Source: https://jmrplens.github.io/phonometry/buildings/design/insulation-prediction/ # Predicting Sound Insulation (EN 12354) A laboratory rating describes an element in isolation; a building also transmits sound along every flanking path. This page covers the EN 12354 prediction of in-situ performance between rooms from laboratory element data: the airborne model of EN 12354-1 with its junction vibration reduction indices, the impact model of EN 12354-2 and the prediction fiches of both. The third and fourth parts of the same family, which cross the building envelope instead of an internal partition, are in [Façade Sound Insulation](https://jmrplens.github.io/phonometry/buildings/insulation/facade-insulation/). The measured quantities the model is checked against live in [Field Insulation Measurement (ISO 16283)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-field/); the laboratory inputs come from [Laboratory Insulation Measurement](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-lab/). ## Predicting performance (EN 12354) A laboratory rating describes an element in isolation, yet the sound a building actually transmits also travels *around* the partition (along the floor, up the façade, through the flanking walls), re-radiating into the receiving room. This **flanking transmission** is the whole difference between the laboratory $R$ and the field $R'$. EN 12354 predicts the in-situ apparent rating from the laboratory ratings of the elements plus the vibration transmission of their junctions. Each junction between a flanking element and the separating element carries three paths, $Ff$ (flanking→flanking), $Df$ (direct→flanking) and $Fd$ (flanking→direct), alongside the single direct path $Dd$. [Watch the high-resolution video (WebM)](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/anim_flanking_paths.webm) The **simplified single-number model** combines them energetically (Formula 26): $$ R'_\mathrm{w} = -10 \log_{10}\Big[ 10^{-R_\mathrm{Dd,w}/10} + \sum 10^{-R_\mathrm{Ff,w}/10} + \sum 10^{-R_\mathrm{Df,w}/10} + \sum 10^{-R_\mathrm{Fd,w}/10} \Big], $$ with the direct path $R_\mathrm{Dd,w} = R_\mathrm{s,w} + \Delta R_\mathrm{Dd,w}$ (Formula 27) and each flanking path (Formula 28a) $$ R_{ij,\mathrm{w}} = \tfrac{R_{i,\mathrm{w}} + R_{j,\mathrm{w}}}{2} + \Delta R_{ij,\mathrm{w}} + K_{ij} + 10 \log_{10}\frac{S_\mathrm{s}}{l_0\ l_\mathrm{f}}, $$ where $l_0 = 1$ m is the reference coupling length, $l_\mathrm{f}$ the junction coupling length and $K_{ij}$ the junction's **vibration reduction index** (Annex E, empirical in the mass ratio $M = \log_{10}(m'_{\perp,i}/m'_i)$). ```python import numpy as np from phonometry import building # EN 12354-1 Annex H.3: a separating wall Rs,w = 57 dB, area Ss = 11.5 m², with # four flanking elements. The simplified model reads each junction's Kij at # 500 Hz from the mass ratio m'perp / m' (Annex E) — here the floor's rigid # cross-junction (the mass ratio is itself rounded, hence 12.5 vs Annex 12.4): print(round(building.junction_vibration_reduction("rigid_cross", "through", 1.61), 1)) # 12.5 KFf print(round(building.junction_vibration_reduction("rigid_cross", "corner", 1.61), 1)) # 8.9 KFd = KDf # Build each element's three flanking paths (Ff, Df, Fd) from the Annex H # tabulated Kij, then combine the direct path Dd energetically (Formula 26). elements = [ # (name, Rw, KFf, KFd = KDf, coupling length lf) ("floor", 49, 12.4, 8.9, 4.50), ("ceiling", 46, 14.4, 9.2, 4.50), ("facade", 42, 12.6, 6.7, 2.55), ("int-wall", 33, 33.5, 15.7, 2.55), ] paths = [] for name, rw, k_ff, k_fd, lf in elements: paths += building.flanking_element(label=name, r_flanking=rw, r_separating=57, k_ff=k_ff, k_fd=k_fd, k_df=k_fd, separating_area=11.5, coupling_length=lf) res = building.predicted_airborne_insulation(r_direct=57.0, flanking_paths=paths) print(round(res.r_prime_w, 1)) # 52.2 -> R'w = 52 dB print(res.dominant.label, round(res.dominant.fraction, 2)) # Dd 0.33 (direct dominates) res.plot() # per-path share of the transmitted energy, largest first (needs matplotlib) ```

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```python import matplotlib.pyplot as plt from phonometry import building # Build each element's three flanking paths (Ff, Df, Fd) from the Annex H # tabulated Kij, then combine the direct path Dd energetically (Formula 26). elements = [ # (name, Rw, KFf, KFd = KDf, coupling length lf) ("floor", 49, 12.4, 8.9, 4.50), ("ceiling", 46, 14.4, 9.2, 4.50), ("facade", 42, 12.6, 6.7, 2.55), ("int-wall", 33, 33.5, 15.7, 2.55), ] paths = [] for name, rw, k_ff, k_fd, lf in elements: paths += building.flanking_element(label=name, r_flanking=rw, r_separating=57, k_ff=k_ff, k_fd=k_fd, k_df=k_fd, separating_area=11.5, coupling_length=lf) res = building.predicted_airborne_insulation(r_direct=57.0, flanking_paths=paths) # Per-path sound reduction index and each path's share of the transmitted # energy for the Annex H.3 result computed above. labels = [p.label for p in res.paths] r_w = [p.r_w for p in res.paths] frac = [100.0 * p.fraction for p in res.paths] fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(9, 6), sharex=True) ax1.bar(labels, r_w, color="tab:blue") ax1.axhline(res.r_prime_w, ls="--", color="k", label=f"R'w = {res.r_prime_w:.1f} dB") ax1.set_ylabel("Path Rij,w [dB]"); ax1.legend() ax2.bar(labels, frac, color="tab:orange") ax2.set_ylabel("Energy share [%]"); ax2.set_xlabel("Transmission path") for ax in (ax1, ax2): ax.tick_params(axis="x", rotation=45) fig.suptitle("EN 12354-1 Annex H.3 — flanking transmission") fig.tight_layout() plt.show() ```

Every added flanking path strictly lowers $R'_\mathrm{w}$ below the direct $R_\mathrm{Dd,w} = 57$; `res.paths` exposes each path's share of the transmitted energy so the dominant path is visible. `flanking_element` is a convenience that builds one junction's three paths at once; the single-path constructor behind it, `flanking_path`, builds one `Ff`, `Df` or `Fd` path at a time (Formula 28a). Clause 4.4.2 also enforces a floor $K_{ij} \ge K_{ij,\min}$ from the junction geometry (Formula 29). Pass the flanking-element area to `flanking_element(..., flanking_area=...)` and the clamp is applied automatically per path; or compute the floor yourself with `junction_min_vibration_reduction` and pass it to `flanking_path(..., kij_min=...)`, which raises a below-floor $K_{ij}$ to the minimum: ```python from phonometry import building # Kij,min = 10 lg[lf·l0·(1/Si + 1/Sj)]; large elements give a low (here negative) # floor, so a realistic tabulated Kij is rarely clamped; but small, light # elements can push it above the tabulated value (e.g. lf = 4 m, S = 1.5 m² # gives 7.3 dB, over the 5 dB lightweight floor). print(round(building.junction_min_vibration_reduction(coupling_length=4.5, s_i=11.5, s_j=11.5), 1)) # -1.1 ``` The impact counterpart (EN 12354-2, Formula 21) is a direct subtraction: $L'_\mathrm{n,w} = L_\mathrm{n,w,eq} - \Delta L_\mathrm{w} + K$, with the bare-floor equivalent level $L_\mathrm{n,w,eq} = 164 - 35 \log_{10}(m'/m'_0)$ (Annex B), the covering improvement $\Delta L_\mathrm{w}$ (ISO 717-2) and the flanking correction $K$ from Table 1. ```python from phonometry import building # EN 12354-2 Annex E.3: a 0.14 m concrete floor (m' = 322 kg/m²) with a floating # floor (ΔLw = 33 dB), rooms one above the other, mean flanking mass 145 kg/m². ln_eq = building.equivalent_impact_level(322.0) # 164 - 35 lg(m') k = building.impact_flanking_correction(322.0, 145.0) # Table 1 (sep 322, flk 145) imp = building.predicted_impact_insulation(ln_w_eq=ln_eq, delta_l_w=33.0, k_correction=k) print(round(ln_eq, 1), k, round(imp.l_prime_n_w, 1)) # 76.2 2 45.2 -> L'n,w = 45 dB # Exact Formula (3): L'nT,w = L'n,w - 10 lg(0.032 V). Annex E.3's own rounding # of the factor to 10 lg(V/30) sits 0.18 dB below; both give L'nT,w = 43 dB. print(round(building.standardized_impact_level(imp.l_prime_n_w, 50.0), 1)) # 43.2 L'nT,w imp.plot() # the Formula (21) terms as bars: Ln,w,eq - dLw + K -> L'n,w (needs matplotlib) ``` *The whole EN 12354-2 simplified model is one subtraction: the massive bare floor starts at $L_\mathrm{n,w,eq} = 76.2$ dB, the floating floor buys back 33 dB, and the flanking correction returns 2 dB, landing at $L'_\mathrm{n,w} = 45$ dB.*

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```python import matplotlib.pyplot as plt import numpy as np from phonometry import building # EN 12354-2 Annex E.3: 0.14 m concrete floor (m' = 322 kg/m2), floating # floor delta-Lw = 33 dB, mean flanking mass 145 kg/m2. ln_eq = building.equivalent_impact_level(322.0) k = building.impact_flanking_correction(322.0, 145.0) imp = building.predicted_impact_insulation(ln_w_eq=ln_eq, delta_l_w=33.0, k_correction=k) # One line — the Formula (21) terms as bars: imp.plot() plt.show() # By hand, from the result's fields: labels = ["Ln,w,eq", "-dLw", "+K", "L'n,w"] values = [imp.ln_w_eq, -imp.delta_l_w, imp.k_correction, imp.l_prime_n_w] fig, ax = plt.subplots() ax.bar(np.arange(4), values) ax.axhline(0.0, color="k", lw=0.8) ax.set_xticks(np.arange(4), labels) ax.set_ylabel("Level / correction [dB]") ax.set_title(f"L'n,w = {imp.l_prime_n_w:.1f} dB (EN 12354-2 Annex E.3)") plt.show() ```

The airborne counterpart of that closure is Formula (5b), $D_\mathrm{nT} = R' + 10\log_{10}(0.32\,V/S_\mathrm{s})$, exposed as `standardized_level_difference`; it closes the Annex H.3 example (`standardized_level_difference(52.2, 50.0, 11.5)` gives 53.6 dB, the printed $V/(3S)$ chain 53.8 dB, both rounding to $D_\mathrm{nT,w} = 54$ dB). The three insulation guides close a loop: the [laboratory](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-lab/) measures $R$ and $K_{ij}$ element by element and junction by junction, this model assembles them into a predicted $R'_\mathrm{w}$, and the [field measurement](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-field/) checks the built result. When the measured value lands well below the prediction, look for a construction defect on the dominant path the model reports: a rigid bridge across a resilient junction, a missing lining, a leak around the separating element. ### `junction_vibration_reduction()` / `flanking_element()` parameters | Parameter | Type | Units | Range / default | Notes | | :--- | :--- | :--- | :--- | :--- | | `junction_type` | str | — | `'rigid_cross'` / `'rigid_t'` / `'flexible_t'` / `'lightweight_facade'` / `'lightweight_double_homogeneous'` / `'lightweight_double_coupled'` / `'corner'` / `'thickness_change'` | Junction geometry (Annex E.3-E.9) | | `path` | str | — | `'through'` ($K_{13}$) / `'corner'` ($K_{12} = K_{23}$) / `'double_leaf'` ($K_{24}$) | Path branch | | `mass_ratio` | float | — | > 0 | $m'_{\perp,i}/m'_i$ (Formula E.2) | | `frequency` | float | Hz | default `500` | `flexible_t` and the E.7/E.8 double-leaf junctions are frequency-dependent | | `r_flanking` / `r_separating` | float | dB | — | Weighted indices of the flanking / separating element | | `k_ff` / `k_fd` / `k_df` | float | dB | — | Junction $K_{ij}$ for the three paths | | `separating_area` | float | m² | > 0 | Separating-element area $S_\mathrm{s}$ | | `coupling_length` | float | m | > 0 | Junction coupling length $l_\mathrm{f}$ | | `delta_r_ff` / `delta_r_fd` / `delta_r_df` | float | dB | default `0` | Lining improvements per path | | `flanking_area` | float | m² | default `None` | Flanking-element area $S_\mathrm{F}$; enables the automatic $K_{ij,\min}$ clamp (Clause 4.4.2 / Formula 29) | ### `flanking_path()` parameters | Parameter | Type | Units | Range / default | Notes | | :--- | :--- | :--- | :--- | :--- | | `label` | str | — | — | Display name of the path | | `kind` | str | — | `'Ff'` / `'Df'` / `'Fd'` | Which flanking branch the path is | | `r_source` / `r_receive` | float | dB | — | Weighted indices of the source-side / receive-side elements | | `k_ij` | float | dB | — | Junction vibration-reduction index for this path | | `separating_area` | float | m² | > 0 | Separating-element area $S_\mathrm{s}$ | | `coupling_length` | float | m | > 0 | Junction coupling length $l_\mathrm{f}$ | | `delta_r` | float | dB | default `0` | Lining improvement on this path | | `kij_min` | float | dB | default `None` | When given, `k_ij` is floored at this Formula (29) minimum | `predicted_airborne_insulation()` returns an `AirbornePredictionResult` (`r_prime_w`, `r_direct_w`, `paths` of `PathContribution`, `dominant`); `predicted_impact_insulation()` an `ImpactPredictionResult` (`l_prime_n_w`, `ln_w_eq`, `delta_l_w`, `k_correction`). The simplified model carries a reported standard deviation of about 2 dB (Clause 5). ### EN 12354 prediction report (`.report()`) Both prediction results write a one-page **prediction** report through a `report(path)` method. Unlike the measurement fiches, the reported result is an *estimate* of the in-situ performance from the elements' laboratory data plus the flanking transmission across the junctions; the sheet states this explicitly and is labelled a prediction, never a measurement. `AirbornePredictionResult.report()` renders the predicted apparent sound reduction index fiche (the transmission-path table beside the per-path share-of-energy plot, the boxed $R'_\mathrm{w}$); `ImpactPredictionResult.report()` renders the predicted apparent impact-level fiche (the Formula (21) term table beside the term plot, the boxed $L'_\mathrm{n,w}$). Each names EN/ISO 12354-1/-2 and the ISO 717 rating part in its basis line, prints the model's ~2 dB standard deviation and, when a `requirement` is supplied, adds a PASS/FAIL verdict (airborne passes at or above it, impact at or below it). `verbose=True` annexes each transmission path's share of the transmitted energy to the airborne table; metadata, `language="es"` and the `phonometry[report]` extra behave as in the measurement fiches. ```python from phonometry import building, ReportMetadata # Airborne prediction (EN 12354-1 Annex H.3): a separating wall Rs,w = 57 dB # flanked by four elements -> R'w = 52 dB. paths = [] for label, rw, kff, kfd, lf in [ ("floor", 49.0, 12.4, 8.9, 4.5), ("ceiling", 46.0, 14.4, 9.2, 4.5), ("facade", 42.0, 12.6, 6.7, 2.55), ("intwall", 33.0, 33.5, 15.7, 2.55), ]: ff, df, fd = building.flanking_element( label=label, r_flanking=rw, r_separating=57.0, k_ff=kff, k_fd=kfd, k_df=kfd, separating_area=11.5, coupling_length=lf) paths += [ff, df, fd] air = building.predicted_airborne_insulation(r_direct=57.0, flanking_paths=paths) air.report("Rpw_prediction.pdf", metadata=ReportMetadata( specimen="Separating wall, Rs,w = 57 dB", area=11.5, source_volume=53.0, receiving_volume=50.0, requirement=50.0, notes="Flanking: floor/ceiling/facade/internal wall.")) # R'w = 52 dB # Impact prediction (EN 12354-2 Annex E.3): a concrete floor (m' = 322 kg/m2) # with a floating floor (DLw = 33 dB) -> L'n,w = 45 dB. ln_eq = building.equivalent_impact_level(322.0) k = building.impact_flanking_correction(322.0, 145.0) imp = building.predicted_impact_insulation(ln_w_eq=ln_eq, delta_l_w=33.0, k_correction=k) imp.report("Lnw_prediction.pdf", metadata=ReportMetadata(mass_per_area=322.0, requirement=53.0)) # L'n,w = 45 dB ``` [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iso12354_airborne_prediction_example.pdf) [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iso12354_impact_prediction_example.pdf) ## Across the envelope: Parts 3 and 4 The two remaining parts of EN 12354 predict the same way but across the building envelope rather than between two rooms: EN 12354-3 the airborne insulation against outdoor sound, EN 12354-4 the sound power an indoor source radiates outwards. Both are built on the same area-weighted summation of element transmission factors used above, and both are covered, beside the ISO 16283-3 measurement they are compared against, in [Façade Sound Insulation](https://jmrplens.github.io/phonometry/buildings/insulation/facade-insulation/). ## References - Hopkins, C. (2007). *Sound insulation*. Butterworth-Heinemann. ISBN 978-0-7506-6526-1. [doi:10.4324/9780080550473](https://doi.org/10.4324/9780080550473). The full treatment of flanking transmission and the EN 12354 prediction framework, from the vibration reduction index to its statistical basis. ## Standards EN 12354-1:2000 and EN 12354-2:2000, which give the simplified flanking-transmission predictions between rooms (Annex E junctions, worked examples H.3 and E.3). The façade and outdoor-radiation predictions of EN 12354-3:2000 and EN 12354-4:2000 have their own page, and the absorption member of the family is EN 12354-6. **Not covered.** The *detailed* per-band models of both parts are a separate page, [Detailed per-band prediction (ISO 12354)](https://jmrplens.github.io/phonometry/buildings/design/detailed-prediction/): the same standard run band by band, with the laboratory element and junction data converted to their in-situ values before the paths are formed. Use the simplified model here when only the weighted element ratings are known and the question is whether the room passes; use the detailed one when the element spectra exist and the question is which path sets which band. The element inputs themselves — $R_\mathrm{w}$, $\Delta R_\mathrm{w}$, $\Delta L_\mathrm{w}$, mass per unit area — are taken as given, from laboratory data or from the mass-law estimates of [Predicting panel sound insulation](https://jmrplens.github.io/phonometry/buildings/design/panel-sound-insulation/). **EN 12354-5** (service equipment) is in [Installed structure-borne sound](https://jmrplens.github.io/phonometry/buildings/design/installed-structure-borne/). ## See also - [Façade Sound Insulation](https://jmrplens.github.io/phonometry/buildings/insulation/facade-insulation/): the EN 12354-3 and EN 12354-4 predictions across the building envelope, with the ISO 16283-3 measurement they are compared against. - [Field Insulation Measurement (ISO 16283)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-field/): the measured in-situ quantities the prediction is checked against. - [Insulation Ratings (ISO 717)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-ratings/): the reference-curve engine behind the predicted $R'_\mathrm{w}$ and $L'_\mathrm{n,w}$. - [Laboratory Insulation Measurement](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-lab/): the ISO 10140 ratings the model consumes. - [Laboratory Flanking Transmission (ISO 10848)](https://jmrplens.github.io/phonometry/buildings/insulation/flanking-lab/): the measured junction vibration reduction index $K_{ij}$ the model consumes. - [Sound absorption in enclosed spaces (EN 12354-6)](https://jmrplens.github.io/phonometry/buildings/rooms/enclosed-space-absorption/): the absorption member of the same EN 12354 family. - [Dynamic stiffness of resilient materials (EN 29052-1)](https://jmrplens.github.io/phonometry/materials/resilient/dynamic-stiffness/): the $s'$ input to the EN 12354-2 floating-floor term. - API reference: [`building.prediction.simplified_model`](https://jmrplens.github.io/phonometry/reference/api/building/simplified-model/) and [`building.prediction.facade`](https://jmrplens.github.io/phonometry/reference/api/building/facade/).