RACK/LEVEL & SPL
dB\mathrm{dB}

Decibel converter

Make sense of ratios, gain and the decibel scale.

Inputs

YOUR SYSTEM
x
0.011000
Ratio represents

Result

METER
Relative level
+3.01dB
Converted from a power ratio
Equivalent power ratio
2.00x
Equivalent amplitude ratio
1.414x
0.00.61.11.72.2xREFERENCE1.00OUTPUT RATIO2.00LINEAR RATIO
Linear ratio vs. logarithmic gain: Relative level conversion

How it works

A logarithmic shortcut for very big ratios.

Decibels describe ratios, not an absolute quantity by themselves. Use 10 times the base-10 logarithm for power, or 20 times for amplitude quantities such as sound pressure.

The formula

L=10log⁡10(r)(power)L = 10 \log_{10}(r) \quad \text{(power)}
L=20log⁡10(r)(amplitude)L = 20 \log_{10}(r) \quad \text{(amplitude)}
  • rr — measured value / reference value
  • rPr_P — rP=10L/10r_P = 10^{L/10} power ratio
  • rAr_A — rA=10L/20r_A = 10^{L/20} amplitude ratio

Worth knowing

A doubling of power is about +3 dB. A doubling of pressure or voltage is about +6 dB. At the same impedance, doubling voltage quadruples power.

Assumptions

This is a relative dB conversion, not an absolute dBu, dBV, dBm or dB SPL reference. Equivalent power and amplitude ratios assume unchanged impedance.

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