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SeriesCalc

🔊 Sound Pressure Level (SPL) Distance Calculator

Calculate the attenuation of sound pressure level over distance in a free field using the Inverse Square Law.

Inputs

dB

Results

Target SPL (L₂)
0.0dB
Attenuation / Drop
-0.0dB

Sound Attenuation Curve

Distance (r)SPL (dB)L₁L₂r₁r₂

Calculator Description

The sound pressure level (SPL) expresses how loud a sound is, in decibels (dB). For a point source the acoustic energy spreads over an area proportional to the square of distance, so the level decays with distance according to the inverse-square law.

What this calculator finds

Given the SPL L₁ at a reference distance r₁ and a target distance r₂, it computes L₂ in a free field (no reflections) via the inverse-square law. It is used to predict noise propagation and judge required screening distance.

Why it matters

  • Assessing impact of factory/machine noise on nearby buildings/workplaces
  • Finding distance/barrier placement to meet noise limits (e.g. 85 dBA)
  • Designing audible range of speakers and alarms

Formula

Inverse Square Law for Sound

The SPL of a point source falls by 20·log₁₀(r₂/r₁) with distance. Doubling the distance lowers the level by 6 dB (energy drops to one quarter).

L2=L1−20 log⁡10 ⁣(r2r1)L_2 = L_1 - 20\,\log_{10}\!\left(\dfrac{r_2}{r_1}\right)
  • L₁ — Sound pressure level at reference distance [dB]
  • L₂ — Sound pressure level at target distance [dB]
  • r₁ — Reference distance [m or ft]
  • r₂ — Target distance [m or ft]

How the formula works

  • Farther away, the dB drops linearly with the log of the distance ratio (a property of the dB scale).
  • Doubling distance gives −6 dB; ten times distance gives −20 dB.
  • Because the scale is logarithmic, small dB differences mean large energy changes (3 dB ≈ double energy).

Assumptions & scope

This applies to a point source in a free field (open space with no reflection/absorption). Indoors, ground effect, air absorption and obstacles add extra attenuation (or amplification).

Worked example

For a machine at L₁ = 90 dB measured at r₁ = 1 m, what is the level at r₂ = 10 m? L₂ = 90 − 20×log₁₀(10/1) = 90 − 20 = 70 dB — the level drops to 70 dB at 10 m.

Useful Tips

Practical tips

  • A 6 dB drop equals doubling distance; simply increasing distance helps noise control.
  • For multiple sources, sum energies (squares) then convert back to dB — not a simple arithmetic sum.
  • Use A-weighting (dBA) in field measurement to reflect human ear sensitivity.

Limitations & cautions

  • It is a free-field model ignoring indoor/reflection/ground effects, so it may differ from measurements.
  • Air absorption matters only at high frequencies and adds attenuation over long distances.
  • Line/area sources (roads, ducts) have different distance dependence and cannot use this formula directly.