Sound Intensity & Decibel Calculator

Convert between sound intensity (W/m²) and decibels (dB), or find combined sound levels.

Only for combine mode
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Why Sound Levels Use a Logarithmic Scale

The decibel scale compresses an enormous range of sound intensities into manageable numbers. Sound intensity I is power transmitted per unit area in W/m2. Human hearing spans many orders of magnitude, so reporting intensity directly is awkward. Sound intensity level compares I with the reference intensity I0 = 10−12 W/m2, approximately the standard reference near the threshold of hearing.

Because the logarithm is base 10, every increase of 10 dB corresponds to ten times the intensity. An increase of about 3.01 dB corresponds to twice the intensity. Decibels therefore cannot usually be added or averaged like ordinary linear quantities. To combine independent sound sources, convert each level back to intensity, add the intensities, then convert the total to decibels.

L = 10 log10(I/I0)     I = I010L/10
SymbolMeaningWhy it appears / units
LSound intensity levelDecibels (dB), a logarithmic level
ISound intensityW/m2, acoustic power per area
I0Reference intensity10−12 W/m2 for standard airborne sound-intensity level
log10Base-10 logarithmTurns multiplicative intensity ratios into additive level differences

A 90 dB sound has 1000 times the intensity of a 60 dB sound because the 30 dB difference represents three factors of ten. Perceived loudness is related to level but is not identical to intensity; hearing sensitivity depends on frequency, duration, and the listener, so decibels should not be interpreted as a direct linear measure of perceived loudness.

Worked Examples

Example 1: Lawnmower at I=10⁻⁴ W/m²
L = 10 log(10⁻⁴/10⁻¹²)
Result: 80 dB
Typical lawnmower at 1 meter
Example 2: Combine two 70 dB sources
Itotal = 2 × I₇₀
Result: 73 dB
Doubling sources adds only 3 dB
Example 3: Convert 95 dB to intensity
I = 10−12 × 1095/10
Result: I ≈ 3.16 × 10−3 W/m2
A level change that looks modest in dB can represent a very large change in physical intensity.
Example 4: Combine unequal 80 dB and 70 dB sources
Ltotal = 10 log10(108 + 107)
Result: Ltotal ≈ 80.41 dB
The louder source dominates; adding a source 10 dB lower increases the total by only about 0.41 dB.

Common Mistakes

⚠️
Adding decibel values directly

Two independent 70 dB sources produce about 73 dB, not 140 dB. Add their linear intensities first.

⚠️
Using 20 log instead of 10 log for intensity

The 10 log form applies to power-like quantities such as intensity. The 20 log form appears for amplitude ratios such as sound pressure under matching impedance conditions.

⚠️
Forgetting the reference intensity

A decibel level is a ratio relative to a defined reference. For standard sound intensity level in air, I0 is 10−12 W/m2.

⚠️
Assuming dB is a linear loudness scale

A 100 dB sound does not contain twice the intensity of a 50 dB sound. Their intensity ratio is 105.

Frequently Asked Questions

Why does doubling sources only add 3 dB?
Decibels are logarithmic. Doubling intensity (I×2) gives +10 log(2) = +3 dB. You need 10× the intensity for +10 dB, which sounds twice as loud.
What are common dB levels?
0 dB: threshold of hearing. 30 dB: quiet library. 60 dB: conversation. 85 dB: hearing damage threshold. 120 dB: jet engine. 194 dB: theoretical maximum in air.
How much more intense is a sound that is 20 dB higher?
A 20 dB increase corresponds to an intensity factor of 1020/10 = 100. The higher-level sound therefore carries one hundred times the acoustic intensity at the measurement point, assuming both levels use the same reference.
Why are two equal sound sources only about 3 dB louder in level?
Two equal independent sources double the total intensity. Applying the logarithmic definition gives 10 log10(2) ≈ 3.01 dB. The result follows from the logarithm and does not mean the underlying acoustic power increased by only three percent.
Can decibel values be negative?
Yes. A negative sound intensity level means the measured intensity is below the chosen reference intensity; it does not mean negative physical intensity. Highly sensitive measurements can detect sounds below the standard 0 dB reference at some frequencies.
Is sound intensity the same as sound pressure level?
No. Intensity is acoustic power per unit area, while sound pressure is an amplitude quantity measured in pascals. Their level formulas use different logarithmic factors. Under standard propagation conditions they are closely related, but they should not be substituted without considering acoustic impedance and the reference definitions.

Formula Explorer connections

Interpretation: This relationship connects frequency, wavelength, speed, phase, intensity or resonance in an oscillating system. Assumption: Identify the medium, boundary conditions and reference frame. Linear waves, small amplitudes, nondispersive media or ideal resonance may be assumed.

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