Convert Nepers to Centibels

Convert Nepers (Np) to Centibels (cB) instantly and accurately.

Conversion Formula

cB = Np × 86.85889638

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 Centibels

The centibel (cB) is one-hundredth of a bel (1 cB = 0.01 B = 0.1 dB), equal to exactly one-tenth of a decibel. This resolution is the standard for clinical audiometry and professional audio equipment. The pure-tone audiogram (ISO 8253-1, ANSI S3.21) records hearing thresholds at 5 dB (50 cB) steps for screening, but research audiometers adjust in 0.25 dB (2.5 cB) steps for precise threshold measurement. The human just-noticeable difference (JND) for loudness of a 1 kHz tone at 70 dB SPL is ≈ 1–3 cB (Moore, 2012), rising to 5–10 cB near the absolute hearing threshold. IEC 60268-5 specifications for loudspeakers require frequency response plots with centibel (0.1 dB) resolution. In studio monitor calibration (SMPTE RP 200, ITU-R BS.1116), loudspeaker level matching is verified to within 0.1 dB (1 cB). 1 cB = 0.01 B = 0.1 dB ≈ 0.011513 Np.

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