Predicting Sound Insulation (EN 12354)

By José M. Requena Plens · Published Jul 15, 2026, updated Jul 26, 2026

Standards: EN 12354Key references: Hopkins 2007

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 from laboratory element data: the airborne and impact flanking models of EN 12354-1/2 with their junction vibration reduction indices, and the façade insulation and outdoor radiation of EN 12354-3/4. The measured quantities the model is checked against live in Field Insulation Measurement and Ratings; the laboratory inputs come from Laboratory Insulation Measurement.

How do I predict sound insulation with EN 12354 in Python?

Build the three flanking paths of each junction with building.flanking_element(), then combine them with building.predicted_airborne_insulation(r_direct=57.0, flanking_paths=paths). For the EN 12354-1 Annex H.3 example below it returns r_prime_w = 52.2 dB, that is $R_{w}^{'}$ = 52 dB, and names the dominant path. Impact insulation goes through predicted_impact_insulation().

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.

The direct path Dd through the separating element and the three flanking paths Ff, Df and Fd across each junction between a flanking element and the separating element

Each junction between a flanking element and the separating element carries three paths, $F f$ (flanking→flanking), $D f$ (direct→flanking) and $F d$ (flanking→direct), alongside the single direct path $D d$ .

Download the animation (WebM)

The simplified single-number model combines them energetically (Formula 26):

R_{w}^{'} = - 10 lo g_{10} [1 0^{- R_{D d, w} /10} + \sum 1 0^{- R_{F f, w} /10} + \sum 1 0^{- R_{D f, w} /10} + \sum 1 0^{- R_{F d, w} /10}],

with the direct path $R_{D d, w} = R_{s, w} + Δ R_{D d, w}$ (Formula 27) and each flanking path (Formula 28a)

R_{ij, w} = \frac{R _{i, w} + R _{j, w}}{2} + Δ R_{ij, w} + K_{ij} + 10 lo g_{10} \frac{S _{s}}{l _{0} l _{f}},

where $l_{0} = 1$ m is the reference coupling length, $l_{f}$ the junction coupling length and $K_{ij}$ the junction’s vibration reduction index (Annex E, empirical in the mass ratio $M = lo g_{10} (m_{⊥, i}^{'} / m_{i}^{'})$ ).

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)

Show the code for this figure

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 $R_{w}^{'}$ below the direct $R_{D d, w} = 57$ ; 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 $K_{ij} \geq K_{ij, m i n}$ 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:

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: $L_{n, w}^{'} = L_{n, w, e q} - Δ L_{w} + K$ , with the bare-floor equivalent level $L_{n, w, e q} = 164 - 35 lo g_{10} (m^{'} / m_{0}^{'})$ (Annex B), the covering improvement $Δ L_{w}$ (ISO 717-2) and the flanking correction $K$ from Table 1.

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 EN 12354-2 Annex E.3 impact prediction as its Formula 21 terms: the bare-floor equivalent level of 76.2 dB, the minus 33 dB floating-floor improvement, the plus 2 dB flanking correction, and the resulting predicted apparent impact level of 45.2 dB

The whole EN 12354-2 simplified model is one subtraction: the massive bare floor starts at $L_{n, w, e q} = 76.2$ dB, the floating floor buys back 33 dB, and the flanking correction returns 2 dB, landing at $L_{n, w}^{'} = 45$ dB.

Show the code for this figure

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), $D_{n T} = R^{'} + 10 l g (0.32 V / S_{s})$ , 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 $V / (3 S)$ chain 53.8 dB, both rounding to $D_{n T, w} = 54$ dB).

The three insulation guides close a loop: the laboratory measures $R$ and $K_{ij}$ element by element and junction by junction, this model assembles them into a predicted $R_{w}^{'}$ , and the field measurement 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'` (K13) / `'corner'` (K12 = K23) / `'double_leaf'` (K24)	Path branch
`mass_ratio`	float	—	> 0	`m'⊥,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 `Kij` for the three paths
`separating_area`	float	m²	> 0	Separating-element area `Ss`
`coupling_length`	float	m	> 0	Junction coupling length `lf`
`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 `SF`; enables the automatic `Kij,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 `Ss`
`coupling_length`	float	m	> 0	Junction coupling length `lf`
`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'w); ImpactPredictionResult.report() renders the predicted apparent impact-level fiche (the Formula (21) term table beside the term plot, the boxed L'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 exactly as in the measurement fiches; the applicable ReportMetadata fields are the separating element (specimen), the separating-element or floor area (area), the room geometry (source_volume, receiving_volume), the bare floor’s mass (mass_per_area, impact), the manufacturer (manufacturer), the test room or facility (test_room), the calculator/laboratory identity (client, laboratory, operator, report_id, test_date) and a free-text summary of the flanking construction and model assumptions (notes).

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
air.report("Rpw_prediction_paths.pdf", verbose=True)           # + energy share

# Impact prediction (EN 12354-2 Annex E.3): a concrete floor (m' = 322 kg/m²)
# with a floating floor (ΔLw = 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

Both example fiches are regenerated with make reports and kept rendered in the repository; click either preview to open the PDF.

Predicted airborne EN 12354-1 example report (PDF) — Predicted airborne fiche (AirbornePredictionResult.report), R'w.

Predicted impact EN 12354-2 example report (PDF) — Predicted impact fiche (ImpactPredictionResult.report), L'n,w.

Façade insulation & radiated power (EN 12354-3 / -4)

Parts 3 and 4 predict the two directions across the building envelope, both from the same energy summation of the element transmission factors $τ = 1 0^{- R /10}$ , area-weighted by $S_{i} / S$ (a small element or air path enters through its element-normalized level difference $D_{n, e}$ with the reference area $A_{0} = 10 m^{2}$ ):

R^{'} = - 10 lo g_{10} (i \sum \frac{S _{i}}{S} 1 0^{- R_{i} /10} + k \sum \frac{A _{0}}{S} 1 0^{- D_{n, e, k} /10}) .

Part 3: outdoor → indoor. From $R^{'}$ (Formula 10) follow the loudspeaker- and traffic-referenced indices $R_{45} = R^{'} + 1$ and $R_{t r, s} = R^{'}$ , and the primary output, the standardized level difference at 2 m (Formula 13)

D_{2 m, n T} = R^{'} + Δ L_{f s} + 10 lo g_{10} \frac{V}{6 T _{0} S}, T_{0} = 0.5 s,

with the façade-shape term $Δ L_{f s}$ (Annex C; 0 dB for a flat reflecting façade; facade_shape_level_difference looks it up from the Figure C.2 table for galleries, balconies and terraces, interpolating over the underside absorption $α_{w}$ ). Single-number ratings reuse EN ISO 717-1 (weighted_rating).

Per-element partial sound reduction indices and the resulting façade apparent reduction R' and standardized level difference D2m,nT for the EN 12354-3 Annex F worked example, the air inlet limiting the low bands

from phonometry import building

# EN 12354-3 Annex F: an 11.3 m² façade (V = 50 m³, flat so ΔLfs = 0) of a double
# wall, a window, a small skylight and an acoustically-treated air inlet (a Dn,e
# element).
elements = [
    building.FacadeElement("wall",     area=6.0, r=[41, 46, 52, 58, 64]),   # octave 125-2000
    building.FacadeElement("window",   area=4.5, r=[23, 22, 30, 36, 37]),
    building.FacadeElement("skylight", area=0.5, r=[24, 27, 30, 33, 30]),
    building.FacadeElement("air inlet", dn_e=[28, 23, 25, 38, 44]),         # small element
]
fac = building.facade_sound_reduction(elements, area=11.3, volume=50.0,
                             frequencies=[125, 250, 500, 1000, 2000], bands="octave")
print(fac.r_tr_s_w, fac.c_tr, fac.d_2m_nt_w)   # 31 -3 33  (R'tr,s,w / Ctr / D2m,nT,w)

fac.plot()   # per-element partial indices with R' and D2m,nT overlaid (needs matplotlib)

Show the code for this figure

import numpy as np
import matplotlib.pyplot as plt
from phonometry import building

# EN 12354-3 Annex F: an 11.3 m² façade (V = 50 m³, flat so ΔLfs = 0) of a double
# wall, a window, a small skylight and an acoustically-treated air inlet (a Dn,e
# element).
elements = [
    building.FacadeElement("wall",     area=6.0, r=[41, 46, 52, 58, 64]),   # octave 125-2000
    building.FacadeElement("window",   area=4.5, r=[23, 22, 30, 36, 37]),
    building.FacadeElement("skylight", area=0.5, r=[24, 27, 30, 33, 30]),
    building.FacadeElement("air inlet", dn_e=[28, 23, 25, 38, 44]),         # small element
]
fac = building.facade_sound_reduction(elements, area=11.3, volume=50.0,
                             frequencies=[125, 250, 500, 1000, 2000], bands="octave")

x = np.arange(5)
fig, ax = plt.subplots(figsize=(9, 5.5))
for name, rp in fac.element_r.items():
    ax.plot(x, rp, "--", alpha=0.6, marker=".", label=f"Rp — {name}")
ax.plot(x, fac.r_prime, "k-", lw=2.5, marker="o", label="R′ (façade)")
ax.plot(x, fac.d_2m_nt, lw=2, marker="s", label="D2m,nT")
ax.set_xticks(x); ax.set_xticklabels([125, 250, 500, 1000, 2000])
ax.set_xlabel("Frequency [Hz]"); ax.set_ylabel("Index / level difference [dB]")
ax.set_title("EN 12354-3 façade sound insulation (Annex F)")
ax.legend(ncol=2); ax.grid(alpha=0.4)
fig.tight_layout(); plt.show()

The façade prediction also writes a one-page prediction report through a report(path) method, the same layout as the airborne and impact prediction fiches. FacadePredictionResult.report() renders the façade-element table (each element’s weighted partial index Rp,w) beside the per-element / R' / D2m,nT plot, the boxed predicted D2m,nT,w (with R'tr,s,w and Ctr), the prediction statement and, when a requirement is supplied, a PASS/FAIL verdict (the level difference passes at or above it). verbose=True annexes each element’s share of the transmitted sound energy, which singles out the limiting element (the air inlet here, not the wall). The report needs the ISO 717-1 single-number ratings, so build the result on the 5 octave or 16 one-third-octave bands. The applicable ReportMetadata fields describe the predicted situation: specimen (the façade element set), area (the exposed façade area), the receiving-room receiving_volume, the outdoor/traffic situation in test_room, plus the calculator / laboratory identity fields (client, manufacturer, measurement_standard, laboratory, operator, report_id, test_date), a free-text façade-shape and model summary in notes and the target D2m,nT,w in requirement. Metadata, language="es" and the phonometry[report] extra behave as in the measurement fiches.

from phonometry import building, ReportMetadata

# EN 12354-3 Annex F facade -> D2m,nT,w = 33 dB (R'tr,s,w = 31, Ctr = -3).
elements = [
    building.FacadeElement("Masonry wall", area=6.0, r=[41, 46, 52, 58, 64]),
    building.FacadeElement("Glazing",      area=4.5, r=[23, 22, 30, 36, 37]),
    building.FacadeElement("Roof light",   area=0.5, r=[24, 27, 30, 33, 30]),
    building.FacadeElement("Air inlet", dn_e=[28, 23, 25, 38, 44]),
]
fac = building.facade_sound_reduction(elements, area=11.3, volume=50.0,
                             frequencies=[125, 250, 500, 1000, 2000], bands="octave")
fac.report("D2mnT_prediction.pdf", metadata=ReportMetadata(
    specimen="Masonry wall + window + roof light + air inlet", area=11.3,
    receiving_volume=50.0, requirement=30.0,
    notes="Flat facade, ΔLfs = 0 dB (Annex C)."))          # D2m,nT,w = 33 dB

Predicted facade EN 12354-3 example report (PDF) — Predicted facade fiche (FacadePredictionResult.report), D2m,nT,w.

Part 4: indoor → outdoor. The sound power level radiated by a segment (Formula 2) is $L_{W} = L_{p, in} + C_{d} - R^{'} + 10 lo g_{10} (S / S_{0})$ with $S_{0} = 1$ m² and the inside-field diffusivity term $C_{d}$ (Annex B; −6 dB ideal diffuse, −5 dB average industrial). Openings are elements whose “R” is the silencer insertion loss (a bare opening is 0 dB). The exterior level follows from the simplified Annex E attenuation $A_{t o t}$ of a finite radiating side, $L_{p} = L_{W} - A_{t o t}$ .

from phonometry import building

# EN 12354-4 Annex G, side 1: a 10×20 m concrete wall segment with a 6×4 m
# industrial door, inside level Lp,in, Cd = -5 dB. The 40 dB cap on R' is an
# Annex G example footnote (field leaks), not part of Formula (2)/(3): pass it
# explicitly to reproduce Annex G; by default no cap is applied.
bands = [63, 125, 250, 500, 1000, 2000, 4000, 8000]
seg = building.radiated_sound_power(
    [building.FacadeElement("wall", area=176.0, r=[32, 36, 36, 33, 39, 49, 57, 63]),
     building.FacadeElement("door", area=24.0,  r=[21, 23, 28, 30, 30, 30, 30, 30])],
    lp_in=[70, 74, 76, 72, 70, 67, 62, 57], area=200.0, c_d=-5.0,
    r_prime_cap=40.0, octave_bands=bands)
print(round(seg.l_w[0], 1), round(seg.l_w[1], 1))     # 59.8 61.2  (LW at 63/125 Hz)

# Exterior level 5 m in front of the centre of the 60×10 m side (LWA = 62.9 dB(A)).
a_tot = building.outdoor_attenuation(width=60.0, height=10.0, distance=5.0)
print(round(a_tot, 1), round(building.outdoor_level(62.9, a_tot), 1))   # 26.3 36.6

seg.plot()   # radiated LW per octave with the A-weighted LWA line (needs matplotlib)

Radiated sound power level per octave band of the EN 12354-4 Annex G wall segment with an industrial door, with the A-weighted single number drawn as a dashed line across the bars

The Annex G side-1 segment: the wall dominates the area but the door’s weaker $R$ carries the radiated power, so the octave spectrum stays flat where the wall alone would fall. The dashed line is the A-weighted single number $L_{W A}$ formed from the octave bands.

Show the code for this figure

import matplotlib.pyplot as plt
import numpy as np
from phonometry import building

# EN 12354-4 Annex G, side 1: a 10×20 m concrete wall segment with a 6×4 m
# industrial door, inside level Lp,in, Cd = -5 dB.
bands = [63, 125, 250, 500, 1000, 2000, 4000, 8000]
seg = building.radiated_sound_power(
    [building.FacadeElement("wall", area=176.0, r=[32, 36, 36, 33, 39, 49, 57, 63]),
     building.FacadeElement("door", area=24.0,  r=[21, 23, 28, 30, 30, 30, 30, 30])],
    lp_in=[70, 74, 76, 72, 70, 67, 62, 57], area=200.0, c_d=-5.0,
    r_prime_cap=40.0, octave_bands=bands)

# One line — LW per octave with the A-weighted LWA line:
seg.plot()
plt.show()

# By hand, from the result's fields:
x = np.arange(len(bands))
fig, ax = plt.subplots()
ax.bar(x, seg.l_w, label="radiated LW per octave")
ax.axhline(seg.l_w_dba, ls="--", color="tab:red",
           label=f"LWA = {seg.l_w_dba:.1f} dB(A)")
ax.set_xticks(x, [str(b) for b in bands])
ax.set_xlabel("Frequency [Hz]")
ax.set_ylabel("Radiated sound power level [dB re 1 pW]")
ax.set_title("EN 12354-4 radiated sound power (Annex G)")
ax.legend()
plt.show()

Worked-example note. The 2000 worked examples carry small internal rounding inconsistencies at the higher octave bands (Part 3’s printed $R^{'}$ disagrees with its own per-element partial indices at 1 k/2 k; Part 4’s $R^{'}$ rows above 500 Hz disagree with its Table G.2 inputs). The implementation is faithful to the formulas: it reproduces the low bands, every single-number rating and the whole Annex E propagation exactly.

`FacadeElement` / `facade_sound_reduction()` / `radiated_sound_power()` parameters

Parameter	Type	Units	Range / default	Notes
`FacadeElement.area`	float	m²	> 0 for `r` / `insertion_loss`	Element area $S_{i}$ (ignored for `dn_e`)
`FacadeElement.r` / `dn_e` / `insertion_loss`	float or seq	dB	give exactly one	Area element $R_{i}$ / small-element $D_{n, e}$ / opening insertion loss
`facade_sound_reduction(area)`	float	m²	> 0	Total façade area $S$
`facade_sound_reduction(volume)`	float	m³	> 0	Receiving-room volume $V$ (Formula 13)
`facade_sound_reduction(delta_l_fs)`	float	dB	default `0`	Façade-shape term $Δ L_{f s}$ (Annex C; look it up with `facade_shape_level_difference`)
`radiated_sound_power(lp_in)`	float or seq	dB	—	Inside level $L_{p, in}$ per band
`radiated_sound_power(c_d)`	float	dB	default `-6`	Diffusivity term $C_{d}$ (Annex B)
`radiated_sound_power(r_prime_cap)`	float	dB	default `None` (off)	Optional field cap on $R^{'}$ , an Annex G example footnote (it uses 40 dB), not part of Formula (2)/(3)
`radiated_sound_power(octave_bands)`	seq of int	Hz	default `None`	Octave centres matching the bands; enables the A-weighted $L_{W A}$
`facade_sound_reduction(frequencies)`	seq	Hz	default `None`; length = band count	Band centres carried on the result for plotting
`outdoor_attenuation(width, height, distance)`	float	m	> 0	Finite radiating side and reception distance (Annex E)
`outdoor_level(l_w, attenuation)`	float or seq	dB	broadcast-compatible	Exterior $L_{p}$ from one or more sides (Formula E.1)

facade_sound_reduction() returns a FacadePredictionResult (r_prime, r_45, r_tr_s, d_2m_nt, element_r, and the r_tr_s_w / d_2m_nt_w / c_tr single numbers); radiated_sound_power() a RadiatedPowerResult (l_w, r_prime, l_w_dba). Both expose .plot().

References

European Committee for Standardization. (2000). Building acoustics — Estimation of acoustic performance of buildings from the performance of elements — Part 1: Airborne sound insulation between rooms (EN 12354-1:2000). The simplified airborne flanking-transmission prediction (Annex E junctions, worked example H.3). The linked catalogue record is the BSI Knowledge page for BS EN 12354-1:2000.
European Committee for Standardization. (2000). Building acoustics — Estimation of acoustic performance of buildings from the performance of elements — Part 2: Impact sound insulation between rooms (EN 12354-2:2000). The simplified impact flanking-transmission prediction (worked example E.3). The linked catalogue record is the BSI Knowledge page for BS EN 12354-2:2000.
European Committee for Standardization. (2000). Building acoustics — Estimation of acoustic performance of buildings from the performance of elements — Part 3: Airborne sound insulation against outdoor sound (EN 12354-3:2000). The façade sound insulation prediction (Annex F worked example). The linked catalogue record is the BSI Knowledge page for BS EN 12354-3:2000.
European Committee for Standardization. (2000). Building acoustics — Estimation of acoustic performance of buildings from the performance of elements — Part 4: Transmission of indoor sound to the outside (EN 12354-4:2000). The outdoor-radiation prediction (Annex G worked example). The linked catalogue record is the BSI Knowledge page for BS EN 12354-4:2000.
Hopkins, C. (2007). Sound insulation. Butterworth-Heinemann. https://doi.org/10.4324/9780080550473The full treatment of flanking transmission and the EN 12354 prediction framework, from the vibration reduction index to its statistical basis. ISBN 978-0-7506-6526-1.

Created and maintained byJosé Manuel Requena Plens· GitHub· PyPI· All projects

Predicting Sound Insulation (EN 12354)

How do I predict sound insulation with EN 12354 in Python?

Predicting performance (EN 12354)

junction_vibration_reduction() / flanking_element() parameters

flanking_path() parameters

EN 12354 prediction report (.report())

Façade insulation & radiated power (EN 12354-3 / -4)

FacadeElement / facade_sound_reduction() / radiated_sound_power() parameters

See also

References

`junction_vibration_reduction()` / `flanking_element()` parameters

`flanking_path()` parameters

EN 12354 prediction report (`.report()`)

`FacadeElement` / `facade_sound_reduction()` / `radiated_sound_power()` parameters