Audio

Decibel Distance Calculator

Calculate sound pressure level drop over distance using the inverse square law: −6 dB per doubling of distance.

Quick Answer

Inverse square law: SPL drop = 20 × log₁₀(new distance / reference distance). −6 dB per doubling. 110 dB at 1m → 104 dB at 2m → 98 dB at 4m → 92 dB at 8m.

Calculate SPL at Distance

Reference SPL (dB)

Reference Distance (m)

Target Distance (m)

SPL at 20 m

84.0 dB

Hair dryer, loud TV

Drop from reference: −26.0 dB

SPL at Common Distances

Distance (m)DropSPL (dB)
1−0.0110.0
2−6.0104.0
4−12.098.0
8−18.191.9
16−24.185.9
32−30.179.9
50−34.076.0
100−40.070.0

About This Tool

The Decibel Distance Calculator applies the inverse square law to predict how loud a sound source will be at any distance from its known reference. Live sound engineers use this for venue coverage planning. Concert organizers use it for hearing safety calculations. Architects use it for noise mitigation design. Anyone working with PA, speakers, or environmental noise needs this math.

The Inverse Square Law

For a point source radiating into free air, sound intensity (in watts per square meter) drops as 1 over the distance squared. This is geometric — the sound's energy spreads out over an ever-larger sphere. Doubling the distance quadruples the surface of that sphere, so each square meter receives 1/4 the energy. SPL, measured in decibels, is logarithmic, so this 4× drop in intensity corresponds to a 6.02 dB drop in SPL.

The 6 dB Per Doubling Rule

Memorize this: every time you double the distance from a sound source, SPL drops by 6 dB. From 1m to 2m: −6 dB. From 2m to 4m: another −6 dB. From 4m to 8m: another −6 dB. The cumulative effect is huge — going from 1m to 64m drops SPL by 36 dB, which is the difference between a rock concert front row and a quiet conversation. This rule fails inside reverberant rooms (where reflected sound dominates beyond a critical distance) but holds well outdoors.

Real-World Caveats

The inverse square law assumes a point source in free field. Real-world sources deviate. Line arrays (used in concert PA) behave like cylinders rather than points in their near field, dropping only 3 dB per doubling. Reverberant rooms produce a sound field where reflected energy maintains roughly constant level beyond about 1-2 meters from the source — the "reverberant field." Outdoor sources also lose energy to atmospheric absorption (especially highs) and ground reflection.

Practical Use Cases

Live sound: measure stage volume at 1 meter, then predict SPL at the front, middle, and back of the venue. Use the prediction to choose appropriate PA reinforcement levels. Hearing safety: if a sound source measures 110 dB at 1m, calculate the safe distance at which exposure stays under 85 dB (the OSHA daily limit). 110 − 85 = 25 dB drop, which corresponds to roughly 18× distance. So at 18m or beyond, exposure is safer for extended listening. Neighbor noise: a 100 dB band practice at 1m drops to about 70 dB at 30m — annoying, but legal in most residential noise codes if confined to daytime hours.

Hearing Damage Thresholds

OSHA permits 8 hours at 90 dBA. NIOSH recommends a stricter 8 hours at 85 dBA. Each 5 dB (OSHA) or 3 dB (NIOSH) increase halves the safe duration. At 110 dB, OSHA allows only 30 minutes; NIOSH would allow about 2 minutes. Concerts routinely hit 100-115 dB at the front rows; ear protection is essential for repeat exposure. Musicians' earplugs (typically -15 to -25 dB attenuation, with relatively flat frequency response) preserve sound quality while protecting hearing.

Pair With Other Tools

Use our Reverb Time Calculator for room acoustics, the Speaker Impedance Calculator for amp matching, the Subwoofer Crossover Calculator for sub setup, the Headphone Impedance Matching for personal listening, the LUFS Calculator for streaming targets, or the Note Frequency Calculator for wavelength math.

Frequently Asked Questions

What is the inverse square law?
The inverse square law states that sound intensity from a point source decreases proportionally to 1/distance². For sound pressure level (SPL) in dB, this works out to a 6 dB drop every time the distance doubles. The formula is: SPL drop = 20 × log₁₀(new_distance / reference_distance). At 2× distance, you lose 6 dB. At 4× distance, you lose 12 dB. At 10× distance, you lose 20 dB.
Does the inverse square law always apply?
It applies cleanly only for an idealized point source in free field (no reflections). Real-world sources rarely meet these conditions. Reverberant rooms have a 'critical distance' beyond which reflected sound dominates and SPL stops dropping with distance. Line arrays (used in concerts) behave like cylinders rather than points and lose only 3 dB per doubling in their near field. Outdoor concerts approach inverse square law behavior at a distance.
How loud will my band be at the back of the venue?
If your stage volume measures 110 dB at 1 meter from the speakers, expect ~98 dB at 4 meters, ~92 dB at 8 meters, ~86 dB at 16 meters. Most clubs are about 15-25 meters deep, so the back row is roughly 84-90 dB — well below pain threshold but loud enough that ear protection is wise. PA system design uses this math to ensure adequate SPL at all listener positions.
What is the safe SPL exposure limit?
OSHA permits 90 dBA for 8 hours, with halving the duration for every 5 dB increase: 95 dBA for 4 hours, 100 dBA for 2 hours, 105 dBA for 1 hour. NIOSH uses a stricter 3 dB exchange rate. Above 120 dB, damage can be immediate. Concert venues routinely hit 100-115 dB; ear protection (musicians' earplugs at -15 to -25 dB) is essential for repeated exposure.
Why is doubling distance only -6 dB?
Sound intensity (W/m²) drops by 1/4 when distance doubles, but SPL is measured in decibels using 20 × log₁₀(pressure ratio). Pressure scales with the square root of intensity, so doubling distance gives 1/2 pressure, which is 20 × log₁₀(0.5) = -6.02 dB. The decibel scale is logarithmic, which is why huge intensity drops produce relatively small dB numbers.

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