This architectural acoustics calculator evaluates room reverberation time ($RT_{60}$) and surface absorption using Wallace Sabine's classical reverberation equation. $RT_{60}$ represents the time in seconds required for sound energy density within an enclosed space to decay by 60 decibels ($60\text{ dB}$) after the acoustic source ceases.

### Governing Acoustic Physics & Sabine Equation In imperial units (feet and cubic feet), the Sabine reverberation equation states: $RT_{60} = \frac{0.049 \times V}{A_{\text{total}}}$ Where: - **Enclosed Room Volume ($V$):** $ ext{Volume (cu ft)} = \text{Length} \times \text{Width} \times \text{Height}$ - **Total Room Boundary Surface Area ($S$):** Evaluates floor and ceiling areas plus four surrounding walls: $S = 2(L \times W) + 2(L \times H) + 2(W \times H)$ - **Baseline Room Absorption ($A_{\text{base}}$):** Untreated drywall, wood flooring, and painted surfaces exhibit an average acoustic absorption coefficient ($\alpha \approx 0.08$): $A_{\text{base}} = S \times 0.08\text{ Sabins}$ - **Acoustic Treatment Panel Absorption ($A_{\text{panels}}$):** Each standard $2 \times 4\text{ ft}$ porous acoustic absorber ($8\text{ sq ft}$) provides a Noise Reduction Coefficient (NRC) of $0.85$: $A_{\text{panels}} = \text{Panel Count} \times 8 \times 0.85\text{ Sabins}$ - **Total Absorption ($A_{\text{total}}$):** $A_{\text{base}} + A_{\text{panels}}$ - **Studio Target Range:** For critical audio mixing and vocal tracking, recommended decay time ranges between $0.25\text{ s}$ and $0.40\text{ s}$.

### Worked Numeric Example A typical project studio space: - Length: 16 feet, Width: 12 feet, Height: 9 feet - Treatment: 6 wall-mounted $2 \times 4\text{ ft}$ acoustic panels

**Step-by-Step Acoustic Evaluation:** 1. **Room Volume:** $16 \times 12 \times 9 = 1,728\text{ cu ft}$. 2. **Floor & Ceiling Area:** $2 \times (16 \times 12) = 384\text{ sq ft}$. 3. **Wall Area:** $2(16 \times 9) + 2(12 \times 9) = 288 + 216 = 504\text{ sq ft}$. 4. **Total Surface Area ($S$):** $384 + 504 = 888\text{ sq ft}$. 5. **Base Boundary Absorption:** $888 \times 0.08 = 71.04\text{ Sabins}$. 6. **Panel Absorption:** $6 \times 8 \times 0.85 = 40.80\text{ Sabins}$. 7. **Total Absorption ($A$):** $71.04 + 40.80 = 111.84\text{ Sabins}$. 8. **Sabine Decay Time:** $RT_{60} = (0.049 \times 1,728) / 111.84 = 84.672 / 111.84 \approx 0.76\text{ seconds}$. *Note:* To achieve the $0.35\text{ s}$ mix target in this room, total absorption must reach $\approx 242\text{ Sabins}$, requiring approximately 25 total treatment panels.

### Client-Side Processing Note All architectural volume calculations and Sabine formulas evaluate locally in browser JavaScript. No room blueprints, dimensions, or audio configurations are uploaded to external servers.