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 by Manoj Kumar, Mathematics Educator
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\nVacuum cleaner: dB = 10 x log10(1e-4 / 1e-12) = 10 x log10(1e8) = 10 x 8 = 80 dB\nDifference = 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\n50 = 10 x log10(I2/I1)\nlog10(I2/I1) = 5\nI2/I1 = 10^5 = 100,000\nThe 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.
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
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy