Definition
Schroeder integral — the energy decay the RT is extracted from
\[ L(t) = 10 \log_{10} \left( \int_{t}^{\infty} h^2(\tau)\, d\tau \right) \]
What the symbols mean
- L(t) — Schroeder integrated decay curve (dB)
- h(τ) — room impulse response (Pa)
- t — time (s)
- T₆₀ — reverberation time, read from the slope (s)
Measurement
A speaker plays pink noise; you cut it and the mic records the decay.
Ready. Pick a method and start the measurement.
Low frequencies (63–125 Hz): reliability depends on your speaker.
Decay curve — last measurement
Per octave band results
Measurement series
No measurement in the series yet.
Report
Understand the theory — reverberation timeinteractive
The reverberation time (RT, often written RT60) is the time for the sound level to decay by 60 dB after the source stops. It is the most universal descriptor of room acoustics: a single number that tells whether a room is "dead" or "live", and that drives both speech intelligibility and acoustic comfort. Drag the slider below to see how the decay reshapes as the RT changes.
Drag the RT slider. The decay line (in dB) tilts, and you can see the ranges used for EDT (0 → −10), T20 (−5 → −25) and T30 (−5 → −35).
Measuring is observing. Predicting is anticipating: Sabine's formula links RT to the room volume and its total absorption. Play with volume and absorption to feel the relationship.
RT = 0.161 × V / A. Increase the absorption A (Sabine m²) or reduce the volume V (m³) to bring the reverberation time down.
What does reverberation time describe?
When a source stops in a room, the sound does not vanish instantly: it lingers through successive reflections off the surfaces, losing a little energy at each bounce. This decay is exponential in energy; plotted in decibels, it becomes a straight descending line. The RT is, by definition, the time the level would take to drop by 60 dB — a factor of one million in energy. The more absorptive the room (carpet, audience, panels), the steeper the slope and the shorter the RT; the barer and more reflective it is (concrete, glass), the longer the sound trails.
The Schroeder integral
We never estimate the slope on the raw, fluctuating signal. We use Schroeder's integrated decay curve: by integrating the energy of the impulse response \(h(t)\) backwards in time, we obtain a smooth, monotone curve, ideal for a linear regression:
In practice we first filter the signal into octave bands (or third-octave) — because RT is frequency-dependent — then apply this integral band by band. The slope of the resulting line gives the reverberation time directly.
EDT, T20, T30: three reads of the same slope
From the Schroeder curve, we fit a line over different ranges, always extrapolating to a 60 dB drop:
- EDT (Early Decay Time): slope over 0 → −10 dB, ×6. Driven by the early field, it correlates best with perceived reverberance.
- T20: slope over −5 → −25 dB, ×3. Robust when signal-to-noise is limited.
- T30: slope over −5 → −35 dB, ×2. The reference when dynamics allow (≈ 45 dB SNR).
We start at −5 dB (not 0) to ignore the very onset, disturbed by the direct sound and first reflections. Each estimate's quality is judged by the regression's R²: above 0.99, the decay is nicely linear.
Sabine and Eyring: predicting RT
Sabine's historic formula (1898) links RT to the room volume \(V\) and its equivalent absorption area \(A = \sum_i S_i \alpha_i\) (surfaces × absorption coefficients):
Sabine overestimates RT in highly absorptive rooms. Eyring's formula corrects this using the mean absorption \(\bar\alpha\): \(T = 0.161\,V / (-S\ln(1-\bar\alpha))\). The two converge when \(\bar\alpha\) is small; prefer Eyring once the mean absorption exceeds ~0.2.
Interrupted noise or impulse?
ISO 3382 describes two method families. Interrupted noise excites the room with broadband (pink) noise, then cuts it abruptly: the mic records the decay. Simple, but you must average several cuts because each realisation fluctuates. The impulse response starts from a short sound (balloon, clapper, or a deconvolved sine sweep): more reproducible and better at low frequencies. This tool offers both. In either case, average several mic positions in the room: RT is a property of the volume, not of one point.
Measuring well with a phone
Three precautions make all the difference. (1) Disable the mic's automatic processing (auto-gain, noise suppression, echo cancellation): they distort the slope — handled automatically here. (2) RT is a relative measurement (you read a slope, not an absolute level), so an uncalibrated mic is perfectly fine. (3) For interrupted noise, a Bluetooth speaker is required: latency does not matter (we detect the decay onset in the recorded signal), but low-frequency capability depends on the speaker. Aim for at least 45 dB between source and background noise to use T30.
A few common targets by room type
| Room type | Target RT (s) | Reference |
|---|---|---|
| Classroom (V ≤ 250 m³) | 0.4 – 0.8 | Arrêté 25/04/2003 |
| Meeting room / office | 0.4 – 0.6 | NF S 31-080 |
| Dining hall | 0.6 – 1.2 | Arrêté 25/04/2003 |
| Classical music | 1.4 – 2.0 | Beranek |
| Gym (V < 5000 m³) | 1.5 – 2.0 | Recommendation |
- Measuring in a too-noisy room: without 45 dB of dynamics, T30 is wrong — fall back to T20.
- A single mic position: RT varies in space, average several points.
- Leaving the mic's auto-gain on: it "pulls up" the level during the decay and skews the slope.
- Comparing a mean RT to a target without looking at the spectrum: a room can meet target at 1 kHz yet be too reverberant in the lows.
Related tools
Sources : ISO 3382 (measurement of room acoustic parameters); W. C. Sabine, Collected Papers on Acoustics; C. F. Eyring (1930); J.-C. Pascal, Vibrations et Acoustique (ENSIM, Le Mans University); D. A. Bies & C. H. Hansen, Engineering Noise Control.