Conversion method
Dimensionless level differences only. Power level uses 10 log₁₀(P₂/P₁); field-amplitude level uses 20 log₁₀(A₂/A₁) for equal impedance. No dBA, loudness, hearing-risk or absolute sound-pressure conversion is inferred.
P₂/P₁ = (1 × 10^(x/10))/1
10 dB = 10 P₂/P₁.
| dB | P₂/P₁ |
|---|---|
| 1 | 1.258925 |
| 5 | 3.162278 |
| 10 | 10 |
| 25 | 316.227766 |
| 50 | 100000 |
| 100 | 10000000000 |
Unit definitions and sources
Dimensionless level differences only. Power level uses 10 log₁₀(P₂/P₁); field-amplitude level uses 20 log₁₀(A₂/A₁) for equal impedance. No dBA, loudness, hearing-risk or absolute sound-pressure conversion is inferred.
| Unit and system | Use | Definition | Relationship |
|---|---|---|---|
| Decibel (power ratio) (dB); si | Common units | Decibel (power ratio): base (ratio) = 10^(value/10). Common use: Sound Level Ratios. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
| Power ratio (P₂/P₁); si | Common units | Power ratio: base (ratio) = value × 1. Common use: Sound Level Ratios. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
| Bel (power ratio) (B); si | Specialist units | Bel (power ratio): base (ratio) = 10^(value/1). Common use: Sound Level Ratios. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
| Neper (field-amplitude ratio) (Np); si | Specialist units | Neper (field-amplitude ratio): base (ratio) = 2.718281828459045^(value/0.5). Common use: Sound Level Ratios. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
Sources: NIST: SP 811 Chapter 8: logarithmic quantities and units
Precision of sound level ratios conversions
All 4 sound level ratios units convert through Power ratio (P₂/P₁). 4 have an exact defined relationship to the base unit and 0 are conventional or measured values. Results and the tables on this page come from the same engine, so a table value can be checked against the converter directly.
Standard display shows up to six decimal places, switching to scientific notation for very large or small values. Calculation uses JavaScript binary floating point independently of display rounding, so extra digits are not a claim about measurement accuracy. Each unit lists its own source; a citation records where the definition comes from, not an independent review. See Conversion methodology for the review and correction process.