Formula
Formula used (Sabine)
\[ T_{60} = 0.161 \, \dfrac{V}{A} = 0.161 \, \dfrac{V}{\sum_i S_i \alpha_i} \]
What the symbols mean
- T₆₀ — reverberation time (s)
- V — room volume (m³)
- A — equivalent absorption area (m²)
- Sᵢ — area of surface i (m²)
- αᵢ — absorption coefficient of surface i (dimensionless)
- 0.161 — Sabine constant (s/m)
Inputs
Recommended for large volumes — effect mostly at 2–4 kHz (≈ 20 °C, 50 % RH).
Surfaces and materials
Pick a material (α pre-filled, editable) or “Custom” to enter your own coefficients.
In third-octave and fine-band, α are interpolated from the octave data (material tables are published per octave).
Result
Reverberation time per band
Understand the theory — physics concept and calculationsinteractive
The reverberation time (RT or RT60) is the time a sound takes to decay by 60 dB after the source stops. It is the number-one indicator of a room's acoustic comfort. The good news: you can predict it at the design stage, without measuring anything, from just two ingredients — the room volume and the amount of absorption on its surfaces. Drag the sliders below to feel how volume and absorption pull the RT in opposite directions.
The Sabine formula
Wallace Sabine established experimentally (around 1900) that the reverberation time is proportional to the volume and inversely proportional to the total absorption:
\(V\) is the volume (m³), \(A\) the equivalent absorption area (m²), and \(0.161\) a constant tied to the speed of sound (≈ \(0.161\) s/m at 20 °C). The absorption is the sum, over each surface, of its area times its absorption coefficient:
The equivalent absorption area A
Each material has a coefficient \(\alpha\) between 0 (perfectly reflecting) and 1 (perfectly absorbing), which depends on frequency. That is why the RT is computed octave band by octave band: a carpet absorbs the highs strongly but almost not the lows, and a room's RT follows that frequency signature.
The Eyring correction
The Sabine formula assumes weak, uniformly spread absorption. When the room is very absorptive it overestimates the RT (it predicts a non-zero RT even for \(\bar\alpha = 1\), which is absurd). Carl Eyring proposed in 1930 a correction based on the mean number of reflections:
where \(S\) is the total surface and \(\bar\alpha = A/S\) the mean absorption. When \(\bar\alpha\) is small, \(-\ln(1-\bar\alpha) \approx \bar\alpha\) and Sabine is recovered. When \(\bar\alpha \to 1\), the Eyring RT correctly tends to zero. Rule of thumb: Sabine for "live" rooms (\(\bar\alpha < 0.2\)), Eyring for treated rooms.
Both formulas give nearly the same answer for a live (low-absorption) room. But as the mean absorption \(\bar\alpha\) rises, Sabine overestimates the RT while Eyring stays right. Sweep \(\bar\alpha\) to watch the gap open up.
Air absorption
In large volumes the air itself absorbs sound, mostly at high frequencies (2–4 kHz) and in dry conditions. A \(4mV\) term is then added to the total absorption, where \(m\) is the air attenuation coefficient (m⁻¹), a function of temperature and humidity. Negligible in a classroom, it matters in an auditorium or a sports hall.
Limits of the statistical formulas
Sabine and Eyring rely on the diffuse-field assumption: the sound energy is taken to be the same everywhere and arriving from all directions. This breaks down when absorption is unevenly distributed (all the treatment on the ceiling, say), in very long or very flat rooms (corridors, open-plan offices), and at low frequencies where the room modes dominate. In those cases one uses the Millington-Sette formula (which weights each surface separately), ray-tracing models or finite-element simulation. For a first sizing, Sabine/Eyring remain the go-to tools: fast, robust and accurate enough.
What targets to aim for?
The "right" RT depends on use. For speech (classrooms, meeting rooms, offices) you want a short RT (0.4–0.8 s) for intelligibility. For music, a longer RT is welcome (1.4–2.2 s in a classical concert hall) as it adds warmth and fullness. In France, the 25 April 2003 decree sets regulatory ranges for teaching spaces; the NF S 31-080 standard frames offices. Pick a room type in the tool to compare your prediction with the matching target.
Worked examples
| Situation | RT ≈ | Reading |
|---|---|---|
| Room 200 m³, A = 20 m² | 1.6 s | bare classroom, too reverberant |
| Same room, A = 40 m² | 0.8 s | absorption doubled → RT ÷2 |
| Auditorium 2000 m³, A = 250 m² | 1.3 s | good for speech |
| Studio 60 m³, A = 30 m² | 0.32 s | very dead room (high ᾱ → Eyring) |
- Forgetting that \(\alpha\) is frequency-dependent: a single number won't do — reason per band.
- Counting a surface twice, or leaving out the floor / ceiling in the area budget.
- Using Sabine on a heavily treated room: it overestimates the RT — switch to Eyring.
- Confusing prediction (from materials) with measurement (in situ, ISO 3382).
- Putting panels only on the ceiling and being surprised the diffuse field no longer holds.
Related tools
Sources : W. C. Sabine, Collected Papers on Acoustics (1922); C. F. Eyring, JASA (1930); H. Kuttruff, Room Acoustics; absorption coefficients from standard tables (Bies & Hansen, Vorländer); ISO 3382-2 (measurement); 25 April 2003 decree; NF S 31-080.