Decibel Calculator
Calculate the decibel difference between two intensity levels on the logarithmic scale, using dB = 10 log10 of the intensity ratio.
Decibel Calculator
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Formula: dB = 10 × log₁₀(I₂/I₁)
Worked example — Conversation = 60 dB | Vacuum cleaner = 80 dB | Difference = 20 dB (100x the intensity)
Formula
dB = 10 × log₁₀(I₂/I₁)
Decibels express the ratio between two intensity levels on a logarithmic scale.
Worked Examples
Example 1: Comparing Conversation to a Vacuum Cleaner
Problem:Normal conversation has an intensity of about 1e-6 W/m^2, while a vacuum cleaner has an intensity of about 1e-4 W/m^2 (using the standard reference intensity I1 = 1e-12 W/m^2 for 0 dB). What is the decibel level of each, and how much louder is the vacuum in dB?
Solution:Conversation: dB = 10 x log10(1e-6 / 1e-12) = 10 x log10(1e6) = 10 x 6 = 60 dB Vacuum cleaner: dB = 10 x log10(1e-4 / 1e-12) = 10 x log10(1e8) = 10 x 8 = 80 dB Difference = 80 - 60 = 20 dB, meaning the vacuum's intensity is 100 times greater than conversation
Result:Conversation = 60 dB | Vacuum cleaner = 80 dB | Difference = 20 dB (100x the intensity)
Example 2: Finding the Intensity Ratio from a Decibel Difference
Problem:A rock concert measures 110 dB and a normal conversation measures 60 dB relative to the same reference. What is the ratio of their intensities?
Solution:dB difference = 110 - 60 = 50 dB 50 = 10 x log10(I2/I1) log10(I2/I1) = 5 I2/I1 = 10^5 = 100,000 The rock concert is 100,000 times more intense than normal conversation, even though it sounds only moderately louder to the ear
Result:Intensity ratio = 100,000:1 for a 50 dB difference
Frequently Asked Questions
What is a decibel and why is it logarithmic?
The decibel (dB) is a logarithmic unit used to express the ratio between two intensity levels, defined as dB = 10 x log10(I2/I1). It's logarithmic because human hearing perceives loudness roughly logarithmically, not linearly — a sound with 10 times the intensity is perceived as only moderately louder, not 10 times louder. This compresses the enormous range of intensities the ear can detect (a factor of about one trillion, from a whisper to a jet engine) into a manageable 0-140 dB scale.
How do you calculate a decibel level from two intensities?
Divide the measured intensity by the reference intensity, take the base-10 logarithm, then multiply by 10: dB = 10 x log10(I2/I1). For example, if I2 is 100 times I1, dB = 10 x log10(100) = 10 x 2 = 20 dB. If the intensities are equal (I2 = I1), the result is 0 dB, meaning no change in level, not zero sound.
Why does a 10 dB increase sound twice as loud?
A 10 dB increase corresponds to a 10-fold increase in sound intensity (power), but human perception of loudness does not scale linearly with intensity. Extensive psychoacoustic testing has found that, on average, a 10 dB increase is perceived as roughly a doubling of loudness, even though the actual acoustic energy increased by a factor of 10. This mismatch between physical intensity and perceived loudness is why the decibel scale exists in the first place.
What do common decibel levels correspond to in everyday sound?
0 dB is the threshold of human hearing. A quiet whisper is about 30 dB. Normal conversation is roughly 60-65 dB. City traffic noise is around 80-85 dB. A rock concert can reach 110-120 dB. A jet engine at close range can exceed 140 dB, which is at the threshold of pain and immediate hearing damage. Because the scale is logarithmic, 80 dB is 10 times more intense than 70 dB, not just 10 units louder.
Is the decibel scale only used for sound?
No. The decibel is a general-purpose logarithmic ratio unit used throughout science and engineering wherever quantities span an enormous range, including signal power in electronics and telecommunications (dB, dBm), voltage gain in amplifiers (dBV), radio signal strength (dBi for antenna gain), and even earthquake energy comparisons. The formula dB = 10 x log10(ratio) applies to power-like quantities; for amplitude-like quantities such as voltage, the formula becomes dB = 20 x log10(ratio) because power is proportional to amplitude squared.
How much does the OSHA/NIOSH exposure limit change with decibel level?
Occupational noise exposure limits are set on a time-intensity tradeoff because of the logarithmic scale: OSHA permits 8 hours of exposure at 90 dB, but only 4 hours at 95 dB, 2 hours at 100 dB, and roughly 15 minutes at 115 dB — each 5 dB increase in level cuts the safe exposure time roughly in half, reflecting the underlying doubling of acoustic intensity for every 3 dB.
What is the difference between sound intensity level and sound pressure level?
Sound intensity level compares acoustic power per unit area and uses dB = 10 x log10(I2/I1), with the standard reference intensity of 1e-12 W/m^2. Sound pressure level compares pressure amplitudes and uses dB = 20 x log10(p/p0), with a reference pressure of 20 micropascals. The factor of 20 appears because intensity is proportional to pressure squared, so the two definitions give the same number for the same sound field. Microphones measure pressure, so almost every field meter reports SPL.
How do you combine the levels of two separate noise sources?
Decibels cannot be added arithmetically because they are logarithms. Convert each level back to a linear intensity ratio, sum those, then convert back: L_total = 10 x log10(10^(L1/10) + 10^(L2/10)). Two uncorrelated machines each producing 60 dB give 10 x log10(2 x 10^6), which is about 63 dB, not 120 dB. This 3 dB rule for doubling explains why silencing just one of two identical noise sources barely helps the overall level.
Why does the level drop by about 6 dB each time you double the distance?
A point source radiating into free space spreads its power over a sphere whose area grows with the square of the radius, so intensity falls as 1 over r squared. Doubling the distance quarters the intensity, and 10 x log10(0.25) equals -6.02 dB. Moving from 1 m to 4 m therefore drops the level by roughly 12 dB. The rule weakens indoors, where reflections build a reverberant field that keeps the level nearly constant beyond a certain distance.
What does A-weighting do to a measured decibel level, and when is dBA used?
dBA denotes A-weighting, a frequency filter applied before the level is computed that de-emphasises low and very high frequencies to approximate the ear's reduced sensitivity there. Because hearing risk and annoyance track perceived loudness rather than raw energy, occupational and environmental noise limits are normally written in dBA. Unweighted dB or C-weighted dBC is preferred for machinery diagnostics and low-frequency work, where the physical energy below a few hundred hertz matters and A-weighting would discard it.
References
Background & Theory
Decibel Levels of Common Sounds
The decibel scale exists because the ear's dynamic range is enormous — roughly a factor of 10 trillion between the quietest audible sound and the threshold of pain — and a logarithmic scale compresses that range into manageable numbers while roughly tracking how loudness is actually perceived.
| Sound source | Approx. level |
|---|---|
| Threshold of hearing | 0 dB |
| Quiet whisper | ~30 dB |
| Normal conversation | 60-65 dB |
| City traffic / vacuum cleaner | 80-85 dB |
| Rock concert / power tools | 110-120 dB |
| Jet engine at close range | 130-140 dB (threshold of pain) |
Because the scale is logarithmic, every +10 dB represents a 10x increase in raw intensity but is perceived as only roughly a doubling in loudness — this mismatch between physical intensity and perceived loudness is the entire reason the decibel scale was adopted instead of a raw linear intensity scale.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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