A concert hall is the most acoustically demanding room type a designer can encounter. Unlike offices or classrooms where the primary goal is reducing reverberation, a concert hall requires a precise positive value of RT60 — long enough for music to bloom but short enough to preserve clarity. This article designs an 1,800-seat symphonic concert hall for a target occupied RT60 of 2.0 seconds, showing every calculation step.
The Hall
An 1,800-seat concert hall with a rectangular (shoebox) plan — the form preferred for long RT60 values:
- Length: 45 m (stage wall to rear wall)
- Width: 26 m (clear)
- Height: 14 m (to soffit of reflector array)
- Volume: 45 × 26 × 14 = 16,380 m³
V = 16,380 m³
Volume per seat = 16,380 / 1,800 = 9.1 m³/seat — slightly below the 10 m³/seat rule of thumb for symphony halls (Carnegie Hall: 9.4 m³/seat; Musikverein Vienna: 11.9 m³/seat), but within the acceptable range.
Surface Inventory
| Surface | Dimensions | Area (m²) | Notes |
|---|---|---|---|
| Floor (parquet hardwood) | 45 × 26 | 1,170 | Includes stage area |
| Ceiling (plaster, with reflector panels) | 45 × 26 | 1,170 | Overhead reflector array at 12 m |
| Side walls (upper — plaster) | 2 × 45 × 5 | 450 | Above balcony level |
| Side walls (lower — wood panelling) | 2 × 45 × 5 | 450 | Below balcony level |
| Stage rear wall (curved wood) | 26 × 14 | 364 | Curved for diffusion |
| Rear wall of hall | 26 × 14 | 364 | Concave treatment — diffusing panels |
| Balcony soffits (underside) | 2 × 14 × 5 | 140 | Splayed plaster |
| Balcony fronts | 2 × 45 × 1.1 | 99 | Hardwood facing |
| Stage floor | 12 × 26 | 312 | Hardwood boards on resilient mount |
| Total surface area S | 4,519 m² | Approximate |
Seating area (approximate, not a separate surface — counted as part of floor and lower walls):
- 1,800 upholstered seats arranged in main floor (1,100) and balcony (700)
- Stage: 100 musicians (orchestral occupancy), modelled as occupied seating
Absorption Coefficients
Concert hall surfaces must be mostly reflective. The reverberation comes from the room volume, not from absorptive surfaces.
| Material | 125 Hz | 250 Hz | 500 Hz | 1000 Hz | 2000 Hz | 4000 Hz |
|---|---|---|---|---|---|---|
| Parquet hardwood on battens (floor) | 0.10 | 0.07 | 0.06 | 0.07 | 0.08 | 0.08 |
| Plaster ceiling (smooth) | 0.02 | 0.02 | 0.03 | 0.03 | 0.04 | 0.04 |
| Curved wood panelling (walls, 25 mm) | 0.20 | 0.15 | 0.12 | 0.08 | 0.06 | 0.06 |
| Upper plaster walls | 0.02 | 0.02 | 0.03 | 0.04 | 0.05 | 0.05 |
| Balcony soffits (splayed plaster) | 0.02 | 0.02 | 0.03 | 0.03 | 0.04 | 0.04 |
| Balcony fronts (hardwood) | 0.10 | 0.07 | 0.06 | 0.06 | 0.07 | 0.07 |
Audience Absorption
Beranek's 1962 data (updated 1996) for audience in upholstered seats, per person, in m² (metric sabins):
| 125 Hz | 250 Hz | 500 Hz | 1000 Hz | 2000 Hz | 4000 Hz |
|---|---|---|---|---|---|
| 0.28 | 0.40 | 0.52 | 0.60 | 0.64 | 0.64 |
These values include the seat itself (upholstered seat with arm rests).
Unoccupied upholstered seat absorption (per seat):
| 125 Hz | 250 Hz | 500 Hz | 1000 Hz | 2000 Hz | 4000 Hz |
|---|---|---|---|---|---|
| 0.16 | 0.24 | 0.28 | 0.30 | 0.30 | 0.28 |
The difference between occupied and empty seats represents the contribution of the person's body and clothing.
Orchestral Musicians (100 players, occupied)
Musicians are treated as seated persons with additional absorption from instruments. Per Beranek, orchestral musician ≈ 0.6 m² at 500 Hz (slightly higher than audience due to instrument bodies).
Step 1 — Unoccupied Hall RT60
Calculate with 1,800 empty upholstered seats and no musicians.
Total Absorption at 500 Hz — Unoccupied
| Surface/Element | Area/Count | α or abs/unit | Si × αi or N × a |
|---|---|---|---|
| Parquet floor | 1,170 m² | 0.06 | 70.2 |
| Ceiling plaster | 1,170 m² | 0.03 | 35.1 |
| Wood panelling (lower side walls) | 450 m² | 0.12 | 54.0 |
| Upper plaster walls | 450 m² | 0.03 | 13.5 |
| Stage rear wall (curved wood) | 364 m² | 0.12 | 43.7 |
| Rear wall (diffusing panels, hardwood) | 364 m² | 0.12 | 43.7 |
| Balcony soffits | 140 m² | 0.03 | 4.2 |
| Balcony fronts | 99 m² | 0.06 | 5.9 |
| Stage floor (hardwood boards) | 312 m² | 0.06 | 18.7 |
| Empty upholstered seats | 1,800 seats | 0.28 m²/seat | 504.0 |
| Total A_unoccupied (500 Hz) | 793.0 m² |
RT60_unoccupied (500 Hz) = 0.161 × 16,380 / 793.0 = 2,637 / 793.0 = 3.33 s
That is very long — a typical finding for an empty concert hall. The audience will add approximately 900 m² of absorption and reduce this dramatically.
Step 2 — Occupied Hall RT60
Replace empty seat absorption with occupied seat absorption:
- Remove empty seat contribution: 1,800 × 0.28 = 504.0 m²
- Add occupied seat contribution: 1,800 × 0.52 = 936.0 m²
- Net change: +432.0 m²
- Add musician absorption: 100 × 0.60 = 60.0 m²
RT60_occupied (500 Hz) = 0.161 × 16,380 / 1,285 = 2,637 / 1,285 = 2.05 s
This is very close to the 2.0 s target. The design is calibrated correctly at 500 Hz.
Step 3 — Full Octave-Band RT60 (Occupied)
Repeating the calculation at all octave bands:
Absorption Components by Band — Occupied
| Band (Hz) | Surfaces (m²) | Seats (1800 occ) | Musicians (100) | Air (4mV) | A_total |
|---|---|---|---|---|---|
| 125 | 381.2 | 504.0 | 56.0 | 0 | 941.2 |
| 250 | 367.8 | 720.0 | 58.0 | 0 | 1,145.8 |
| 500 | 289.0 | 936.0 | 60.0 | 0 | 1,285.0 |
| 1000 | 295.8 | 1,080.0 | 62.0 | 65.5 | 1,503.3 |
| 2000 | 319.6 | 1,152.0 | 64.0 | 131.0 | 1,666.6 |
| 4000 | 319.6 | 1,152.0 | 64.0 | 261.9 | 1,797.5 |
Note: Air absorption (4mV) is significant for this large room. Using m values from ISO 9613-1:
- 500 Hz and below: negligible
- 1000 Hz: m = 0.001 m⁻¹ → 4mV = 4 × 0.001 × 16,380 = 65.5 m²
- 2000 Hz: m = 0.002 m⁻¹ → 4mV = 131.0 m²
- 4000 Hz: m = 0.004 m⁻¹ → 4mV = 261.9 m²
RT60 by Band (Occupied)
| Band (Hz) | A_total (m²) | RT60 (s) | Target range |
|---|---|---|---|
| 125 | 941.2 | 0.161 × 16,380 / 941.2 = 2.80 s | 2.0–2.5 s (bass warmth) |
| 250 | 1,145.8 | 0.161 × 16,380 / 1,145.8 = 2.30 s | 1.9–2.2 s |
| 500 | 1,285.0 | 0.161 × 16,380 / 1,285.0 = 2.05 s | 1.9–2.1 s ✓ |
| 1000 | 1,503.3 | 0.161 × 16,380 / 1,503.3 = 1.75 s | 1.8–2.0 s ← slightly low |
| 2000 | 1,666.6 | 0.161 × 16,380 / 1,666.6 = 1.58 s | 1.6–1.9 s |
| 4000 | 1,797.5 | 0.161 × 16,380 / 1,797.5 = 1.47 s | — |
The 1000 Hz band at 1.75 s is slightly below the ideal 1.8 s minimum. This is driven by the large air absorption term. To raise it, either reduce air absorption (by controlling temperature and relative humidity during performances) or add slightly more reflective area at the walls.
Step 4 — Occupied vs Unoccupied Comparison
| Band (Hz) | RT60 Unoccupied (s) | RT60 Occupied (s) | Difference (s) |
|---|---|---|---|
| 125 | 4.12 | 2.80 | −1.32 s |
| 250 | 3.60 | 2.30 | −1.30 s |
| 500 | 3.33 | 2.05 | −1.28 s |
| 1000 | 2.61 | 1.75 | −0.86 s |
| 2000 | 2.24 | 1.58 | −0.66 s |
| 4000 | 1.95 | 1.47 | −0.48 s |
The audience reduces RT60 by 1.3 s at low-to-mid frequencies. This enormous difference explains why concert halls must be designed for the occupied condition — an empty hall at 3.3 s sounds completely different from a full hall at 2.0 s.
Step 5 — EDT Estimation
Early Decay Time (EDT) is measured from the first 10 dB of the sound pressure level decay. In a perfectly diffuse room, EDT = RT60. In real concert halls, EDT tends to be somewhat shorter than RT60 due to the presence of direct sound and early strong reflections.
A simplified estimate of EDT uses the early-arrival portion of the reverberant energy. For a shoebox hall with a well-designed reflector array at 12 m height, the early reflections from ceiling and side walls arrive within 20–30 ms of direct sound, effectively increasing the apparent direct-to-reverberant ratio for the first 10 dB of decay.
Empirical approximation (Barron, 1993): EDT ≈ RT60 × (1 − 0.08 × (C80 − 0))
Where C80 is clarity (typically −2 to +2 dB for a well-designed concert hall).
For C80 = 0 dB (balanced clarity): EDT ≈ RT60 × 1.0 = 2.05 s at 500 Hz
For C80 = −3 dB (rich, reverberant feel): EDT ≈ RT60 × (1 + 0.08 × 3) = RT60 × 1.24 → EDT = 2.05 × 1.24 = 2.54 s
The actual EDT depends heavily on the reflector geometry, which is beyond the scope of Sabine calculations. Measuring EDT requires a full impulse response, either from a physical model, physical measurement, or wave-based acoustic simulation.
Design Summary
| Parameter | Value |
|---|---|
| Volume | 16,380 m³ |
| Seats | 1,800 |
| V/seat | 9.1 m³/seat |
| RT60 occupied (500 Hz) | 2.05 s |
| RT60 unoccupied (500 Hz) | 3.33 s |
| Bass ratio (125+250) / (500+1000) | (2.80+2.30) / (2.05+1.75) = 5.10/3.80 = 1.34 |
| Target bass ratio | 1.1–1.45 for full warm sound ✓ |
The bass ratio of 1.34 is within the preferred range for symphonic music, indicating warm and full bass relative to mid-frequency reverberance. The 1000 Hz band at 1.75 s is slightly below ideal and would be addressed in detailed design by reducing slightly the wood panelling coverage on the lower walls (wood absorbs mid frequencies through panel resonance).
For any concert hall project, this Sabine calculation provides the essential first check: is the volume-to-absorption ratio in the right ballpark? Detailed design then proceeds with room acoustic simulation software (CATT, ODEON, or similar) that models the angle-dependent effects of reflective surfaces, the distribution of early and late energy, and parameters such as Lateral Energy Fraction and Strength (G) that are beyond the scope of Sabine calculations.