MotionLab

Decibel Calculator

A logarithmic scale because our ears perceive loudness logarithmically.

Sound intensity (W/m²)

Reference intensity (W/m²)

Sound level (dB)

dB = 10 × log₁₀(I / I₀)

What you entered

Sound intensity (W/m²): 0.001Reference intensity (W/m²): 1e-12

1
Intensity ratio
1.00e-3 ÷ 1.00e-12= 1000000000
2
dB = 10 × log₁₀(I ÷ I₀)
10 × log₁₀(1000000000)= 90 dB

Result

Sound level (dB): 90

An intensity of 1.00e-3 W/m² is 90 dB relative to the reference of 1.00e-12 W/m².

Sound intensity in decibels

Decibels are ten times the base-10 logarithm of the intensity ratio, referenced to 1e-12 W/m2, the threshold of hearing.

Intensity (W/m2)	Reference (W/m2)	Decibels	Roughly
1e-12	1e-12	0.00	Threshold of hearing
1e-6	1e-12	60.00	Conversation
1e-4	1e-12	80.00	Busy traffic
1e-2	1e-12	100.00	Pneumatic drill
1	1e-12	120.00	Threshold of pain

The scale is logarithmic, so every 10 dB is ten times the intensity: 80 dB carries a hundred times the energy of 60 dB, not a third more. Across the table, the top row has a trillion times the intensity of the bottom - which is exactly why the decibel exists, since a linear scale would be unusable. Perceived loudness roughly doubles every 10 dB, so 80 dB sounds about four times as loud as 60. Hearing damage depends on both level and duration, with risk beginning around 85 dB over sustained exposure.

Why a logarithmic scale

Human hearing spans an enormous range — from the threshold of hearing (10⁻¹² W/m²) to the threshold of pain (about 1 W/m²), a factor of 10¹². The decibel scale compresses this trillion-fold range into a manageable 0–120 dB span by using logarithms.

Every 10 dB sounds roughly twice as loud

A 10 dB increase represents a 10× increase in intensity but is perceived as roughly double the loudness — so 80 dB (busy traffic) sounds about twice as loud as 70 dB (normal conversation), even though it carries 10 times more acoustic energy.

Frequently asked questions

A lawn mower produces 90 dB and a chainsaw produces 110 dB. How much louder is the chainsaw?

The difference is 20 dB = two 10 dB steps. Each 10 dB doubles perceived loudness, so the chainsaw sounds about 4× louder. In intensity, 20 dB = 100× more acoustic power — the relationship between perceived loudness and actual intensity is logarithmic.

What does 0 dB mean — is it total silence?

No — 0 dB is the threshold of human hearing (10⁻¹² W/m²), not the absence of sound. Negative dB values are possible and represent sounds below the hearing threshold. An anechoic chamber can measure -20 dB, which is simply 100× quieter than the faintest sound most people can hear.

At what decibel level does hearing damage begin?

Sustained exposure above 85 dB causes gradual hearing damage (busy traffic, food blender). At 100 dB (concert, power tools), damage can begin within 15 minutes. At 120 dB (jet takeoff nearby), pain begins instantly. At 140 dB, immediate permanent damage is likely. Always wear hearing protection above 85 dB.