Noise barrier calculator.

How it works

How do you use the tool?

Choose the source type (line or area) and set the spectrum and sound power (Lw′ per metre or Lw″ per m²). Draw the source on the map, set the barrier height and draw it. Configure the receiver grid, atmosphere and acoustic class, then click “Compute”: the tool shows the Insertion Loss on the map and the statistics.

1. Choose the source type (line or area)
2. Set the spectrum and sound power (Lw′ per metre or Lw″ per m²)
3. Click "Draw on map" and draw the source
4. Set the barrier height, click "Draw on map" and draw the barrier
5. Configure receiver grid, atmosphere, acoustic class
6. Click "Compute" — see Insertion Loss on the map + statistics

How does the calculation work?

For each grid receiver the tool computes two A-weighted Leq, without and with the barrier; the Insertion Loss is the difference IL = Leq_without − Leq_with. Point, line and area sources are discretised into independent point sources. For each point→receiver pair it sums A_div = 20·log₁₀(d) + 11, atmospheric absorption A_atm (ISO 9613-1), ground effect A_gr with factor G, and diffraction A_dif (ISO 9613-2:2024 §7.4).

For each receiver in the grid, the tool computes two A-weighted Leq levels: Leq_without_barrier and Leq_with_barrier. The Insertion Loss is the difference: IL = Leq_without − Leq_with.

Acoustic sources are modelled in three typologies (point, line, area), each with its own equivalent Lw formula and discretisation scheme into point sources. The formulas and selection criteria are described in the "Source types and discretisation" section below. After discretisation, regardless of typology, the model treats each point source as an acoustically independent source.

For each point→receiver pair:

• A_div = 20·log₁₀(d) + 11 — spherical geometric divergence of the single point (for extended sources see note in the "Line source" section below)
• A_atm — atmospheric absorption per 1/3-octave band (63 Hz – 8 kHz), per ISO 9613-1:1993 as a function of temperature and relative humidity
• A_gr — ground effect with factor G (0=acoustically hard, 1=porous), general formula ISO 9613-2:1996 §7.3.2
• A_dif — barrier diffraction, ISO 9613-2:2024 §7.4 (see below)

Source types and discretisation

Real acoustic sources are rarely perfectly point-like. The tool's model handles three typologies. The choice of source type determines the equivalent Lw formula for propagation and the way the source is discretised into point sources for the calculation.

Point source

When to use. Compact sources observed from a distance greater than 2× their characteristic dimension. Typical examples: air-conditioning condenser unit, fixed generator, industrial fan, transmitting antenna.

Equivalent Lw. Lw_eq = Lw — the total sound power level of the source (dB).

Propagation (free field). The geometrical spherical divergence attenuation is A_div = 20·log₁₀(d) + 11 where d is the source-receiver distance in metres. The term 11 = 10·log₁₀(4π) represents free-space radiation (ideal sphere). The level at the receiver: Lp = Lw − A_div − A_atm − A_gr − A_dif, where A_atm, A_gr, A_dif are atmospheric absorption, ground effect, and diffraction terms (see next section).

Line source

When to use. Sources whose length is significant with respect to the receiver distance. Typical examples: road traffic, railway line, industrial pipeline, open drainage channel. Practical rule: if the source length is greater than one third of the minimum receiver distance, the line model is preferable.

Equivalent Lw. The level is specified as power per unit length Lw′ (dB/m). The source is discretised into N equivalent point sources spaced by step metres along the path. Each point represents a section of source of length equal to the local step, and carries:

Lw_i = Lw′ + 10·log₁₀(step)

Adaptive discretisation. The tool uses a 2.5 m step in the zone of barrier projection on the source (extending ±L_barrier/2 from the projection point), 5 m step in the external lateral zones. This improves calculation resolution in the most barrier-shielded region while keeping computational cost contained for long sources. If no barrier is drawn, the discretisation remains uniform at 5 m.

Propagation. Each point propagates as an individual point source with spherical geometric divergence (formula A_div = 20·log₁₀(d) + 11) and its own Lw_i. The total level at the receiver is the energy sum of contributions (see final composition).

Didactic note. The geometric divergence of a real line source (e.g. long road) is cylindrical: −3 dB per doubling of distance, vs −6 dB for spherical. The tool model does not use a direct cylindrical formula: by summing energetically the contributions of many spherical points along the path, when the source is long enough and densely discretised the sum converges to the cylindrical behaviour observed in practice. This is why the dense discretisation (2.5 m step) is particularly important in the barrier projection zone, where point contributions vary rapidly.

Model validity. The line source model is a simplification. Directivity of real sources (e.g. asymmetric emission of vehicular traffic) is not modelled. For expert analyses, specific models are used: NMPB-Routes-2008 for road traffic, NMPB-Fer for railway traffic, which describe the emission spectrum and directivity as a function of vehicle flow and vehicle category.

Area source

When to use. Extended surfaces that emit distributed noise. Typical examples: parking lot with frequent manoeuvres, loading-unloading area, open industrial zone (sum of closely-spaced point sources), large radiating façade.

Equivalent Lw. The level is specified as power per unit area Lw″ (dB/m²). The area is discretised into a regular 10×10 m grid. Each cell has a point source at its centre carrying:

Lw_cell = Lw″ + 10·log₁₀(cell_area) = Lw″ + 20

where cell_area = 100 m².

Propagation. As for line sources: each cell point propagates individually with spherical geometric divergence (A_div = 20·log₁₀(d) + 11), contributions summed energetically at the receiver.

Didactic note. The effective propagation of an area source depends on relative distance: for nearby receivers (distance << area dimension) the behaviour is pseudo-planar (~−3 dB per doubling of distance), for distant receivers (distance >> dimension) it returns spherical (−6 dB per doubling). The model discretised into spherical points reproduces this transition automatically: nearby, adjacent cell contributions dominate; far away, the area appears as a single equivalent point source.

Validity. The 10×10 m discretisation is adequate for typical industrial extensions (100-10000 m²). For very small areas (<100 m²) the area model degenerates to a point source and the latter is preferable. For very large areas (>10000 m²) computational cost grows; subdividing into zones with distinct acoustic characteristics is preferable.

Composition of contributions. Regardless of source type, after discretisation the model treats all point sources as acoustically independent. The attenuation terms (A_div, A_atm, A_gr, A_dif) are computed for each point, and the level at the receiver is the logarithmic sum of sound pressures:

Lp_receiver = 10·log₁₀(Σ 10^(L_pi/10))

This is the incoherent sum of sound levels — consistent with the assumption that points are independent sources (no coherent interference).

Diffraction formulas

The ISO 9613-2 standard is available in two editions (1996 and 2024) and is historically compared with the Maekawa (1968) formula. The tool implements the current ISO 9613-2:2024 §7.4 — the 1996 and Maekawa formulas are reported here as didactic reference and to allow comparison with results from software still based on earlier editions.

1. ISO 9613-2:2024 §7.4 — Current edition (implemented in the tool)

Dz = 10·log₁₀[1 + (2 + (C₂/λ)·C₃·z)·Kmet]   for z > z_min
Dz = 0                                       for z ≤ z_min
z_min = -2λ / (C₂·C₃)

Kmet = exp{-(1/2000)·√[max(d_SS,d_SR)+e]·min(d_SS,d_SR)·d / [2·(z - z_min)]}

C₂ = 20  (ground effect modelled separately)
C₃ = 1   for single diffraction (e = 0)
C₃ = [1 + (5λ/e)²] / [1/3 + (5λ/e)²]   for multiple diffraction

ISO standard in force since January 2024 (supersedes 9613-2:1996). The new Dz formulation introduces the z_min threshold below which the barrier produces no attenuation (correcting the anomalous behaviour of the 1996 edition for very low barriers). The new Kmet explicitly includes the direct distance d and treats the source-edge and edge-receiver distances asymmetrically. Cap 20 dB single / 25 dB multi-barrier (e > 0). The 2024 method also computes lateral diffraction §7.4.3 around the barrier's vertical end edges, combined with the over-the-top path via formula (25) of §7.4.4: near the barrier ends the attenuation drops because sound bends around the side.

2. ISO 9613-2:1996 §7.4 — Previous edition (didactic reference)

Dz = 10·log₁₀(3 + (C2/λ)·C3·z·Kmet)

C2 = 20        (ground reflections modelled separately)
C3 = 1         (single barrier; ≠1 for double barrier, placeholder here)
z = δ          (path difference, equivalent)
Kmet = exp(−(1/2000)·√(d_ss·d_sr/(2z)))   (downwind weather correction)

First edition of the ISO standard for outdoor propagation. More conservative than Maekawa (typically 1-3 dB less) and includes a meteorological factor K_met that reduces barrier effectiveness under wind from source toward receiver. Maximum 20 dB for a single barrier. For over twenty years it was the reference for expert reports in Europe; reported here as a didactic reference, to compare with results from software based on earlier editions of the standard. Proto limitation: C3 fixed at 1 (no double barrier).

3. Maekawa (1968) — original formula, cited in CONCAWE and Bies & Hansen

A_dif = 10·log₁₀(3 + 20·N)
N = 2·δ/λ                  (Fresnel number)
δ = (d_st + d_tr) − d_sr   (path difference)

Assumes an infinitely long barrier, no meteorological correction. Maximum 25 dB. It is the most widespread historical formula, still used today in many commercial software packages. It tends to slightly overestimate attenuation compared to measurements.

The three formulas converge to similar levels for short urban scenarios (<200 m, ordinary barrier height) and diverge for low barriers and long distances — where the 2024 edition introduces the z_min threshold and the revised K_met, and is the most accurate. The 1996 edition is reported as a didactic reference; Maekawa, lacking a weather correction, tends to overestimate attenuation over long range.

All band levels are summed logarithmically with A-weighting. The contribution of all point sources at the receiver is finally summed energetically: Leq = 10·log₁₀(Σ 10^(L_p/10)).

Normative references

• ISO 9613-1:1993 — Acoustics — Attenuation of sound during propagation outdoors. Part 1: Calculation of the absorption of sound by the atmosphere.
• ISO 9613-2:2024 — Acoustics — Attenuation of sound during propagation outdoors. Part 2: Engineering method for the prediction of sound pressure levels outdoors. Current edition, implemented in the tool. Implements updated Dz and Kmet formulas (§7.4.1) compared to the 1996 edition.
• ISO 9613-2:1996 — Earlier edition. Reported in this documentation as didactic reference, to allow verification of continuity with results from software based on earlier editions of the standard.
• Maekawa, Z. (1968). Noise reduction by screens. Applied Acoustics, 1(3), 157-173. DOI 10.1016/0003-682X(68)90020-0.
• Italian Law 447/1995 — Framework law on noise pollution (Italian regulatory framework).
• Italian DPCM 14/11/1997 — Noise source limit values: immission, emission, quality limits by acoustic zone class (Tables A, B, C, D).
• Italian DM 16/03/1998 — Technical methods for measuring noise pollution (reference for sound level surveys imported into the tool).
• Italian Legislative Decree 194/2005 — Implementation of EU Directive 2002/49/EC on strategic noise mapping.

Note on the ISO 9613-2 standard. The calculation engine implements the second edition ISO 9613-2:2024, which redefines the diffraction loss D_z and the meteorological correction K_met compared to the first 1996 edition. The 2024 edition corrects known "shortcomings" with low barriers and large source-to-receiver distances. The 1996 formulation is reported in this documentation as didactic reference, useful for verifying continuity with results from software still based on the previous edition — transition still ongoing internationally. Figures from the two formulations diverge appreciably for low barriers and long-range propagation, and negligibly for short-range urban scenarios.

When the "buildings participate in calculation" option is active, the model uses a worst-screen-wins approach: for each source–receiver pair only one obstacle is considered — building or barrier, whichever has the larger path-difference. This is NOT rigorous multi-screen ISO 9613-2. With multiple cascaded obstacles, real attenuation is typically greater than computed here.

What are the declared limitations?

Line sources do not use real traffic models (no NMPB-Routes-2008 or NMPB-Fer): the user enters Lw′ directly. Multi-barrier is not considered (only the first intercepted segment, C3 fixed at 1). The barrier is opaque (no transmission, solid materials such as concrete), there are no reflections, and the atmosphere is standard: K_met is an average correction, not a vertical profile.

• Line sources ≠ real models: no NMPB-Routes-2008 (traffic flow), no NMPB-Fer for railways. The user enters Lw′ directly.
• Multi-barrier not considered: only the first intercepted barrier segment (C3 fixed at 1 in ISO 9613-2)
• Lateral diffraction (§7.4.3, around the barrier's vertical end edges): computed with the ISO 9613-2:2024 method implemented in the tool. The 1996 edition and the Maekawa formula, reported in the documentation, consider diffraction over the top edge of the barrier only. Diffraction around buildings is not computed.
• Opaque barrier (no transmission): assumes solid materials such as concrete
• No reflections from the source or between barriers
• Standard atmosphere: no profiled thermal/wind gradients (K_met is an average correction, not a vertical profile)