Decibel changes: convert a difference into a power ratio
Interpret a logarithmic change without confusing power ratios, amplitude ratios and absolute sound levels.
Method
A decibel difference compares quantities through a logarithm. For positive powers, the difference is ten times the base-ten logarithm of P2 divided by P1. The reverse calculation raises ten to the difference divided by ten. Use powers in the same unit before dividing. Zero or negative power does not have a finite value in this logarithmic ratio. An absolute sound-intensity level also needs a specified reference intensity; a difference between levels is not itself an absolute measurement.
Worked example
Start with the powers below and calculate the ratio before taking the logarithm. Reversing their order gives the negative of the original decibel difference. The additional examples show why a small-looking difference can represent a substantial ratio. Use Decibel power ratio for a comparison and Sound intensity level when you have an intensity and a reference. Round only the displayed result, because early rounding can distort the reconstructed ratio.
P1 = 2 W; P2 = 8 W; P2 / P1 = 4
10 log10(4) ≈ 6.0206 dB
10^(6.0206 / 10) ≈ 4
10 dB → 10; 20 dB → 100; −10 dB → 0.1
Checks and limits
Do not use the power formula directly on voltage, pressure or another amplitude. Under appropriate equal-impedance conditions, a voltage-amplitude ratio uses twenty times the base-ten logarithm because power is proportional to voltage squared. The conditions matter when comparing different loads. Decibels also do not translate directly into a fixed perceived loudness multiplier. Sound frequency, weighting, measurement position and duration affect interpretation; a calculated ratio is not a hearing-safety assessment.