Calculate decibels from power or amplitude ratios, or convert dB to linear ratio and compare two values in a dB calculator for signals.
dB to Ratio Formula
The conversion depends on whether the quantity is a power-like quantity (watts, mW) or an amplitude-like quantity (volts, pascals, current).
Power ratio: ratio = 10^(dB / 10) Amplitude ratio: ratio = 10^(dB / 20) dB from power: dB = 10 * log10(P / P0) dB from amplitude: dB = 20 * log10(V / V0)
- dB — decibel value
- P, P0 — output and reference power
- V, V0 — output and reference amplitude (voltage, pressure, etc.)
Use the factor of 10 for power, energy, and intensity. Use 20 for voltage, current, sound pressure, and any field quantity. Both ratios must be positive. dB is dimensionless, so the two values being compared must share the same units.
Reference Tables
Common dB values and their linear equivalents.
| dB | Power Ratio | Amplitude Ratio |
|---|---|---|
| −20 | 0.01 | 0.1 |
| −10 | 0.1 | 0.316 |
| −6 | 0.251 | 0.501 |
| −3 | 0.501 | 0.708 |
| 0 | 1 | 1 |
| 3 | 1.995 | 1.413 |
| 6 | 3.981 | 1.995 |
| 10 | 10 | 3.162 |
| 20 | 100 | 10 |
| 30 | 1,000 | 31.62 |
| 60 | 1,000,000 | 1,000 |
Which formula applies depends on the quantity. If you pick the wrong one, your result is off by a factor of two in dB.
| Quantity | Type | Use |
|---|---|---|
| Power, intensity, energy | Power | 10·log₁₀ |
| Voltage, current | Amplitude | 20·log₁₀ |
| Sound pressure (SPL) | Amplitude | 20·log₁₀ |
| Antenna gain, signal-to-noise | Power | 10·log₁₀ |
Worked Examples
Convert 14 dB to a power ratio.
ratio = 10^(14/10) = 10^1.4 ≈ 25.12. A 14 dB amplifier puts out about 25× the input power.
Convert a voltage ratio of 4 to dB.
dB = 20·log₁₀(4) ≈ 12.04 dB.
Find the dB drop from 50 W to 5 W.
dB = 10·log₁₀(5/50) = 10·log₁₀(0.1) = −10 dB.
FAQ
Why 10 for power and 20 for amplitude? Power is proportional to amplitude squared. The factor of 2 from the squaring moves outside the log and doubles the coefficient.
Can dB be negative? Yes. Negative dB means the output is smaller than the reference. −3 dB is roughly half power.
What does 0 dB mean? The ratio is exactly 1. The output equals the reference.
Is dB the same as dBm or dBW? No. Plain dB is a ratio. dBm and dBW are absolute levels referenced to 1 mW and 1 W.
