Convert Nepers to Millinepers

Convert Nepers (Np) to Millinepers (mNp) instantly and accurately.

Conversion Formula

mNp = Np × 1000

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 Millinepers

The millineper (mNp) equals one-thousandth of a neper (1 mNp = 10⁻³ Np), representing a level change of (20/ln(10)) × 10⁻³ ≈ 0.008686 dB. In transmission-line theory, the attenuation constant α (Np/m) is expressed in millinepers per metre (mNp/m) for modern low-loss coaxial and twisted-pair cables. Standard single-mode optical fibre (ITU-T G.652.D) has an attenuation coefficient of ≈ 0.2 dB/km ≈ 23.04 mNp/km at 1550 nm. A standard ITU-T hypothetical reference circuit (HRC) of 27,500 km was allocated 13.0 Np total attenuation, averaging about 0.47 mNp/km. The gap between normal hearing (0 dB HL) and mild impairment (25 dB HL) spans ≈ 2,876 mNp, while the JND of ≈ 0.25 dB ≈ 28.8 mNp is resolvable by trained listeners. 1 mNp = 10⁻³ Np ≈ 0.008686 dB = 8.686 × 10⁻⁴ B.

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