Combining Decibels Calculator
Add multiple sound pressure levels in decibels to find the combined total.
Use for noise studies, mixing, and OSHA compliance with up to eight sources.
Combining Decibels
Decibels are logarithmic — you cannot simply add them. Two equal-loudness sources do not give 2× the dB; they add only 3 dB. This is one of the most common acoustic mistakes in noise reports and live-sound mixing.
Formula
L_total = 10 × log₁₀(Σ 10^(L_i / 10))
Convert each dB level back to linear power, sum them, and convert back to dB.
Worked Example — Two 80 dB Sources
L = 10 × log₁₀(10⁸ + 10⁸) = 10 × log₁₀(2 × 10⁸) = 80 + 3.01 = 83.0 dB
Two equal sources add only 3 dB.
Quick Mental-Math Rules
| dB Difference | Add this much to the louder |
|---|---|
| 0 dB (equal) | 3.0 dB |
| 1 dB | 2.5 dB |
| 2 dB | 2.1 dB |
| 4 dB | 1.5 dB |
| 6 dB | 1.0 dB |
| 10 dB | 0.4 dB |
| 15 dB | 0.1 dB (negligible) |
A whisper next to a jet engine adds essentially nothing — the larger source dominates.
Why dB Is Logarithmic
Human hearing spans roughly 12 orders of magnitude in sound pressure (from 20 µPa threshold to about 200 Pa for damage). Linear units would be unreadable; logarithmic dB compresses this huge range into a manageable 0–140 scale.
Common Levels
| Level | Source |
|---|---|
| 0 dB SPL | Threshold of human hearing |
| 30 dB | Quiet bedroom |
| 60 dB | Conversation |
| 70 dB | Vacuum cleaner |
| 85 dB | OSHA 8-hour exposure limit |
| 100 dB | Subway, blender |
| 120 dB | Rock concert front row |
| 140 dB | Jet engine at 30 m |
| 194 dB | Loudest possible sound in air |
Subtracting Backgrounds
To remove a known background level B from a measured total M:
L_signal = 10 × log₁₀(10^(M / 10) − 10^(B / 10))
Useful for environmental noise — subtract background traffic from a peak measurement to isolate the source. The signal must be at least 3 dB above the background for this to be reliable.
A-Weighting
Most regulations use dB(A) — sound levels weighted to match human hearing’s frequency response. The combining math is identical for dB(A); just keep the weighting consistent across all your inputs.
Worked Example — Factory Floor
Three machines at 88, 90, and 85 dB(A):
- 10⁸·⁸ + 10⁹·⁰ + 10⁸·⁵ = 6.31 × 10⁸ + 1.00 × 10⁹ + 3.16 × 10⁸ = 1.95 × 10⁹
- L = 10 × log₁₀(1.95 × 10⁹) = 92.9 dB(A)
The combined floor noise is 92.9 dB(A) — significantly above the 85 dB OSHA permissible exposure limit, requiring hearing protection.