Reverberation Time Calculator (RT60)

The reverberation time T60 is the time it takes the sound pressure level to drop by 60 dB after the source stops, which corresponds to a decay to one thousandth of the pressure. In practice it is usually extrapolated from the decay between 5 and 35 dB (T30), because 60 dB of interference-free dynamic range is rarely available. Wallace Sabine derived his relation empirically from 1895 onwards, based on measurements in lecture halls at Harvard University; the first publication appeared in 1900. The form still used today is: T = 0.161 · V / A, where V is the room volume in cubic metres and A the equivalent absorption area in square metres.

The constant packs the term 24·ln(10)/c, that is the speed of sound and the unit conversion. At 20 °C (c = 343 m/s) it works out to the clean value 0.161 s/m; the equally common value 0.163 corresponds to a somewhat lower temperature of around 12 °C. Both values are usual in the literature; the more common textbook value at 20 °C is 0.161.

The equivalent absorption area A is not a physical surface but a computed quantity: A = Σ Sᵢ · αᵢ + Σ Aⱼ. Each partial surface Sᵢ (wall, floor, ceiling, window) is multiplied by its absorption coefficient αᵢ between 0 (fully reflective) and 1 (fully absorbent), and all contributions are added up. A fully absorbent surface of 10 m² contributes 10 m² of equivalent absorption area, a glass surface of the same size with α = 0.03 only 0.3 m². Furniture and people are added on top as individual absorption areas Aⱼ in square metres.

The absorption coefficient depends on frequency, so reverberation time is calculated per frequency band, usually in octave bands from 125 Hz to 4000 Hz. A single T value is always a simplification. For assessment against DIN 18041 the behaviour between 250 Hz and 2000 Hz matters most, because that is where the tightest tolerance band of ±20 percent applies; at 125 Hz and 4000 Hz the tolerances are wider.

Sabine assumes a diffuse sound field in which the energy is evenly distributed throughout the room and the absorption is low and evenly spread across the surfaces. These assumptions hold well as long as the mean absorption coefficient ᾱ stays small. Above roughly ᾱ = 0.2, Sabine clearly overestimates the reverberation time compared with Eyring. The ratio of Sabine to Eyring is −ln(1 − ᾱ)/ᾱ: at ᾱ = 0.30 the overestimate is around 19 percent, at ᾱ = 0.54 around 43 percent. Eyring itself is an approximation too, just a more consistent one.

The mathematical reason is the model assumption. Sabine treats absorption as if only a small linear share were lost at each reflection. If you set α = 1 for all surfaces (a fully absorbent, reflection-free room), A becomes S and Sabine yields T = 0.161 · V / S, a finite, non-zero reverberation time. Physically, a fully absorbent room has no reverberation at all. That is the well-known weakness of the Sabine formula.

Carl F. Eyring corrected this in 1930 in the Journal of the Acoustical Society of America with T = 0.161 · V / (−S · ln(1 − ᾱ)). Here S is the total room surface and ᾱ the mean absorption coefficient A/S. For ᾱ → 1, ln(1 − ᾱ) goes to minus infinity, so T goes to zero, as it must. At small ᾱ both formulas agree, because −ln(1 − ᾱ) ≈ ᾱ. Rule of thumb for practice: for normally furnished rooms with distributed absorption, Sabine is sufficient. In heavily damped rooms such as recording studios or voice booths, and when absorption is concentrated on one side, calculate with Eyring instead.

DIN 18041:2016-03, "Acoustic quality in small to medium-sized rooms", defines what reverberation time a room should have depending on its use. The German standard separates two room groups. Group A covers listening over medium and larger distances, for example teaching, lectures or music. Group B covers communication over short distances and noise reduction, for example open-plan offices and canteens.

For group A there are five usage types, each with its own target value Ttarget that depends on room volume: A1 music, A2 speech/lecture, A3 teaching/communication, A4 inclusive teaching/communication and A5 sport. "Inclusive" refers to rooms where many listeners are hearing-impaired or are not listening in their native language; the targets are shorter there. Ttarget rises with the logarithm of the volume. For teaching/communication (A3), Ttarget = (0.32 · lg(V/m³) − 0.17) s; for the inclusive variant (A4), Ttarget = (0.26 · lg(V/m³) − 0.14) s. The targets for A1, A2 and A5 are volume-dependent as well and given in the standard. The target refers to the average of 500 Hz and 1000 Hz; the other bands must stay inside the tolerance band around Ttarget, within ±20 percent between 250 Hz and 2000 Hz.

Concretely: a classroom of around 250 m³ should have a reverberation time of 0.60 seconds under A3, around 0.48 seconds for inclusive use (A4), and values around 0.4 seconds are common where language support matters. The validity ranges of the formulas are limited: A1 roughly 30 to 1000 m³, A2 roughly 50 to 5000 m³, A3 roughly 30 to 5000 m³. For sport (A5) roughly 200 to 10000 m³ applies; only sports and swimming halls are considered up to 30000 m³.

Rooms in group B do not get a Ttarget but a minimum absorption requirement via the ratio A/V (equivalent absorption area to volume). For clear room heights up to 2.5 m: B2 (several people, e.g. service counters) A/V ≥ 0.15 m⁻¹, B3 (talking to each other, e.g. private office) ≥ 0.20, B4 (open-plan office) ≥ 0.25, B5 (e.g. teaching pool, canteen) ≥ 0.30. For greater room heights the standard's height-dependent formulas of the form A/V ≥ [c + 4.69 · lg(h/1 m)]⁻¹ apply, with the constant c = 4.80 for B2, 3.13 for B3, 2.13 for B4 and 1.47 for B5.

Once the current state and the target are known, the missing absorption follows directly from Sabine. Rearrange the formula for A: A = 0.161 · V / T. Compute A once with the measured or estimated current reverberation time and once with Ttarget. The difference ΔA = A_target − A_current is the additional equivalent absorption area you need to bring in. This approach is clean as long as ᾱ stays small so Sabine applies; otherwise calculate with Eyring.

Because A is inversely proportional to T, a shorter target reverberation time means more required absorption. Note that ΔA is an equivalent absorption area, so it already contains the absorption coefficient. One square metre of physical panel area only contributes one square metre of ΔA if its absorption coefficient is 1.0. Real panels are below that; the physical area is ΔA divided by the absorption coefficient and therefore always larger than ΔA.

For converting to products, the weighted absorption coefficient αw per ISO 11654 is the practical single-number value, because it is stated on every product datasheet. αw is derived from the practical absorption coefficients αp, which in turn are aggregated from the αs third-octave values into octave values (250 to 4000 Hz). A reference curve is shifted in steps of 0.05 until the sum of the unfavourable deviations (measured value below the reference curve) is at most 0.10; the value of the shifted curve at 500 Hz is αw. For accurate, frequency-resolved planning, however, you should calculate with the per-band αs or αp values, because αw can underrate the low frequencies.

An office with 50 m² of floor area and a height of 3 m, so V = 150 m³. A pure two-person office would actually fall under room group B (A/V requirement); here we assume meeting and phone use and classify it as A2/A3 to show the Ttarget calculation transparently. With Ttarget = 0.32 · lg(150) − 0.17 we get Ttarget = 0.32 · 2.176 − 0.17 = 0.53 s. As a practical target inside the tolerance band we use 0.55 s.

Current state: an empty office with a hard floor, a glass partition and a plasterboard ceiling typically sits around 0.8 s (an estimate, not a measurement). A_current = 0.163 · 150 / 0.8 = 30.6 m². Target: A_target = 0.163 · 150 / 0.55 = 44.5 m². So ΔA = 44.5 − 30.6 ≈ 14 m² of equivalent absorption area is missing. With the stricter target of 0.53 s, ΔA rises to around 16 m². (With the more precise constant 0.161 the values would sit about 1 percent lower, which changes nothing substantial.)

Now the panels. The count follows from n ≈ ΔA / (αw · panel area). With wall panels of 1.2 m × 0.6 m = 0.72 m² and αw = 0.9 (a porous absorber with an air gap to the wall), each panel contributes 0.9 · 0.72 = 0.65 m² of absorption. For ΔA = 16 m² that gives n = 16 / 0.65 ≈ 25 panels. With weaker panels at αw = 0.7 it would be around 32; with ceiling baffles reaching αw close to 1.0, correspondingly fewer units at a smaller individual area. αw is a single-number value; for a guaranteed reverberation time, summing per frequency band is more accurate, but as a rough sizing method this approach is common and defensible.

The calculation shows the two levers: target value and panel quality. 0.55 s instead of 0.53 s saves about two panels here; an αw of 0.9 instead of 0.7 saves around seven. This is exactly the chain the calculator above solves automatically. A note on accuracy: at ΔA = 16 m² on S ≈ 190 m² of room surface, ᾱ is around 0.08, clearly inside Sabine's validity range. Pushing the office down to 0.3 s would raise A_target to around 81 m² and ᾱ above 0.4, where Eyring is more accurate.