Convert decibels to linear power, intensity, voltage, current, or amplitude ratios, reverse a ratio to dB, or compare two positive signal values.

Convert logarithmic and linear signal levels

Required: a decibel value and ratio type.

Use for power gain/loss, intensity, energy, antenna gain, or signal-to-noise ratios.

Positive values indicate gain; negative values indicate attenuation.

Enter output divided by reference; the ratio must be greater than zero.

Both positive values must use the same units.

Converted result

Plain dB expresses a ratio, not an absolute level such as dBm or dBW. The amplitude formula assumes the same impedance reference.

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.

dBPower RatioAmplitude Ratio
−200.010.1
−100.10.316
−60.2510.501
−30.5010.708
011
31.9951.413
63.9811.995
10103.162
2010010
301,00031.62
601,000,0001,000

Which formula applies depends on the quantity. If you pick the wrong one, your result is off by a factor of two in dB.

QuantityTypeUse
Power, intensity, energyPower10·log₁₀
Voltage, currentAmplitude20·log₁₀
Sound pressure (SPL)Amplitude20·log₁₀
Antenna gain, signal-to-noisePower10·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.