What formula does this calculator use?

The inverse-square law for free-field sound propagation: L2 = L1 - 20·log10(d2/d1). Sound pressure is proportional to 1/r in a free field, so doubling distance drops SPL by 20·log10(2) ≈ 6 dB. The 20-factor comes from the dB definition for pressure quantities (20·log10), which in turn reflects the fact that intensity — a power quantity — follows 1/r², so it would use 10·log10, but SPL is pressure-based.

Why does doubling the distance reduce level by approximately 6 dB and not 3 dB?

Doubling distance quadruples the area over which sound energy is spread (surface area of a sphere = 4πr²), so intensity drops by a factor of 4 (−6 dB on a power basis). Because SPL is expressed as 20·log10 of pressure (not 10·log10), the −6 dB result is the same: 20·log10(2) ≈ 6.02 dB. In contrast, electrical power (-3 dB = halved power) uses 10·log10, which is why the numbers differ between acoustic and electrical decibel problems.

When should I enable the hemispherical spreading correction?

Enable it when the sound source sits on or very close to a hard reflective surface (e.g., a road-level lorry engine, a generator on concrete, a speaker cabinet on a floor). The ground acts as a perfect mirror, effectively doubling the radiated power into the upper half-space — adding +3 dB. For an elevated source (e.g., a speaker on a pole, an aircraft overhead) leave it off and use the standard spherical model.

Is this accurate for outdoor noise assessments?

This is a free-field (anechoic) model. For most open-air scenarios it gives a good first estimate. Real-world predictions differ because of ground absorption (soft ground absorbs more than hard), atmospheric refraction (wind and temperature gradients bend sound), obstacles and barriers, and excess attenuation from humidity. For formal noise impact assessments use ISO 9613-2 or CRTN, which add correction terms for each effect.

What is a reference distance of 1 m used for?

1 m is the standard measurement distance used in data-sheet specifications for speakers, tools, and industrial machinery. When a manufacturer says "90 dB SPL at 1 m" you can plug 1 m as d1 and any listening distance as d2 to find the expected level anywhere in a free field.

Can I use this for indoor rooms?

Only as a rough estimate for the direct-field component (the sound that travels in a straight line from source to listener without reflections). Indoors, the reverberant field adds sound from all directions and dominates beyond the critical distance (the point where direct and reverberant energy are equal). For room acoustics use Sabine or Eyring equations in addition to this direct-field estimate.

Decibel Distance Calculator

Sound follows the inverse-square law: as distance from a source doubles, sound pressure level (SPL) drops by roughly 6 dB. This calculator makes that relationship concrete — enter any three of the four quantities (source level, reference distance, new distance, level at new distance) and it solves for the fourth instantly. It also carries a one-click hemispherical spreading correction for ground-level sources, and a quick-reference table showing how common distance multipliers translate to dB changes.

Typical uses include checking whether a speaker array will be intelligible at the back of a hall, estimating noise levels from industrial equipment at a site boundary, verifying that a PA system meets a venue’s sound-ordinance limit, or reverse-engineering the source strength of a measured noise from a known distance.

How it works

The core formula is derived from two acoustic fundamentals. First, in a free field (no reflections), a point source radiates energy equally in all directions; the same total power passes through every spherical surface, so intensity decreases as the inverse of area:

I ∝ 1 / r²

Second, sound pressure level is defined as a pressure ratio expressed on a logarithmic scale: L = 20·log10(p / p_ref). Because acoustic pressure also falls as p ∝ 1/r in the far field, the change in SPL between two distances d1 and d2 is:

L2 = L1 − 20·log10(d2 / d1)

This is the 6 dB per doubling rule: if d2 = 2·d1 then 20·log10(2) ≈ 6.02 dB is subtracted from L1. Every doubling of distance costs approximately 6 dB; every halving gains 6 dB. Moving ten times further away loses 20·log10(10) = 20 dB exactly.

Hemispherical spreading

When a source sits flush with a large hard reflective plane (road surface, concrete floor, asphalt apron), sound that would have gone downward is instead reflected upward and adds constructively to the direct-field radiation. The effective radiated power into the upper half-space is doubled (+3 dB). Toggling the correction in this calculator adds 3 dB to L2 (or subtracts it when solving for d2 or d1) to model this effect.

Solve modes

The same formula rearranges for any of its four variables:

Solve for	Formula
L2 (level at new distance)	`L2 = L1 − 20·log10(d2/d1)`
L1 (source level at d1)	`L1 = L2 + 20·log10(d2/d1)`
d2 (distance for target level)	`d2 = d1 × 10^((L1−L2)/20)`
d1 (inferred reference distance)	`d1 = d2 / 10^((L1−L2)/20)`

All four modes are available from the drop-down in the calculator above.

Worked example

A portable generator is measured at 90 dB SPL at 1 m in the open air. You want to know the expected level at the site boundary, 25 m away:

L2 = 90 − 20·log10(25 / 1)
   = 90 − 20·log10(25)
   = 90 − 20 × 1.3979
   = 90 − 27.96
   ≈ 62 dB SPL

If the generator sits on a concrete pad (hemispherical), add 3 dB: ≈ 65 dB SPL.

To meet a planning limit of 55 dB at the boundary, solve for the required setback:

d2 = 1 × 10^((90 − 55) / 20)
   = 1 × 10^(35/20)
   = 10^1.75
   ≈ 56 m

The generator needs to be at least 56 m from the boundary in free-field conditions.

Formula note

The 20·log10 factor applies to pressure quantities (SPL, voltage, current). For power quantities (acoustic intensity, electrical power) use 10·log10. The two differ because power is proportional to the square of pressure: doubling pressure quadruples power. This calculator works exclusively with dB SPL — a pressure-domain quantity — so the 20-factor is always correct here.