Why Sabine's Formula Gives Wrong Results in Open Plan Offices

Sabine's reverberation formula is the most widely used equation in architectural acoustics. It is also the most misapplied. In small to medium rooms with relatively uniform absorption, it produces reasonable predictions of reverberation time. In open plan offices, it produces a number that is technically correct and practically useless. The number tells you how long sound takes to decay by 60 dB. It tells you nothing about whether your 50-person floor plate is a productive workspace or an acoustic disaster. Here is why.

What "Diffuse Sound Field" Actually Means

Every statistical reverberation formula — Sabine, Eyring, Millington-Sette — rests on a foundational assumption: the sound field inside the room is diffuse. A diffuse sound field has two defining properties.

Property 1: Uniform energy density. The sound energy per unit volume is the same at every point in the room. There are no "loud spots" or "quiet spots." If you place a measurement microphone at any position in the room, the reverberant sound pressure level is the same (within measurement uncertainty).

Property 2: Equal probability of arrival from all directions. At any point in the room, sound arrives with equal intensity from all directions — up, down, left, right, front, back. There is no preferred propagation direction. The reverberant field is isotropic.

These two conditions are achieved when several physical criteria are met:

• The room is large relative to the wavelength of sound. At 500 Hz, the wavelength of sound in air is approximately 0.69 m. A room with dimensions at least 10 times the wavelength (roughly 7 m or more in each dimension) supports enough room modes to produce statistical averaging.
• Multiple reflective surfaces redirect sound energy. Each reflection redistributes energy. After 10 to 20 reflections, the directionality of the original source is randomized. This requires surfaces with moderate to low absorption — if surfaces absorb most of the energy on first or second contact, there are not enough reflections to achieve randomization.
• No dominant parallel surfaces. Large parallel reflective surfaces create flutter echoes and standing waves that bias the sound field in one direction. Irregular geometry, splayed walls, or diffusing elements break up specular reflection patterns and promote diffusion.
• Absorption is distributed across multiple surfaces. When absorption is concentrated on a single surface (for example, only the ceiling), the sound field becomes directionally biased. Energy is quickly absorbed in the vertical direction but persists in the horizontal plane.

Why Open Plan Offices Violate the Diffuse Field Assumption

An open plan office is not a room in the classical acoustic sense. It is a very wide, very long, very flat volume. Consider a typical floor plate: 50 m long, 30 m wide, 2.7 m floor-to-ceiling height. The aspect ratio is extreme — the horizontal dimensions are 11 to 19 times the height. This geometry creates a propagation environment that is fundamentally different from the approximately cubic volumes that Sabine studied at Harvard.

The Flat Geometry Problem

With a ceiling height of 2.7 m, the vertical dimension of the space is small relative to the horizontal dimensions. Sound emitted by a speaker at a workstation radiates outward in all directions. Vertically, it reaches the ceiling after travelling just 1.5 to 2.7 m (depending on the angle of emission). Horizontally, it can travel 15, 20, or 30 m before encountering a perimeter wall.

In a diffuse field, vertical and horizontal propagation would be equivalent. In an open plan office, they are not. The ceiling is close and typically highly absorptive (NRC 0.85 or higher in any competently designed office). Sound energy that propagates vertically is absorbed within one or two ceiling reflections. But sound energy that propagates horizontally — along the plane of the desks, at ear height — encounters no absorptive barriers. It travels outward as a direct field, spreading geometrically but not being absorbed until it finally reaches a perimeter wall, a partition, or a screen.

The Absorption Asymmetry Problem

Modern open plan offices are designed to have short reverberation times. The standard approach is to install a high-NRC ceiling tile across the entire ceiling area. This is correct for controlling RT60, but it creates a severe asymmetry in absorption distribution.

Consider the 50 m x 30 m x 2.7 m office:

The ceiling provides 80% of the total room absorption. The floor provides 19%. The walls provide 1%. This is not a uniformly absorptive room. It is a room where one surface — the ceiling — dominates absorption completely. Sound energy propagating vertically (bouncing between floor and ceiling) decays rapidly. Sound energy propagating horizontally (spreading across the floor plate at desk height) decays slowly because the surfaces it encounters (the floor and distant walls) are comparatively reflective.

The result is a sound field that is anything but diffuse. The vertical decay is fast. The horizontal decay follows a pattern closer to direct-field propagation — approximately 6 dB per doubling of distance, modified by whatever reflections occur from the floor, furniture, and distant walls.

What Sabine Gets Wrong

Sabine's formula does not know about this directional asymmetry. It takes the total absorption (1,596.6 m2 Sabine), divides it into the room volume, and produces a single number:

T60 = 0.161 x V / A = 0.161 x 4,050 / 1,596.6 = 0.41 s

This 0.41-second RT60 passes every standard. It passes WELL v2 Feature S04 (limit: 0.60 s for spaces under 500 m2, 0.75 s for spaces over 500 m2). It passes BS 8233 guidance. It passes DIN 18041. The acoustic consultant writes "RT60 compliant" in the report, and the project moves forward.

But the RT60 number describes the temporal decay of the diffuse reverberant field — a field that barely exists in this room. What actually matters to the 50 workers on this floor plate is not how quickly the reverberant energy dies out, but how far direct and early-reflected speech propagates horizontally before it becomes unintelligible. Sabine's formula has nothing to say about that.

The Correct Metric: Distraction Distance (rD)

ISO 3382-3:2012 was written specifically to address the acoustic evaluation of open plan offices. The standard recognizes that RT60, while useful for enclosed rooms with approximately diffuse fields, is insufficient for open plan spaces. It defines four parameters that together characterize the acoustic quality of an open office environment. The most important of these for speech privacy is the distraction distance, rD.

Definition

rD is the distance from a speaker at which the Speech Transmission Index (STI) drops below 0.50. STI is a metric defined by IEC 60268-16:2020 that quantifies how well a speech signal is preserved as it travels from source to receiver. An STI of 1.0 means perfect transmission (every modulation of the original speech is preserved). An STI of 0.0 means the speech signal is completely destroyed.

The threshold of 0.50 is critical. Above STI 0.50, speech is intelligible enough that the brain involuntarily processes it. You hear words, recognize sentences, and your cognitive system allocates resources to decoding the content — whether you want it to or not. This is the distraction mechanism. Below STI 0.50, speech degrades into an indistinct murmur. The brain registers it as background noise and does not attempt to decode it. The cognitive load drops dramatically.

rD is therefore the radius of the "distraction zone" around every speaker in the office. Within rD, anyone speaking at normal conversational volume (approximately 60 dBA at 1 m) is a potential distraction to every colleague. Beyond rD, speech fades into the background.

Target Values

ISO 3382-3 does not prescribe a specific rD target, but the acoustic engineering consensus based on the standard and supporting research is:

A well-designed open plan office achieves rD below 5 m. This means that a colleague speaking at a workstation 5 m away cannot distract you with normal-volume conversation. You might hear a murmur, but you cannot decode the words.

What Drives rD

rD is determined by the interaction of three factors:

1. Speech level at distance. How loud is the speech signal at the receiver's position? This depends on the source level (approximately 60 dBA at 1 m for normal speech), the geometric spreading (6 dB per doubling of distance in free field), and any additional attenuation from screens, furniture, or absorptive barriers. In an open plan office without screens, the speech level at 8 m is approximately 42 dBA. With 1.4 m screens, it drops to approximately 34-36 dBA.

2. Background noise level (BGN). The ambient noise level at the receiver's position, including HVAC, equipment noise, and sound masking if installed. Higher BGN reduces STI by reducing the signal-to-noise ratio. An office with 36 dBA BGN (quiet HVAC, no masking) preserves high STI at distance. An office with 45 dBA BGN (HVAC plus sound masking) pushes the STI below 0.50 much closer to the source.

3. Ceiling absorption and spatial decay rate. The absorptive ceiling controls the reverberant contribution to speech levels. Higher ceiling absorption reduces the reverberant build-up that would otherwise supplement the direct field at distance. This is captured by the D2,S parameter (spatial decay rate of A-weighted speech, in dB per distance doubling). Higher D2,S means faster spatial decay and shorter rD.

The relationship can be expressed approximately as:

rD increases when:

• Background noise level is low (no masking system, quiet HVAC)
• Ceiling absorption is insufficient (NRC below 0.80)
• Screens are absent or low (below 1.2 m above finished floor)
• The floor plate is open with long unobstructed sight lines

• Sound masking raises BGN to 42-46 dBA
• Ceiling tiles have NRC 0.85 or above with full coverage
• Desk screens are 1.4 m or higher with absorptive faces
• Layout breaks long sight lines with furniture, storage, or partition elements

Worked Example: The Office That Passes RT60 and Fails on Privacy

Room Specification

Consider a medium-density open plan office on a commercial floor plate:

• Dimensions: 40 m (length) x 20 m (width) x 2.7 m (ceiling height)
• Volume: 2,160 m3
• Floor area: 800 m2
• Workstations: 70 desks at approximately 11.4 m2 per person
• Ceiling: Mineral fiber tiles, NRC 0.85, full coverage
• Floor: Commercial loop-pile carpet, alpha 0.20
• Walls: Painted plasterboard, alpha 0.05
• Screens: None
• Masking: None
• HVAC BGN: 36 dBA at workstation height

Sabine RT60 Calculation

T60 (Sabine) = 0.161 x 2,160 / 856.2 = 0.41 s

This RT60 comfortably passes WELL v2 Feature S04 (limit 0.75 s for spaces over 500 m2). It passes BS 8233. It passes every reverberation-based criterion in every standard. An acoustic report based solely on Sabine RT60 would declare this office compliant.

ISO 3382-3 Analysis: Distraction Distance

Now calculate what actually matters to the 70 workers in this space. With NRC 0.85 ceiling and no screens, the spatial decay rate D2,S is approximately 5.5 dB per distance doubling. Normal speech at 1 m is 60 dBA. The speech level at distance r (in meters) follows the spatial decay:

Lp(r) = Lp(1m) - D2,S x log2(r)

At 4 m: Lp = 60 - 5.5 x 2.0 = 49.0 dBA At 8 m: Lp = 60 - 5.5 x 3.0 = 43.5 dBA At 12 m: Lp = 60 - 5.5 x 3.58 = 40.3 dBA

STI at each distance is determined by the signal-to-noise ratio between the speech level and the background noise (36 dBA):

rD = 9.2 m

The distraction distance is 9.2 m. In a room that is 20 m wide, this means a speaker at one edge of the floor plate can distract colleagues almost halfway across the entire width. In a 40 m x 20 m floor plate with 70 workstations, roughly 80% of the floor is within someone's distraction zone at any given time.

The Sabine RT60 of 0.41 s is a true number. It accurately reflects the temporal decay of the reverberant field. But it describes a phenomenon that is almost irrelevant to the lived experience of workers in this space. The problem is not reverberation. The problem is horizontal direct-field speech propagation in a low-noise environment with no physical barriers.

Adding Sound Masking: The Transformation

Now add a sound masking system commissioned at 42 dBA. Nothing else changes — same ceiling, same lack of screens, same layout. Only the background noise level increases by 6 dB.

rD = 4.8 m

The distraction distance dropped from 9.2 m to 4.8 m. That single intervention — raising the background noise by 6 dB with a sound masking system — halved the distraction radius. Now only colleagues within approximately 5 m can understand your speech. The 70 workers on this floor plate went from 80% distraction coverage to roughly 25%.

This is the insight that Sabine's formula cannot provide. The RT60 did not change. It is still 0.41 seconds. The Sabine calculation gives the same answer before and after masking because Sabine does not model background noise, does not model spatial decay, and does not model speech intelligibility. It models reverberant decay in a diffuse field — a field that does not exist in this room.

Sabine-Only vs. ISO 3382-3 Analysis: What Each Captures

The table makes the gap explicit. A Sabine-only analysis answers one question: does the reverberant decay time meet the target? An ISO 3382-3 analysis answers the question that actually matters: can workers concentrate without being distracted by nearby conversations?

When Sabine Is Still Valid for Open Plan Spaces

Sabine's formula retains value in two specific situations within open plan acoustic design:

1. As a preliminary screening tool. If the Sabine RT60 exceeds the target (for example, 0.8 s in a space where 0.6 s is required), the ceiling treatment is definitely insufficient. Sabine is a useful lower bound on the treatment needed. However, passing the Sabine RT60 check is necessary but not sufficient — it does not guarantee that D2,S or rD targets will be met.

2. For enclosed rooms adjacent to the open plan. Meeting rooms, phone booths, and private offices that open onto the floor plate are enclosed volumes where diffuse field conditions are more closely approximated. Sabine (or preferably Eyring, when average absorption exceeds 0.20) provides reasonable RT60 predictions for these spaces.

For the open plan area itself, Sabine RT60 should be reported but never used as the sole acoustic performance metric. It must be supplemented with D2,S, Lp,A,S,4m, and rD per ISO 3382-3.

The Fitzroy Alternative: A Partial Improvement

When absorption is concentrated on one surface — as it always is in open plan offices, where the ceiling dominates — the Fitzroy formula offers a partial improvement over Sabine. Proposed by D. Fitzroy in 1959, the formula calculates separate reverberation contributions for each pair of opposing surfaces and produces a weighted average:

1/T60 = (Sx/S) x (1/Tx) + (Sy/S) x (1/Ty) + (Sz/S) x (1/Tz)

Where Sx, Sy, Sz are the areas of opposite surface pairs (floor/ceiling, left/right walls, front/back walls), S is the total surface area, and Tx, Ty, Tz are the reverberation times calculated for each pair using the Eyring formula applied to that pair's average absorption coefficient.

For an open plan office with a highly absorptive ceiling and reflective walls, Fitzroy produces a longer RT60 than Sabine because it accounts for the slow horizontal decay that Sabine averages away. This is directionally correct. However, Fitzroy is still a statistical reverberation formula that produces a single number. It does not calculate D2,S, STI, or rD, and it does not model the spatial variation of the sound field across the floor plate.

Fitzroy is a better tool than Sabine for estimating the reverberant field in rooms with non-uniform absorption, but it is not a substitute for a full ISO 3382-3 analysis in open plan environments.

What AcousPlan Does Differently

AcousPlan calculates Sabine and Eyring RT60 for every room type because RT60 remains a required parameter for standards compliance. But for open plan office configurations — detected automatically when the room type is set to "open plan office" or when the floor area exceeds 200 m2 with a ceiling height below 3.5 m — the platform also computes the ISO 3382-3 parameters.

The calculation process follows these steps:

1. RT60 via Eyring (not Sabine) because the high ceiling absorption in open plan offices pushes the mean absorption coefficient above 0.20, where Eyring is more accurate per ISO 3382-2:2008 Annex A.2.
2. D2,S estimation based on ceiling absorption, screen height (if specified), and room geometry, using the empirical relationships established in ISO 3382-3 Annex A.
3. Lp,A,S,4m calculation from source level, D2,S, and room contribution.
4. STI spatial profile computed across the distance range from 1 m to the maximum room dimension, incorporating the user-specified background noise level and any masking system.
5. rD determination as the distance at which the STI profile crosses 0.50.

This dual analysis prevents the most common error in open plan acoustic design: declaring victory based on RT60 alone while workers suffer from speech distraction that RT60 was never designed to measure.

Practical Recommendations

1. Never evaluate an open plan office on RT60 alone. RT60 is a necessary parameter but an insufficient one. Always compute or measure D2,S, Lp,A,S,4m, and rD per ISO 3382-3:2012.

2. Specify sound masking from the start. Masking is not a remediation measure. It is a design element. The most common path to rD below 5 m is a high-NRC ceiling (0.85+) combined with masking at 42-46 dBA. Without masking, even excellent ceiling treatment will leave rD above 8 m in a quiet office.

3. Model the effect of screens before selecting screen height. Each additional 200 mm of screen height above the desk surface adds approximately 2-3 dB to D2,S. The difference between 1.0 m screens and 1.4 m screens can reduce rD by 2-3 m, which is the difference between an acceptable and excellent acoustic environment.

4. Do not trust Sabine's formula in any room where one surface provides more than 50% of the total absorption. This condition triggers the non-uniform absorption problem. Use Eyring as a minimum, and for large open plan spaces, supplement with ISO 3382-3 spatial analysis.

5. Measure after occupancy. ISO 3382-3 specifies measurement procedures for D2,S, Lp,A,S,4m, rD, and rP in occupied or furnished open plan offices. Post-occupancy measurement is the only way to confirm that the modelled performance has been achieved. Budget for it during the design phase.

Try It Yourself

Enter your open plan office dimensions, ceiling material, screen height, and masking level in the AcousPlan calculator. The tool computes both Sabine/Eyring RT60 and the ISO 3382-3 distraction distance, so you can see exactly where standard RT60 analysis gives you a false sense of compliance — and what it takes to achieve genuine speech privacy on your floor plate.

Open the RT60 calculator — model your open plan office and see the difference between RT60 compliance and actual acoustic performance.

Related Articles

• Open Plan Office Acoustic Design: The Complete Guide — Full ABC treatment methodology with cost analysis and compliance checklists
• Your RT60 Calculation Is Probably Wrong — And Sabine's Formula Is Why — The Sabine vs Eyring comparison with worked examples
• WELL v2 Feature 74 Acoustic Requirements Decoded — What WELL Sound features require and how to verify compliance

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 3382-3:2012 — Acoustics — Measurement of room acoustic parameters — Part 3: Open plan offices
• 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.
• Virjonen, P., Keraenen, J., and Hongisto, V. (2009). "Determination of acoustical conditions in open-plan offices: proposal for new measurement method and target values." Acta Acustica united with Acustica, 95(2), 279-290.
• Haapakangas, A., et al. (2014). "Effects of Five Speech Masking Sounds on Performance and Acoustic Satisfaction." Acta Acustica united with Acustica, 100(4), 641-655.