Decibel Unit Converter

This decibel unit converter changes a logarithmic level between decibels, bels and nepers. Formula: 1 bel = 10 dB; 1 neper = 20/ln(10) dB for amplitude ratios. One bel is exactly 10 dB. One neper equals 20/ln 10 ≈ 8.685890 dB, the factor used for amplitude (field) quantities such as voltage or sound pressure.

How to use the decibel unit converter

1. Enter the level, for example 3 Np.
2. In the decibel unit converter, choose its unit and the target unit, such as neper to dB.
3. Read the decibel unit converter result: 3 Np ≈ 26.06 dB.

For dB to neper, divide by 8.68589; for neper to dB, multiply by 8.68589. For bel to dB, multiply by 10.

What is sound level units?

The decibel (dB) expresses a ratio on a logarithmic scale: 10 dB is a tenfold change in power. The bel equals 10 dB, and the neper is a natural-logarithm unit used in signal theory. The decibel unit converter changes between these level units; it does not convert decibels to sound pressure.

Conversion formula

The decibel unit converter stores every unit as a multiple of the base unit, the decibel (dB). To convert:

value in target unit = value × (factor of source unit ÷ factor of target unit)

where each factor is the size of the unit in decibels.

Common sound level units conversions

Decibel unit converter worked example

Convert 25 decibels to bels:

1. Factor of dB = 1 dB
2. Factor of B = 10 dB
3. 25 × 1 ÷ 10 = 2.5 B

Sound level units unit reference

Reverse factors for each sound level units unit

The reference table gives each unit in decibels. To go the other way, divide by that factor; the list below does the division for you.

• Bel (B), Logarithmic: 1 B = 10 dB, so 1 dB = 0.1 B.
• Neper (Np), Logarithmic: 1 Np = 8.68589 dB, so 1 dB = 0.1151293 Np.

Decibels as power and amplitude ratios

A level in dB is 10 log₁₀ of a power ratio, or 20 log₁₀ of an amplitude ratio:

So +3 dB roughly doubles power, while +6 dB roughly doubles voltage or sound pressure.

Noise exposure limits in dB

OSHA (29 CFR 1910.95) allows 90 dBA for 8 hours with a 5 dB exchange rate. NIOSH recommends 85 dBA for 8 hours with a 3 dB exchange rate, which halves the time for every 3 dB:

OSHA times follow T = 8 ÷ 2^((L − 90)/5) hours and NIOSH times T = 8 ÷ 2^((L − 85)/3). Sound pressure level uses a reference of 20 µPa. See the frequency to wavelength converter for sound and radio waves.

Adding sound levels

Decibels do not add like ordinary numbers. Two equal sources at 80 dB together give about 83 dB, not 160 dB, because doubling the power adds about 3 dB. Ten equal sources add 10 dB, so ten 80 dB machines make about 90 dB. To combine unequal levels, convert each to a power ratio, add, and convert back: 10 × log₁₀(10^(L₁/10) + 10^(L₂/10)).

This works the other way too. If a workshop reads 90 dB and you switch off a machine that alone measured 87 dB, the level drops to about 87 dB, not to 3 dB. The louder remaining sources dominate.

dBm and dBW

Radio and network gear uses decibels relative to a fixed power. 0 dBm is 1 mW, 30 dBm is 1 W, and dBW is dBm minus 30. A Wi-Fi signal around −67 dBm is usually good enough for video calls, while −80 dBm is weak. In the decibel unit converter, −67 dBm is about 0.0000002 mW, or 200 picowatts, which shows how small received radio power is.

Each 10 dB is a factor of ten in power, and each 3 dB is roughly a factor of two. A 6 dB antenna gain therefore about quadruples the power in the favored direction.

Related converters and calculators

Related tools:

• Frequency to wavelength converter: Hz to m
• Power unit converter: W and BTU/h
• Pressure converter: psi, bar, kPa
• SI prefix converter: powers of ten
• Scientific notation calculator: powers of ten

Sources

OSHA 29 CFR 1910.95: Occupational noise exposure; NIOSH: Noise and hearing loss; NIST Special Publication 811, Appendix B.

Questions about this calculator