Decibel Calculator
Free Decibel Calculator for waves. Enter variables to compute results with formulas and detailed steps. Free to use with no signup required.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Decibel Calculator
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.
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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