Editing Decibel (section)

=== Examples ===
The unit dBW is often used to denote a ratio for which the reference is 1&nbsp;W, and similarly [[dBm]] for a {{nowrap|1 mW}} reference point.
* Calculating the ratio in decibels of {{nowrap|1 kW}} (one kilowatt, or {{val|1000}} watts) to {{nowrap|1 W}} yields: <math display="block">
L_G = 10 \log_{10} \left(\frac{1\,000\,\text{W}}{1\,\text{W}}\right)\,\text{dB} = 30\,\text{dB}
</math>
* The ratio in decibels of {{nowrap|1={{radic|1000}} V ≈ 31.62 V}} to {{nowrap|1 V}} is: <math display="block">
L_G = 20 \log_{10} \left(\frac{31.62\,\text{V}}{1\,\text{V}}\right)\,\text{dB} = 30\,\text{dB}
</math>
{{nowrap|1=(31.62 V / 1 V)<sup>2</sup> ≈ 1 kW / 1 W}}, illustrating the consequence from the definitions above that ''L''<sub>''G''</sub> has the same value, 30&nbsp;dB, regardless of whether it is obtained from powers or from amplitudes, provided that in the specific system being considered power ratios are equal to amplitude ratios squared.
* The ratio in decibels of {{nowrap|10 W}} to {{nowrap|1 mW}} (one milliwatt) is obtained with the formula: <math display="block">
L_G = 10 \log_{10} \left(\frac{10\text{W}}{0.001\text{W}}\right)\,\text{dB} = 40\,\text{dB}
</math>
* The power ratio corresponding to a {{nowrap|3 dB}} change in level is given by: <math display="block">
G = 10^\frac{3}{10} \times 1 = 1.995\,26\ldots \approx 2
</math>

A change in power ratio by a factor of 10 corresponds to a change in level of {{nowrap|10 dB}}. A change in power ratio by a factor of 2 or {{sfrac|2}} is approximately a [[Half-power point|change of 3&nbsp;dB]]. More precisely, the change is ±{{val|3.0103}}&nbsp;dB, but this is almost universally rounded to 3&nbsp;dB in technical writing.{{Citation needed|date=January 2025}}  This implies an increase in voltage by a factor of {{nowrap|{{sqrt|2}} ≈}} {{val|1.4142}}.  Likewise, a doubling or halving of the voltage, corresponding to a quadrupling or quartering of the power, is commonly described as 6&nbsp;dB rather than ±{{val|6.0206}}&nbsp;dB.

Should it be necessary to make the distinction, the number of decibels is written with additional [[significant figures]].  3.000&nbsp;dB corresponds to a power ratio of 10<sup>3/10</sup>, or {{val|1.9953}}, about 0.24% different from exactly 2, and a voltage ratio of {{val|1.4125}}, about 0.12% different from exactly {{sqrt|2}}.  Similarly, an increase of 6.000&nbsp;dB corresponds to a power ratio of {{nowrap|10<sup>6/10</sup> ≈}} {{val|3.9811}}, about 0.5% different from 4.