Convert Nepers to Millibels

Convert Nepers (Np) to Millibels (mB) instantly and accurately.

Conversion Formula

mB = Np × 868.5889638

About Nepers

The neper (Np) is the SI-coherent logarithmic unit for levels of field quantities, defined in IEC 80000-3 as L = ln(A₁/A₂) nepers for a field ratio and L = (1/2) × ln(P₁/P₂) nepers for a power ratio. The BIPM 9th edition SI Brochure (2019) lists the neper among non-SI units accepted for use with the SI. Named after John Napier (1550–1617), the unit was formalised for telecommunications by the ITU in the 1930s–1940s. The exact conversion: 1 Np = 20/ln(10) dB ≈ 8.685890 dB; 1 dB = ln(10)/20 Np ≈ 0.115129 Np. In wave physics, the propagation constant γ = α + jβ has the attenuation constant α in Np/m: 1 Np/m means amplitude decays by 1/e per metre. In digital signal processing, a z-plane pole at radius r decays as r^n = e^{n×ln(r)}, with ln(r) in nepers per sample. 1 Np = 20/ln(10) dB ≈ 8.685890 dB ≈ 0.868589 B.

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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