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Calcimator

Outdoor Noise Barrier Calculator

Calculate sound barrier insertion loss using the Maekawa method with Fresnel number analysis for outdoor noise barriers.

About this calculator

Barrier Height has the largest measured effect on Insertion Loss at this calculator's defaults, ahead of Frequency, Source to Barrier distance, and Barrier to Receiver distance -- taller barriers force sound to diffract around a longer path, which the Maekawa formula (Z. Maekawa's 1968 published diffraction relationship, IL = 10 x log10(3+20N) for Fresnel number N) converts directly into more attenuation. That relationship is not open-ended, though: the Maekawa method's underlying Fresnel-number formula would keep predicting ever- increasing loss for an ever-taller barrier, but this calculator caps the displayed Insertion Loss at 24 dB, the practical maximum recognized for a single barrier. At the calculator's default source and receiver geometry, that cap is reached once Barrier Height climbs to roughly 8.5-9 m -- well within the input's 20 m maximum -- so raising barrier height past that point no longer changes the result at all, even though the underlying diffraction physics is still technically improving.

Don't assume a barrier is working proportionally better just because it's taller once you're already reading the maximum; check whether Insertion Loss has plateaued at 24 dB before spending more on barrier height. Frequency matters because higher frequencies (shorter wavelengths) produce a larger Fresnel number for the same physical path difference, which is why the calculator's helpText correctly notes that higher frequencies are blocked more effectively -- the same barrier geometry blocks high-pitched noise better than low-pitched noise. Every one of this calculator's six inputs feeds into the geometry that determines path difference, so none of them are structurally inert on Insertion Loss the way some coded selections are in other calculators here.

Inputs

Results

Insertion loss (dB)

14.74

Fresnel number (N)1.34
Path difference (m)0.46
Wavelength (m)0.69
Effective barrier height (m)2.5

Figures current as of 1968. Source: Maekawa, Z. (1968). "Noise reduction by screens." Applied Acoustics, 1(3), 157-173.

How to Use This Calculator
  1. Enter Barrier height (m), Source to barrier (m), and Barrier to receiver (m).
  2. Set Source height (m), Receiver height (m), and Frequency (Hz).
  3. Review the Insertion loss (dB) result.
  4. Use Fresnel number (N) and Path difference (m) to inform your decision.

How the result changes with Barrier height (m)

Barrier height (m)Insertion loss (dB)
1.58.66
2.2512.1
4.518.46
7.522.97

What each input means

Barrier height (m)
Height of the noise barrier above ground level in meters.
Source to barrier (m)
Horizontal distance from the noise source to the barrier in meters.
Barrier to receiver (m)
Horizontal distance from the barrier to the receiver in meters.
Source height (m)
Height of the noise source above ground level (0 for ground-level sources).
Receiver height (m)
Height of the receiver above ground (typically 1.5 m for ear height).
Frequency (Hz)
Sound frequency in Hz. Higher frequencies are blocked more effectively.

What each result means

Insertion loss (dB)
Sound reduction provided by the barrier using the Maekawa formula (max ~24 dB for single barrier).
Fresnel number (N)
Dimensionless number characterizing diffraction; higher N means more attenuation.
Path difference (m)
Difference between the diffracted path over the barrier and the direct path.
Wavelength (m)
Wavelength of the sound at the specified frequency.
Effective barrier height (m)
Height of the barrier above the line of sight between source and receiver.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Barrier height (m) = 3, Source to barrier (m) = 10, Barrier to receiver (m) = 20, Source height (m) = 0 = 6 input(s) provided
  2. Calculate Insertion loss
    Insertion loss
    14.74 = 14.74
  3. Calculate Fresnel number
    Fresnel number = (2 * delta) / wavelength
    1.338 = 1.338
  4. Calculate Path difference
    Path difference = diffractedPath - directPath
    0.459 = 0.459

Figures and sources

Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Is there a point where making the barrier taller stops helping?

Yes. This calculator caps Insertion Loss at 24 dB, the practical maximum recognized for a single noise barrier. At the default source and receiver geometry, that cap is reached once Barrier Height reaches roughly 8.5-9 m -- well below the input's 20 m maximum -- so increasing barrier height beyond that point produces no further change in the displayed result.

What has the biggest effect on insertion loss?

Barrier Height, at this calculator's default source and receiver positions -- it produces a larger swing in Insertion Loss than Frequency, Source to Barrier distance, or Barrier to Receiver distance for an equivalent percentage change, since taller barriers directly lengthen the diffracted sound path relative to the direct path.

Why does frequency affect how much the barrier blocks?

Because a higher frequency has a shorter wavelength, and the Fresnel number that drives the Maekawa formula is the path difference divided by wavelength. The same physical barrier geometry produces a larger Fresnel number -- and therefore more predicted attenuation -- at higher frequencies, which is why noise barriers are consistently more effective against high-pitched sound than low-pitched sound.

Do source height and receiver height matter as much as the horizontal distances?

They matter, but through a different mechanism: source and receiver height set the effective line-of-sight the barrier has to block, changing how much of the barrier's physical height counts as "effective" clearance above that line of sight. All four position inputs (source distance, receiver distance, source height, receiver height) feed into the same path-difference calculation Barrier Height and Frequency do -- none of them are ignored by the formula.

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