Decibel Calculator

Pick the kind of ratio you have — power, voltage, or sound pressure — enter the two values, and read the dB difference. Or enter a dB value and one of the two quantities to back out the other.

Keep it open while reading audio gear specs (where dB shows up everywhere with subtly different reference points), designing antenna links, or working through an acoustics problem set. The tool flags which scaling factor (10·log or 20·log) it's using based on the ratio type, which removes the most common source of dB errors.

Reference levels for common units (dBV, dBu, dB SPL, dBm) are listed inline — pick the right reference and the conversion auto-fills.

The two formulas. Power-like quantities (power itself, intensity, energy density): dB = 10 · log10(P1/P0). Amplitude-like quantities (voltage, current, sound pressure, electric field): dB = 20 · log10(A1/A0). The factor of two comes from the fact that power scales as the square of amplitude — a doubling of voltage produces a quadrupling of power, and log(x²) = 2·log(x). Mixing up the two factors is the most common dB error in beginner audio engineering.

Worked example. An amplifier outputs 100 W into a speaker; the same amp drives a different speaker at 200 W. Power gain = 10 · log10(200/100) = 10 · log10(2) = 3 dB. Voltage example: an op-amp's output goes from 0.5 V to 4 V. Voltage gain = 20 · log10(4/0.5) = 20 · log10(8) = 18.06 dB. The corresponding power gain into a fixed load is also 18.06 dB (the factor of two and the squaring cancel out — voltage and power dB happen to coincide in this special case).

Reference levels for absolute dB units. dBV: relative to 1 V RMS. dBu: relative to 0.775 V RMS (1 mW into 600 Ω, an artifact of telephony). dBm: relative to 1 mW (impedance-independent). dB SPL: relative to 20 µPa (the threshold of hearing at 1 kHz). dBA: dB SPL with A-weighting curve applied. dBFS: relative to digital full scale (0 dBFS is the loudest digital sample value, all real samples are at or below). Each one means something specific; treat them as not-interchangeable.

A common mistake to avoid: adding dB values that aren't independent. Two 90 dB sources don't sum to 180 dB; they sum to about 93 dB (10 · log10(10^9 + 10^9) = 93.01 dB). This shows up in noise calculations all the time. Three 80 dB fans together produce roughly 84.8 dB, not 240 dB. The tool's combine-sources feature does the conversion automatically: convert each dB to linear, sum the linear values, convert back.

For frequency response and gain plots, the convention is dB on the y-axis, frequency on a log x-axis. A flat response is a horizontal line at 0 dB; a 6 dB/octave roll-off is a straight line slanting down at -6 dB per doubling of frequency. The dB framing turns multiplicative ratios into additive shifts on the chart, which is exactly why audio engineers and electrical engineers use dB everywhere.