Decibel Math — Adding, Subtracting & Comparing dB
The decibel (dB) is a logarithmic unit expressing power or amplitude ratios. Adding two 90 dB sources produces 93 dB, not 180 dB. Mastering decibel arithmetic is essential for every audio measurement and system design calculation involving sound levels and signal processing.
Why Logarithmic?
Hearing spans a trillion-to-one pressure ratio (20 micropascals to 20 pascals). The decibel compresses this into 0-140 dB. SPL = 20 log base 10 of (p/p0) where p0 = 20 micropascals per IEC 61672-1.
The 3 dB Rule
Two identical incoherent sources add 3 dB. Two 90 dB sources = 93 dB. Coherent in-phase sources add up to 6 dB. A source 10 dB quieter adds only 0.4 dB. A source 20 dB quieter adds 0.04 dB (negligible).
Background Noise Subtraction
ISO 1996-2 correction: if total-to-background difference is less than 3 dB, result is unreliable. Must exceed 6 dB for valid correction. Above 10 dB, background has negligible effect on the measurement.
Inverse Square Law
Point sources: -6 dB per distance doubling. 100 dB at 1 m = 94 at 2 m = 88 at 4 m. Line sources: -3 dB per doubling (cylindrical spreading). Critical for environmental noise prediction.
Power vs Pressure
Power: 10 log base 10 of ratio. Pressure/voltage: 20 log base 10. Voltage 2:1 = +6 dB. Power 2:1 = +3 dB. Confusing these is a common error source in audio calculations.
Try It Now
Practice dB measurement with the SPL meter