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Walk-through

How to Use This Calculator

3 steps

1

Convert between intensity and decibels

Use the dB ↔ Intensity tab to convert a sound intensity in watts per square meter (W/m²) into a decibel level, or the other way around. Enter a value in either field — intensity or dB — and the calculator solves for the other using dB = 10·log10(I / I0), where I0 = 1×10⁻¹² W/m² is the threshold of human hearing.

2

Find the level at a new distance

Switch to the Distance tab, enter the decibel level you measured at a reference distance d1, then enter a second distance d2. The calculator applies the inverse-square law (dB2 = dB1 − 20·log10(d2/d1)) to estimate how loud the sound will be at the new distance, and plots the falloff curve.

3

Combine multiple sources

On the Combine tab, enter the decibel level of each independent sound source (up to six) and add or remove rows as needed. The calculator converts each dB value back to intensity, sums the intensities, and converts the total back to a combined decibel level — because decibels are logarithmic, they can't simply be added together.

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Reference

Formula & Methodology

3 formulas

Decibel level from intensity

dB = 10 · log10(I / I0)

I is the sound intensity in watts per square meter (W/m²) and I0 = 1×10⁻¹² W/m² is the reference intensity — the quietest sound the average human ear can detect (the threshold of hearing, defined as 0 dB).

Level at a new distance

dB2 = dB1 − 20 · log10(d2 / d1)

Sound intensity falls off with the square of distance from a point source (the inverse-square law), which becomes a 20·log10 term once converted to the logarithmic decibel scale. Every doubling of distance reduces the level by about 6 dB; every 10× increase in distance reduces it by exactly 20 dB.

Combining independent sources

dB_total = 10 · log10( Σ 10^(dBᵢ/10) )

Decibels are logarithmic, so they cannot be added directly. Each source is converted back to a linear intensity (I0 · 10^(dB/10)), the intensities are summed, and the total is converted back to decibels.

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Glossary

Key Terms Explained

7 terms

Decibel (dB) A logarithmic unit that expresses sound level relative to a fixed reference intensity. Because human hearing spans an enormous range of intensities, decibels compress that range into more manageable numbers — a 10 dB increase represents a 10× increase in intensity.

Sound intensity The rate at which sound energy passes through a unit area, measured in watts per square meter (W/m²). It is the linear (non-logarithmic) physical quantity that decibels are derived from.

Reference intensity (I0) The standard reference point for the decibel scale, I0 = 1×10⁻¹² W/m² — approximately the quietest sound a healthy human ear can detect, defined as 0 dB.

Logarithmic scale A scale where each fixed step represents a multiplicative change rather than an additive one. On the decibel scale, every +10 dB step corresponds to a 10× increase in intensity, not a 10-unit increase.

Inverse-square law The physical principle that intensity from a point source falls off in proportion to 1/distance². It's why sound (and light, and radiation) gets quieter — or dimmer — much faster than distance alone would suggest.

Loudness The subjective, perceived strength of a sound, which correlates with but isn't identical to decibel level. As a rule of thumb, a 10 dB increase is perceived as roughly twice as loud, even though it represents a 10× increase in physical intensity.

Threshold of hearing The quietest sound intensity a healthy human ear can detect under ideal conditions, defined as 0 dB (equal to the reference intensity I0 = 1×10⁻¹² W/m²).

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Scenarios

Real-World Examples

3 worked examples

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Physics student

Converting a measured intensity to decibels

Sound intensity 0.000001 W/m² (1×10⁻⁶)

An intensity of 1×10⁻⁶ W/m² — typical of a quiet room — converts to 10·log10(1×10⁻⁶ / 1×10⁻¹²) = 10·log10(10⁶) = 60 dB. Doubling that intensity to 2×10⁻⁶ W/m² only raises the level to about 63 dB, illustrating how compressed the decibel scale is.

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Site safety officer

Estimating exposure at a new distance

Level at d1 60 dB at 1 m New distance d2 10 m

Moving from 1 m to 10 m — a 10× increase in distance — drops the level by 20·log10(10) = 20 dB, from 60 dB down to 40 dB. This is why standing well back from a loud machine or speaker makes such a large practical difference, even though the source itself hasn't changed.

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Audio engineer

Combining two identical sound sources

Source 1 60 dB Source 2 60 dB

Two 60 dB sources playing together don't add to 120 dB — their intensities sum (1×10⁻⁶ + 1×10⁻⁶ = 2×10⁻⁶ W/m²), which converts back to about 63 dB. Doubling the number of identical sources always adds roughly +3 dB, not double the dB value.

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Deep Dive

Why decibels are logarithmic — and how distance quiets sound

3 chapters · 4 min read

The decibel scale exists because the human ear can detect an enormous range of sound intensities — from a whisper to a jet engine, a span of roughly a trillion-to-one. A linear scale covering that range would be unwieldy, so decibels compress it logarithmically. This calculator converts between intensity and decibels, projects how a level changes with distance, and shows why combining sound sources doesn't work the way simple addition would suggest.

How the decibel scale works

Sound intensity (I) is a physical quantity measured in watts per square meter (W/m²) — the rate at which sound energy passes through a unit area. Because the range of intensities the human ear can perceive is so vast, sound level is instead usually expressed in decibels (dB), a logarithmic ratio relative to a fixed reference intensity I0 = 1×10⁻¹² W/m² (the threshold of human hearing): dB = 10·log10(I / I0). Every +10 dB represents a 10× increase in intensity, but is perceived by most listeners as roughly a doubling of loudness — which is why a jet engine at 120 dB is not merely "twice as intense" as a normal conversation at 60 dB, but a million times more intense (10^((120−60)/10) = 10⁶).

Distance and the inverse-square law

Sound spreading outward from a small source follows the inverse-square law: intensity falls off in proportion to 1/distance². Converted to the logarithmic decibel scale, that becomes dB2 = dB1 − 20·log10(d2/d1) — every doubling of distance from the source reduces the level by about 6 dB, and every 10× increase in distance reduces it by exactly 20 dB. This is a simplified free-field model that assumes a point source radiating equally in all directions with no reflections; real-world results vary with directional sources, reflective surfaces, wind, and absorption, so treat the distance tab as an estimate rather than a precise measurement.

Why you can't just add decibels together

Because the decibel scale is logarithmic, two sources at 60 dB each do not combine to 120 dB — they combine to roughly 63 dB. Combining sources correctly means converting each decibel value back into a linear intensity, summing the intensities, and converting the total back to decibels: dB_total = 10·log10(Σ 10^(dBᵢ/10)). A useful shortcut: two equal-level sources always add about +3 dB to the single-source level, ten equal-level sources add about +10 dB, and a much quieter source contributes almost nothing to the total — it gets swamped by the louder one.

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Questions

Frequently Asked Questions

6 questions

What's the formula for the Sound Intensity Calculator?+

The core formula is dB = 10·log10(I / I0), where I is sound intensity in watts per square meter and I0 = 1×10⁻¹² W/m² is the reference intensity (the threshold of hearing, 0 dB). The calculator also uses dB2 = dB1 − 20·log10(d2/d1) for the Distance tab and sums linear intensities for the Combine tab.

What does a +10 dB increase actually mean?+

A +10 dB increase represents a 10× increase in sound intensity, but is typically perceived by human listeners as roughly a doubling of loudness. That's the nature of a logarithmic scale — equal steps in decibels represent equal multiplicative (not additive) changes in the underlying physical intensity.

How does distance affect sound level?+

Under the inverse-square law for a point source, moving to a new distance changes the level by dB2 = dB1 − 20·log10(d2/d1). Doubling the distance drops the level by about 6 dB; a 10× increase in distance drops it by exactly 20 dB. Real-world results can differ due to reflections, directional sources, and absorption.

How do I add two or more decibel levels together?+

You can't add decibel values directly — convert each to a linear intensity (I0 × 10^(dB/10)), sum the intensities, then convert the total back to decibels. The Combine tab does this automatically for up to six sources. Two identical sources always add about +3 dB to a single source's level.

What is the threshold of hearing?+

The threshold of hearing is the quietest sound intensity a healthy human ear can detect under ideal conditions. It's defined as the reference point for the entire decibel scale: I0 = 1×10⁻¹² W/m², equal to 0 dB.

What units does this calculator use?+

Sound intensity is entered and displayed in watts per square meter (W/m²). Decibel level is unitless but written as dB. Distances are entered in meters (m). The calculator encodes your inputs into the URL hash, so copying the page URL is enough to share a specific scenario.

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Sound Intensity Calculator

Intensity → Decibels

Decibels → Intensity

Decibel level

Distance inputs

Level at d2

Level vs. distance

Sound sources

Combined level

How to Use This Calculator

Convert between intensity and decibels

Find the level at a new distance

Combine multiple sources

Formula & Methodology

Key Terms Explained

Real-World Examples

Physics student

Site safety officer

Audio engineer

Why decibels are logarithmic — and how distance quiets sound

How the decibel scale works

Distance and the inverse-square law

Why you can't just add decibels together

Frequently Asked Questions

Get a branded PDF of your results

Sound Intensity Calculator

Intensity → Decibels

Decibels → Intensity

Decibel level

Distance inputs

Level at d2

Level vs. distance

Sound sources

Combined level

How to Use This Calculator

Convert between intensity and decibels

Find the level at a new distance

Combine multiple sources

Formula & Methodology

Key Terms Explained

Real-World Examples

Why decibels are logarithmic — and how distance quiets sound

How the decibel scale works

Distance and the inverse-square law

Why you can't just add decibels together

Frequently Asked Questions

Get a branded PDF of your results

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