How it works
Decibels are a logarithmic scale for ratios. For power-like quantities (watts, sound intensity) dB = 10 log₁₀ of the ratio. For field quantities (voltage, sound pressure) it is 20 log₁₀, because power goes as the square of amplitude.
Sound levels from separate, uncorrelated sources do not add arithmetically. Two 90 dB machines make about 93 dB, not 180 dB. Each doubling of sources adds about 3 dB.
A 10 dB increase is ten times the sound power and is perceived as roughly twice as loud. A 3 dB change is the smallest difference most people notice outside a lab.
Formula
L_total = 10 log₁₀(Σ 10^(Lᵢ/10)) dB = 10 log₁₀(P₂/P₁) = 20 log₁₀(V₂/V₁)
Questions people ask
Why do two 90 dB sources make 93 dB?
Doubling the sound power adds 10 × log₁₀(2) = 3.01 dB. The levels must be converted to power, summed, then converted back.
When do I use 10 log and when 20 log?
Use 10 log for power, energy and intensity ratios. Use 20 log for voltage, current and sound pressure ratios. Both give the same dB for the same physical change.
How do I subtract background noise?
Convert both to power, subtract, and convert back: 10 log₁₀(10^(L_total/10) − 10^(L_bg/10)). If the difference is under 3 dB the result is unreliable.
What is a safe sound level?
NIOSH recommends limiting exposure to 85 dBA over 8 hours, with the allowed time halving for every 3 dB increase.