Calculation

dB Converter

Convert between dB and linear ratio for power (10·log₁₀) or voltage/amplitude (20·log₁₀), and between dB and nepers (1 Np = 8.686 dB). The decibel, demystified.

redzilla.cl — db

dB —

Ratio —

Nepers —

% change —

dB ↔ nepers

Decibels dB

Nepers Np

Both are logarithmic scales: 1 Np = 8.6859 dB. The neper uses ln on the amplitude ratio; the dB uses log₁₀.

Quick reference (by quantity)

dB	Ratio power	Nepers	Meaning

How it is computed · dB, ratio and nepers

1. For power (P, in W or mW): dB = 10·log₁₀(P₂/P₁) and ratio = 10^(dB/10). That is why ×2 = 3.01 dB and ×10 = 10 dB.

2. For voltage/amplitude (V, A, pressure): dB = 20·log₁₀(V₂/V₁) and ratio = 10^(dB/20). Power scales with the square of voltage, hence the factor of 20. ×2 = 6.02 dB and ×10 = 20 dB.

3. The neper is the natural-log equivalent: Np = ln(amplitude ratio). The fixed conversion is 1 Np = 8.685889638 dB, so dB = Np × 8.6859.

4. Rule of thumb: for power, +3 dB ≈ double and −3 dB ≈ half; +10 dB = ×10.

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How it works

The converter translates between decibels and linear ratio in both conventions: for power quantities (W, mW) it uses dB = 10·log₁₀(ratio) and ratio = 10^(dB/10); for voltage, current or amplitude it uses dB = 20·log₁₀(ratio) and ratio = 10^(dB/20), because power grows with the square of voltage. The two fields are linked: type in either one and the other recalculates instantly, along with the percentage change.

It also includes a dB ↔ nepers converter, the natural-log scale used in telephony and transmission lines: the neper applies ln to the amplitude ratio and the fixed equivalence is 1 Np = 8.685889638 dB. A reference table with the classic points (−20 to +20 dB) shows ratio and nepers for the selected quantity, with the rules of thumb: +3 dB ≈ double the power, +10 dB = ×10.

Example: how many dB is doubling the power?

Select the power quantity (10·log) and type the ratio 2.
The converter computes 10 × log₁₀(2) = 3.01 dB: doubling the power is ~3 dB.
In nepers: 3.01 / 8.6859 ≈ 0.347 Np; the percentage change is +100 %.
Switching to voltage (20·log), that same ratio of 2 equals 6.02 dB: the factor doubles.

Frequently asked questions

Why is it sometimes 10·log and sometimes 20·log?

The decibel always compares powers with 10·log. When you measure voltage, current or amplitude, power goes with the square of the signal, and that square comes out of the logarithm as a factor of 2: hence 20·log. The result is consistent: doubling the voltage (6.02 dB) quadruples the power (also 6.02 dB).

How much is 3 dB exactly? Is it double or not?

It is almost double in power, but not exactly: 3 dB corresponds to a ratio of 10^0.3 ≈ 1.995. The exact figure for doubling is 10·log₁₀(2) = 3.0103 dB. For field work the rule +3 dB = double and −3 dB = half is more than good enough.

What is the difference between dB and dBm?

dB is a unitless ratio: it compares two values (amplifier gain, cable loss). dBm is an absolute power referenced to 1 mW: 0 dBm = 1 mW, 30 dBm = 1 W. That is why dB values are added and subtracted along a link, and the final result is expressed in dBm.

What are nepers used for?

The neper is the natural-log counterpart of the dB, appearing in the attenuation constants of transmission lines and in European telephony standards, where formulas based on ln come out cleaner. The conversion is fixed: 1 Np = 8.6859 dB, so 1 dB ≈ 0.1151 Np.

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We take great care to keep every tool accurate and review it thoroughly; even so, we can't guarantee it is free of errors or take responsibility for how the results are used. We recommend double-checking anything critical.

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