Reverberation Time Calculator Using Sabine Formula — Free, Instant, No Signup

Wallace Clement Sabine measured the reverberation time of Harvard's Fogg Art Museum lecture hall in 1895 and found it was 5.62 seconds — so long that a spoken word blurred into the next before the first had decayed. His subsequent research, published between 1898 and 1906, produced the first mathematical relationship between room volume, surface absorption, and reverberation time: T60 = 0.161V/A. That equation — the Sabine equation — remains the most widely used formula in architectural acoustics 128 years later. This article explains exactly how to use it, shows every calculation step on a real room, demonstrates where and why it fails, and compares its predictions against the Eyring correction that should replace it in treated rooms.

The Sabine Formula: Complete Specification

The Equation

T60 = 0.161 V / A (metric units)

Where:

• T60 = reverberation time in seconds (the time for sound pressure level to decay by 60 dB)
• V = room volume in cubic metres (m³)
• 0.161 = constant derived from 24 ln(10) / c = 24 x 2.3026 / 343
• A = total absorption in the room, in square metres Sabine (m² Sabine, also called metric sabins)

The ISO Reference

ISO 3382-2:2008, "Acoustics — Measurement of room acoustic parameters — Part 2: Reverberation time in ordinary rooms," formalises Sabine's formula in Annex A, Section A.1. The standard notes that this formula assumes a diffuse sound field and that it "is applicable when the mean absorption coefficient is less than about 0.2."

Calculating Total Absorption (A)

Total absorption is the sum of each surface's absorption contribution:

A = sum of (alpha_i x S_i) for all surfaces i

Where:

• alpha_i = absorption coefficient of the i-th surface (dimensionless, from 0.00 to 1.00)
• S_i = area of the i-th surface in square metres

The Unit: Metric Sabin (m² Sabine)

The unit of absorption — m² Sabine — is named after Wallace Sabine himself. One metric sabin equals the absorption provided by one square metre of a perfectly absorptive surface (alpha = 1.00). A 10 m² surface with alpha = 0.30 provides 3.0 m² Sabine of absorption: it absorbs as much sound as 3.0 square metres of a perfect absorber.

Step-by-Step Worked Example: 10m x 7m x 3m Conference Room

Let us compute the reverberation time of a medium conference room using both Sabine and Eyring formulas, showing every intermediate step.

Step 1: Room Geometry

• Length: 10 m, Width: 7 m, Height: 3 m
• Volume: V = 10 x 7 x 3 = 210 m³
• Floor area: 10 x 7 = 70 m²
• Ceiling area: 10 x 7 = 70 m²
• Long walls: 2 x (10 x 3) = 60 m²
• Short walls: 2 x (7 x 3) = 42 m²
• Total surface area: S = 70 + 70 + 60 + 42 = 242 m²

Step 2: Surface Materials and Absorption Coefficients

Step 3: Calculate Absorption at Each Frequency

At 500 Hz:

At 1000 Hz:

Step 4: Compute Mean Absorption Coefficient

At 500 Hz: alpha_bar = 60.89 / 242 = 0.252

At 1000 Hz: alpha_bar = 77.25 / 242 = 0.319

Both values exceed 0.20, which means Sabine's formula will overestimate RT60. Let us compute both Sabine and Eyring to see by how much.

Step 5: Sabine Calculation

At 500 Hz: T60 = 0.161 x 210 / 60.89 = 33.81 / 60.89 = 0.555 s

At 1000 Hz: T60 = 0.161 x 210 / 77.25 = 33.81 / 77.25 = 0.438 s

Broadband Sabine RT60 = (0.555 + 0.438) / 2 = 0.496 s

Step 6: Eyring Calculation

At 500 Hz:

• -ln(1 - 0.252) = -ln(0.748) = 0.290
• Eyring denominator = 242 x 0.290 = 70.24
• T60 = 33.81 / 70.24 = 0.481 s

• -ln(1 - 0.319) = -ln(0.681) = 0.384
• Eyring denominator = 242 x 0.384 = 92.88
• T60 = 33.81 / 92.88 = 0.364 s

Step 7: Compare the Results

Sabine overestimates the broadband RT60 by 0.073 seconds — 17.2% higher than Eyring. For this conference room, both formulas predict compliance with the WELL v2 Feature 74 target of 0.60 seconds. But the Sabine prediction (0.496 s) leaves less margin than the Eyring prediction (0.423 s), which could mislead a designer into specifying a higher-performance (and more expensive) ceiling tile when the standard product already provides comfortable compliance.

Full Octave Band Comparison

The pattern is clear: the Sabine overestimate is smallest at 125 Hz (where absorption is low and both formulas agree) and largest at 2000 Hz (where absorption is highest). This frequency-dependent error means that Sabine distorts the predicted RT60 spectrum — it shows a flatter frequency response than the room actually has, because it compresses the dynamic range between low-absorption and high-absorption bands.

When Sabine Is the Right Choice

Despite its limitations, Sabine's formula remains appropriate in several scenarios:

Untreated rooms with hard surfaces. A room with plaster walls, concrete floor, and plaster ceiling has alpha_bar of 0.03–0.08. At these absorption levels, the Sabine error is less than 5%, and the formula gives reliable predictions. This covers most rooms before acoustic treatment is specified.

Large reverberant spaces. Concert halls (V = 5,000–25,000 m³), churches, and cathedrals with stone walls and hard floors have alpha_bar of 0.05–0.15. Sabine's formula was derived from measurements in exactly these types of spaces, and it remains the standard prediction method for performance venue design.

Preliminary design estimates. At the concept stage, when surface materials have not been specified, Sabine provides a conservative (high) estimate. If Sabine predicts compliance, the room will definitely comply — the actual RT60 will be equal to or lower than the Sabine prediction. This makes Sabine a useful screening tool: any room that passes the Sabine check will pass the Eyring check.

Educational contexts. Sabine's formula is the standard teaching tool for architectural acoustics because of its simplicity. The direct proportionality between T60 and V, and the inverse proportionality between T60 and A, are intuitive and easy to explain.

When Sabine Gives Wrong Answers

Sabine's formula systematically overestimates RT60 whenever alpha_bar exceeds 0.15. The following table quantifies the error across the range of absorption coefficients encountered in practice:

The physical reason for the error is that Sabine approximates ln(1 - alpha_bar) as -alpha_bar — a first-order Taylor expansion that is accurate only when alpha_bar is small. As absorption increases, the higher-order terms (alpha_bar²/2, alpha_bar³/3, ...) become significant, and the approximation diverges.

At the extreme (alpha_bar = 1.00, a room with perfectly absorptive surfaces), Sabine predicts a finite reverberation time (T60 = 0.161V/S), which is physically impossible — a perfectly absorptive room has zero reverberation. Eyring correctly predicts T60 = 0 because -ln(1 - 1) approaches infinity.

The Eyring Formula: What It Changes

Eyring's formula replaces Sabine's linear approximation with the exact logarithmic expression:

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

The denominator -S ln(1 - alpha_bar) is always larger than S x alpha_bar (= A), which means the Eyring RT60 is always equal to or shorter than the Sabine RT60. The two formulas converge as alpha_bar approaches zero.

Per ISO 3382-2:2008, Annex A, Section A.2: "This formula gives more accurate results than Sabine's formula when the mean absorption coefficient is large."

When to Switch from Sabine to Eyring

The calculator switches automatically based on alpha_bar at each octave band:

• alpha_bar < 0.15: Sabine
• alpha_bar >= 0.15 and < 0.20: Sabine with a warning that Eyring may be more accurate
• alpha_bar >= 0.20: Eyring

Advanced: Air Absorption Correction

For rooms larger than approximately 500 m³, or at frequencies above 2000 Hz in any room, air absorption becomes a significant energy loss mechanism. The Sabine formula with air absorption is:

T60 = 0.161 V / (A + 4mV)

Where m is the energy attenuation coefficient of air (in Nepers per metre), which depends on temperature, humidity, and frequency per ISO 9613-1:1993. At 20°C and 50% relative humidity:

For the 210 m³ conference room, the air absorption contribution at 4000 Hz is 4mV = 0.0484 x 210 = 10.2 m² Sabine. Since the surface absorption at 4000 Hz is 79.76 m² Sabine, the air absorption adds approximately 13% — significant enough to affect the predicted T60 at 4000 Hz. The calculator includes this correction automatically.

For rooms smaller than 200 m³ and at frequencies below 2000 Hz, the air absorption term is less than 2% of the surface absorption and can be safely ignored.

Imperial Units

For users working in imperial units, the Sabine formula becomes:

T60 = 0.049 V / A

Where V is in cubic feet and A is in square feet Sabine (ft² Sabine or imperial sabins). The constant 0.049 = 24 ln(10) / c, where c = 1125 ft/s.

The calculator accepts both metric and imperial inputs and displays results in the selected unit system. All internal calculations are performed in metric units.

What the Calculator Shows You

The AcousPlan Sabine calculator generates a complete breakdown of every calculation step:

1. Room geometry summary: Volume, total surface area, surface dimensions
2. Absorption schedule: Each surface with its material, area, and absorption coefficient at each octave band
3. Total absorption per frequency: The sum A(f) at each of the six standard octave bands
4. Mean absorption coefficient: alpha_bar(f) = A(f) / S at each frequency
5. Formula selection: Which formula (Sabine or Eyring) is used at each frequency, and why
6. RT60 per octave band: The predicted reverberation time at 125, 250, 500, 1000, 2000, and 4000 Hz
7. Broadband RT60: Average of the 500 and 1000 Hz values, per ISO 3382-2:2008 §4.2
8. Sabine vs Eyring comparison: Both predictions side by side with the percentage difference
9. Compliance check: Pass/fail against the selected standard

Try the Free Sabine Calculator

Enter your room dimensions and surface materials. The calculator computes RT60 using both Sabine and Eyring formulas, shows you the divergence, and tells you which formula is appropriate for your room. Every intermediate step is visible. No signup required.

Open the Sabine reverberation time calculator

Further Reading

• Deriving Sabine's and Eyring's Reverberation Time Formulas from First Principles — the mathematical derivation of both formulas
• Your RT60 Calculation Is Probably Wrong — And Sabine's Formula Is Why — the practical impact of choosing the wrong formula
• What Is RT60 — And Why It Determines Whether Your Room Sounds Good or Terrible — the fundamentals of reverberation time

References

• ISO 3382-2:2008 — Acoustics — Measurement of room acoustic parameters — Part 2: Reverberation time in ordinary rooms
• 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
• ASTM C423 — Standard Test Method for Sound Absorption and Sound Absorption Coefficients by the Reverberation Room Method
• 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.
• Kuttruff, H. (2009). Room Acoustics. 5th Edition. Spon Press.