๐ Decibel Difference Calculator
Pressure ratio = 10^(differenceรท20), Power ratio = 10^(differenceรท10)
Enter two sound pressure levels (dB SPL) to calculate the difference between them in dB, along with the corresponding sound pressure ratio and acoustic power (intensity) ratio. Handy for comparing audio equipment specs or roughly gauging the effect of soundproofing.
How to use
- Enter the two sound pressure levels (dB) you want to compare.
- The dB difference, pressure ratio, and power ratio are calculated automatically.
How the calculation works
The decibel expresses a ratio between two quantities on a logarithmic scale โ not the ratio itself, but a constant multiplied by its base-10 logarithm. The constant differs between sound pressure and sound power. Sound pressure level is 20 ร log10(ratio); sound power or intensity level is 10 ร log10(ratio). The factor of two comes from intensity being proportional to the square of pressure: since log(xยฒ) = 2 log(x), that squared relationship appears as a doubled coefficient. Inverting those definitions recovers the ratio from a difference in dB: pressure ratio is 10^(difference รท 20), power ratio is 10^(difference รท 10). So the same "+6dB" means roughly double the pressure but roughly four times the power. Perceived loudness is a separate matter from either physical quantity. As a rule of thumb in acoustics, a change of about +10dB is heard as roughly twice as loud.
Worked example
Comparing 70dB and 80dB 1. Difference: 80 โ 70 = 10dB 2. Pressure ratio: 10^(10 รท 20) = 10^0.5 โ 3.162ร 3. Power ratio: 10^(10 รท 10) = 10^1 = 10ร A 10dB difference is about 3.16 times the pressure and exactly ten times the power. Two figures worth remembering: +3dB is about double the power (10^0.3 โ 1.995) and +6dB is about double the pressure. Adding a second identical speaker doubles the acoustic power but raises the level by only about 3dB.
Things to be aware of
- A decibel is a ratio, so on its own it does not describe an absolute loudness. Notations such as dB SPL add a defined reference to make it absolute.
- Which ratio applies depends on the quantity involved. Check which basis a microphone or speaker datasheet is quoting.
- Perceived loudness also varies with frequency, so the same dB difference can feel different in the bass and the midrange.
- This is a conversion from the definition of the decibel. Real measurements are also affected by position and background noise.
FAQ
What's the difference between pressure ratio and power ratio?
Sound pressure level is defined as 20รlog10(ratio), while sound power (intensity) level is 10รlog10(ratio), so the same dB difference maps to different ratios. For example, +6dB is roughly a 2x pressure ratio but about a 4x power ratio.
How big a difference is +10dB?
+10dB is exactly a 10x power ratio, and about a 3.16x pressure ratio. As a rule of thumb in acoustic engineering, a change of about +10dB is perceived by human hearing as roughly "twice as loud."
Can I enter a negative value?
Yes. If dB B is smaller, the difference comes out negative and the ratios are calculated as less than 1 (a decrease in level).