Glossary entry

Decibel (dB, dBm)

A logarithmic unit for a ratio of powers, 10·log₁₀(P₁/P₂); dBm expresses a power on the same scale relative to 1 mW. Gains and losses in dB add along a link, which makes it the standard unit for optical power and loss.

Optics fundamentals Fiber & telecomUpdated October 2026

The decibel expresses the ratio of two powers on a logarithmic scale,

ratio in dB = 10 \log_{10} \frac{P_{1}}{P_{2}},

so a factor of 10 is 10 dB, a factor of 2 is 3.01 dB and a factor of one half is −3.01 dB. The dBm expresses an absolute power on the same scale, relative to 1 mW:

P_{dBm} = 10 \log_{10} \frac{P}{1 mW},

so 0 dBm is 1 mW, +10 dBm is 10 mW and −30 dBm is 1 µW. Because the logarithm turns multiplication into addition, the gains and losses along an optical link add in dB: a 0 dBm transmitter feeding 10 km of fiber with 0.35 dB/km of loss (3.5 dB) and two connectors of 0.5 dB each delivers −4.5 dBm to the receiver.

Ratios in dB

dB	Power ratio as gain	Power remaining after a loss
0.1	1.023	97.7%
0.5	1.122	89.1%
1	1.259	79.4%
3	1.995	50.1%
6	3.98	25.1%
10	10	10%
20	100	1%
30	1,000	0.1%

A ratio of amplitudes, such as voltages or optical fields, whose squares are proportional to power, is expressed with a factor of 20 instead: $20 \log_{10} (E_{1} / E_{2})$ . The same physical ratio has the same dB value either way; a field ratio of 2 is a power ratio of 4, and both are 6.02 dB.

dBm and other absolute units

Power	dBm
1 W	+30 dBm
100 mW	+20 dBm
10 mW	+10 dBm
2.0 mW	+3 dBm
1 mW	0 dBm
0.50 mW	−3 dBm
100 µW	−10 dBm
10 µW	−20 dBm
1 µW	−30 dBm
100 nW	−40 dBm
1 nW	−60 dBm
1 pW	−90 dBm

Other references appear in photonics as well: dBW is relative to 1 W (0 dBW = +30 dBm), dBµW to 1 µW (0 dBµW = −30 dBm), and dBc to the power of a carrier, as in a sideband at −30 dBc, 30 dB below the carrier. Noise densities are quoted per hertz: relative intensity noise in dB/Hz, and noise powers in dBm/Hz. Losses per unit length are quoted in dB/km for fiber and dB/cm for chip waveguides; 0.2 dB/km removes 4.5% of the power per kilometer, and 2 dB/cm removes 37% per centimeter.

Adding powers

Powers in dBm cannot be added directly; they are converted to milliwatts, added and converted back. Two equal signals together are 3 dB above either one, while a 0 dBm signal combined with a −10 dBm signal gives only +0.41 dBm. For $N$ channels of equal power, the total is the channel power plus $10 \log_{10} N$ : forty WDM channels at 0 dBm each carry +16.0 dBm in total, the figure an amplifier's output rating must cover.

Optical and electrical decibels

A photodetector's current is proportional to optical power, and the electrical power it delivers is proportional to the square of that current. A change of 1 dB in optical power is therefore a change of 2 dB in detected electrical power, so a bandwidth quoted at the 3 dB point of the optical response corresponds to the 6 dB point on an electrical network analyzer. Modulator and photodetector bandwidths are quoted on either scale, and the conversion between them is described in Measuring modulator Vπ and bandwidth, How to measure electro-optic modulator bandwidth and How to measure photodetector bandwidth.

Nepers and loss coefficients

Physics writes attenuation as $P (L) = P_{0} e^{- α L}$ , with a natural-log coefficient $α$ . In dB per unit length the same loss is

α_{dB} = 10 \log_{10} (e) α = 4.343 α,

so an absorption coefficient of 1 cm⁻¹ is 4.34 dB/cm, and 1 dB/cm is 0.230 cm⁻¹. The neper is the natural-log unit for field amplitude ratios, with 1 Np = 8.686 dB. Optical density is a base-10 logarithm without the factor of ten, so 1 OD = 10 dB. The Optical Density Calculator converts between optical density, transmission, decibels and attenuation factor.

Common mistakes

A loss or gain is a ratio in dB; a power level is in dBm. A component has 3 dB of insertion loss, and the power after it might be −3 dBm, but never "3 dBm of loss".
Using 20 log for a power ratio, or 10 log for a field ratio, doubles or halves the answer.
Adding dBm values: 0 dBm plus 0 dBm is +3 dBm, not 0 dBm and not "0 + 0".
Mixing optical and electrical dB when comparing bandwidths or signal levels at a detector.

The Photonics Unit Converter converts between dBm, mW, W and dBW, and between a ratio in dB, a linear power ratio, a field ratio and an optical density.

Common questions

How do you convert dBm to milliwatts?

$P = 10^{P_{dBm} / 10}$ mW. For example, −7 dBm is $10^{- 0.7} = 0.200$ mW, and +13 dBm is 20 mW.

What is the difference between dB and dBm?

dB is a ratio between two powers, such as a gain or a loss. dBm is an absolute power, the ratio of that power to 1 mW expressed in dB.

Why is 3 dB half the power?

Because $10 \log_{10} (1 / 2) = - 3.01$ . A 3 dB loss leaves 50.1% of the power, and a 3 dB gain multiplies it by 1.995.

How many dB is a factor of 10?

Ten dB for a power ratio and 20 dB for an amplitude ratio. Each further factor of ten in power adds another 10 dB, so a million is 60 dB.

References: IEC 60027-3, Letter symbols to be used in electrical technology, Part 3: Logarithmic and related quantities, and their units. G. P. Agrawal, Fiber-Optic Communication Systems, 5th ed. (Wiley, 2021).