217–241, January 1930. ISO 3382-2:2008 Annex A acknowledges both methods and notes that "for rooms with higher absorption, the Eyring formula may give more accurate predictions."
How Large Is the Error? A Systematic Comparison
The ratio of Eyring to Sabine predictions depends only on alpha_bar:
T_eyring / T_sabine = alpha_bar / ( -ln(1 - alpha_bar) )
The following table shows the Sabine overestimate for a reference room of 200 m³ volume and 260 m² total surface area (approximately 10 m x 8 m x 2.5 m), across a range of average absorption coefficients:
| Mean alpha | Sabine T60 | Eyring T60 | Sabine overestimate |
|---|---|---|---|
| 0.10 | 1.24 s | 1.18 s | +5% |
| 0.15 | 0.83 s | 0.76 s | +8% |
| 0.20 | 0.62 s | 0.56 s | +12% |
| 0.25 | 0.50 s | 0.43 s | +15% |
| 0.30 | 0.41 s | 0.35 s | +19% |
| 0.35 | 0.35 s | 0.29 s | +23% |
| 0.40 | 0.31 s | 0.24 s | +28% |
| 0.50 | 0.25 s | 0.18 s | +39% |
At alpha_bar = 0.20 — the absorption level of a typical room with suspended ceiling tiles and hard floors — the error is already 12%. For a treated meeting room or classroom with acoustic ceiling and carpet (alpha_bar = 0.25 to 0.35), the error ranges from 15% to 23%. For a heavily treated recording studio or lecture theatre (alpha_bar > 0.40), the error exceeds 28%.
These are not rounding errors. They are systematic biases that can push a prediction across a compliance threshold.
Worked Example: Conference Room That Passes or Fails Depending on Your Formula
Room Specification
Consider a medium-sized conference room designed for a WELL v2 building certification:
- Dimensions: 10 m (length) x 8 m (width) x 3 m (height)
- Volume: 240 m³
- Total surface area: 2(10 x 8) + 2(10 x 3) + 2(8 x 3) = 160 + 60 + 48 = 268 m²
Surface Schedule
| Surface | Area (m²) | Absorption coefficient (alpha) | Absorption A (m² Sabine) |
|---|---|---|---|
| Ceiling — mineral fiber tile | 80 | 0.50 | 40.0 |
| Walls — painted plasterboard | 78 | 0.05 | 3.9 |
| Glass partition wall | 30 | 0.06 | 1.8 |
| Floor — loop-pile carpet | 80 | 0.20 | 16.0 |
| Total | 268 | 61.7 |
This is a realistic, moderately treated conference room. The ceiling has standard mineral fiber tiles (not premium high-NRC product). The floor has loop-pile carpet, common in commercial office buildings. The walls are standard painted plasterboard, and one long wall is a glass partition — a typical configuration in modern office buildings.
Mean Absorption Coefficient
alpha_bar = A / S = 61.7 / 268 = 0.230
This is above the 0.20 threshold where Sabine's formula begins to diverge meaningfully from Eyring.
Sabine Prediction
T60 = 0.161 x V / A = 0.161 x 240 / 61.7 = 38.6 / 61.7 = 0.63 s
Eyring Prediction
First, calculate the effective absorption:
-ln(1 - alpha_bar) = -ln(1 - 0.230) = -ln(0.770) = 0.261
Then the Eyring denominator:
S x (-ln(1 - alpha_bar)) = 268 x 0.261 = 70.1
And the reverberation time:
T60 = 0.161 x 240 / 70.1 = 38.6 / 70.1 = 0.55 s
The Difference
| Formula | T60 | WELL F74 limit (0.60 s) | Result |
|---|---|---|---|
| Sabine | 0.63 s | 0.60 s | FAIL |
| Eyring | 0.55 s | 0.60 s | PASS |
The Sabine prediction is 0.08 seconds higher than Eyring — a 14% overestimate. More critically, Sabine predicts a T60 of 0.63 seconds, which exceeds the WELL v2 Feature S07 (formerly F74) limit of 0.60 seconds for rooms under 500 m³. The Eyring prediction of 0.55 seconds is comfortably within the limit.
The Practical Consequence
An architect using Sabine's formula would conclude that this room fails WELL v2 acoustic compliance. The typical response would be to specify a more expensive ceiling tile — upgrading from a standard mineral fiber tile (NRC 0.50, approximately $8–12/m²) to a premium product (NRC 0.80, approximately $18–30/m²). For an 80 m² ceiling, that is an unnecessary additional cost of $800 to $1,440 — per room. In a 50-room office building, that is $40,000 to $72,000 in unnecessary ceiling upgrades driven entirely by using the wrong formula.
The Eyring prediction correctly shows that the room already complies. No upgrade is needed. The architect can specify the standard product with confidence.
When Sabine Is Still Appropriate
Sabine's formula is not wrong in all cases. It remains the appropriate choice for:
Large, reverberant spaces with low absorption. Concert halls, churches, and atriums typically have average absorption coefficients below 0.15, where the Sabine error is less than 8%. For these spaces, the simpler formula is adequate and the diffuse field assumption is better satisfied by the large number of reflections before decay.
Preliminary design estimates. At the concept stage, when surface materials have not been specified, a Sabine estimate provides a quick order-of-magnitude check. The overestimate is conservative — if Sabine says the room meets the RT60 target, Eyring will confirm it.
Coupled volume systems. In rooms with coupled volumes (such as a hall with a stage house), the reverberation behavior is dominated by energy exchange between the volumes, and neither Sabine nor Eyring provides an accurate prediction. Ray tracing or finite element methods are required.
However, for the most common use case in modern architectural practice — predicting RT60 in treated offices, classrooms, meeting rooms, and healthcare spaces for compliance verification — Eyring should be the default.
Beyond Sabine and Eyring: When Neither Formula Is Enough
Both Sabine and Eyring assume a diffuse sound field, which requires that:
- The room is convex (no deep alcoves or coupled spaces)
- Absorption is distributed across multiple surfaces (not concentrated on one surface)
- The room dimensions are roughly proportional (no extreme aspect ratios)
- There are no strong specular reflections from large flat surfaces
Non-uniform absorption distribution. A room with a highly absorptive ceiling (alpha = 0.85) and reflective walls and floor (alpha = 0.05) has non-uniform absorption that biases the sound field vertically. In this case, the Fitzroy formula — which calculates separate reverberation contributions for each pair of parallel surfaces and takes a weighted average — can provide a more accurate prediction.
Long, narrow spaces. Corridors, bowling alleys, and open-plan offices with length-to-width ratios exceeding 3:1 develop a non-diffuse sound field where energy propagates predominantly along the long axis. ISO 3382-3:2012 provides specific parameters (D2,S, Lp,A,S,4m) for evaluating these spaces, but RT60 prediction requires wave-based or ray-tracing methods.
Rooms with strong flutter echo. Parallel reflective surfaces separated by more than 5 meters can produce flutter echo — a rapid, periodic repetition that is audible and distracting but not captured by statistical reverberation formulas. Geometric analysis (image source method) or ray tracing is needed to identify and quantify flutter echo risk.
Very small rooms. In rooms smaller than approximately 50 m³ (such as vocal booths, audiometry suites, or small consultation rooms), the modal behavior of the room dominates at low frequencies, and statistical methods including both Sabine and Eyring become unreliable below the Schroeder frequency. For a 50 m³ room with T60 = 0.5 s, the Schroeder frequency is approximately 200 Hz, meaning that the 125 Hz and 250 Hz octave bands cannot be reliably predicted by any statistical formula.
For these scenarios, computational room acoustics tools — geometric acoustics (ray tracing and image source methods), boundary element methods (BEM), or finite element methods (FEM) — provide more accurate predictions at the cost of significantly greater computational effort and expertise.
Frequency-Dependent Considerations
Both Sabine and Eyring are typically applied at each octave band frequency independently, using the absorption coefficients measured at that frequency per ISO 354:2003. This is important because absorption coefficients are strongly frequency-dependent.
A standard mineral fiber ceiling tile might have the following octave band absorption coefficients:
| Frequency (Hz) | 125 | 250 | 500 | 1000 | 2000 | 4000 |
|---|---|---|---|---|---|---|
| alpha | 0.15 | 0.30 | 0.55 | 0.75 | 0.80 | 0.75 |
Using the conference room example above with this ceiling, the Sabine-Eyring divergence would be smallest at 125 Hz (where alpha is low and both formulas agree) and largest at 2000 Hz (where alpha is high and Sabine significantly overestimates). This means Sabine will particularly overpredict RT60 at mid and high frequencies — exactly the frequencies that matter most for speech intelligibility and STI calculations.
An STI prediction that chains a Sabine RT60 input will inherit the overestimate and may incorrectly classify a room as having "good" speech intelligibility when it actually has "excellent" intelligibility. While this sounds like a conservative error, it can lead to specifying unnecessary sound reinforcement systems or overly powerful PA equipment — a cost impact of $5,000 to $20,000 per room in conference and classroom applications.
The Air Absorption Term
For completeness, both formulas can be extended to include air absorption, which becomes significant in large rooms (volume above approximately 1,000 m³) and at high frequencies (above 2,000 Hz). The extended Eyring formula is:
T60 = 0.161 V / ( -S ln(1 - alpha_bar) + 4mV )
Where m is the energy attenuation coefficient of air in Nepers per meter, which depends on temperature, relative humidity, and frequency. At 20°C and 50% relative humidity, m is approximately 0.003 at 2,000 Hz and 0.01 at 4,000 Hz per ISO 9613-1:1993.
For rooms smaller than 500 m³, the air absorption term is negligible at frequencies below 4,000 Hz and can be safely omitted. For large auditoria, concert halls, and sports arenas, it must be included — particularly at 2,000 Hz and 4,000 Hz — or the prediction will underestimate RT60 at high frequencies.
Practical Recommendations for Practitioners
Based on the analysis above, here are specific recommendations for choosing between Sabine and Eyring in practice:
1. Calculate alpha_bar first. Before applying either formula, compute the mean absorption coefficient. If alpha_bar is below 0.15, use Sabine. If alpha_bar is above 0.20, use Eyring. Between 0.15 and 0.20, either formula is acceptable, but Eyring will be more accurate.
2. Always report which formula you used. ISO 3382-2 does not mandate one formula over the other, but professional practice requires transparency. State the formula, the absorption coefficients, and the source of the coefficient data in your acoustic report.
3. Use frequency-dependent coefficients. Never use a single NRC value to predict RT60. NRC is a single-number rating (the average of alpha at 250, 500, 1,000, and 2,000 Hz) intended for product comparison, not for room acoustic calculations. Use the full octave band data from the manufacturer's ISO 354 test report.
4. Cross-check with measurement. Predictive formulas are estimates. If the project requires WELL, BREEAM, or LEED acoustic certification, post-construction measurement per ISO 3382-2 is required regardless of the prediction method used. The prediction guides the design; the measurement confirms it.
5. Be cautious with very high alpha_bar. When alpha_bar exceeds 0.50, even Eyring's accuracy degrades because the diffuse field assumption is badly violated. A room with that much absorption has very short reverberation (typically below 0.3 seconds) and a strongly non-diffuse sound field. At this point, consider whether the room genuinely needs further acoustic analysis, or whether the design intent is clearly satisfied.
A Note on Software Implementations
Many commercial acoustic software tools default to the Sabine formula or do not clearly indicate which formula they use. If you are evaluating software for RT60 prediction, check whether the tool:
- Allows selection between Sabine and Eyring
- Defaults to Eyring for rooms with alpha_bar above 0.20
- Applies the air absorption correction for large rooms
- Performs frequency-dependent calculations (not just NRC-based)
- Reports the formula used in the output
Try It Yourself
Enter your room dimensions and surface materials in the AcousPlan calculator. The tool will compute RT60 using both Sabine and Eyring, show you the difference, and flag which formula is being used for the compliance assessment. You will see exactly how large the divergence is for your specific room — and whether it crosses a compliance threshold.
If you have been using Sabine for all your projects, you may find that rooms you thought needed acoustic upgrades are already compliant. That knowledge could save your next project tens of thousands of dollars in unnecessary treatment.
References
- ISO 3382-1:2009 — Acoustics — Measurement of room acoustic parameters — Part 1: Performance spaces
- ISO 3382-2:2008 — Acoustics — Measurement of room acoustic parameters — Part 2: Reverberation time in ordinary rooms
- ISO 11654:1997 — Acoustics — Sound absorbers for use in buildings — Rating of sound absorption
- ISO 354:2003 — Acoustics — Measurement of sound absorption in a reverberation room
- ISO 9613-1:1993 — Acoustics — Attenuation of sound during propagation outdoors — Part 1: Calculation of the absorption of sound by the atmosphere
- IEC 60268-16:2020 — Sound system equipment — Part 16: Objective rating of speech intelligibility by speech transmission index
- Sabine, W. C. (1922). Collected Papers on Acoustics. Harvard University Press.
- Eyring, C. F. (1930). "Reverberation Time in 'Dead' Rooms." Journal of the Acoustical Society of America, 1(2), 217–241.
- Fitzroy, D. (1959). "Reverberation Formula Which Seems to Be More Accurate with Nonuniform Distribution of Absorption." Journal of the Acoustical Society of America, 31(7), 893–897.