Convert Bels to Millibels

Convert Bels (B) to Millibels (mB) instantly and accurately.

Conversion Formula

mB = B × 1000

About Bels

The bel (B) is the original logarithmic unit of sound and signal level, defined as a tenfold power ratio: L = log₁₀(P₁/P₂) bels, or for field quantities L = 2 × log₁₀(A₁/A₂) bels. Introduced at Bell Telephone Laboratories in the 1920s and named in honour of Alexander Graham Bell (1847–1922), the bel was used to quantify telephone transmission line attenuation: 1 bel of loss meant output power was 1/10 of input. Because 1 bel represents a tenfold change - far too coarse for grading (even untrained listeners can detect a 1 dB = 0.1 B change) - the decibel replaced it in virtually all practical use. Key reference points: 0 B = equal-level reference; 3 B = 30 dB (1000:1 power ratio); 6 B = 60 dB (normal speech at 1 m); 12 B = 120 dB (pain threshold). A 1 B (10 dB) increase in SPL roughly doubles perceived loudness (Stevens’s power law at moderate intensities). 1 B = 10 dB = ln(10)/2 Np ≈ 1.151293 Np.

About Millibels

The millibel (mB) is one-thousandth of a bel (1 mB = 10⁻³ B = 0.01 dB), the finest routine subdivision of the bel family in widespread practical use. The AES17-2015 standard for digital audio converter measurement requires frequency response flatness within ±0.01 dB (±1 mB) across 10 Hz–20 kHz for a reference-quality interface. Audiometer calibration (IEC 60645-1, ANSI S3.6) specifies attenuator step accuracy to ±0.1 dB (10 mB) for research-grade psychoacoustic instruments. Modern audio codec chips (ESS Sabre ES9038PRO) specify passband ripple to 0.01 dB = 1 mB. In broadcast loudness metering (EBU R128, ITU-R BS.1770), integrated loudness is calculated at 0.1 LU = 10 mB resolution. IEC 61672-1 Class 1 sound level meters achieve frequency response flatness within ±0.7 dB (70 mB) from 31.5 Hz to 8 kHz. 1 mB = 0.001 B = 0.01 dB ≈ 1.151 × 10⁻³ Np.

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