D Bmto Watts Calculator
Instantly convert bmto watts with our free converter. See conversion tables, formulas, and step-by-step explanations. Get results you can export or share.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
P(W) = 10^((dBm-30)/10) | dBm = 10log10(P) + 30 | V = sqrt(P x Z)
dBm is a logarithmic power unit referenced to 1 milliwatt. Converting to watts uses the inverse logarithm formula. Voltage calculation requires knowing the impedance (typically 50 or 75 ohms in RF systems). Each 3 dB change doubles or halves the power, and each 10 dB change multiplies or divides by 10.
Worked Examples
Example 1: Wi-Fi Router Power
Problem:Convert a Wi-Fi router output of 20 dBm to watts and find the voltage across 50 ohms.
Solution:Watts: 10^((20-30)/10) = 10^(-1) = 0.1 W = 100 mW\nVoltage: sqrt(0.1 x 50) = sqrt(5) = 2.2361 V RMS\nPeak voltage: 2.2361 x 1.4142 = 3.1623 V\ndBW: 20 - 30 = -10 dBW
Result:20 dBm = 100 mW = 0.1 W, 2.236 V RMS at 50 ohms
Example 2: Cell Tower Power
Problem:A cell tower transmits at 40 watts. Express in dBm and dBW.
Solution:dBm = 10 x log10(40) + 30 = 10 x 1.6021 + 30 = 46.02 dBm\ndBW = 10 x log10(40) = 16.02 dBW\nMilliwatts: 40,000 mW
Result:40 W = 46.02 dBm = 16.02 dBW
Frequently Asked Questions
How do I convert dBm to watts?
To convert dBm to watts, use the formula P(W) = 10 raised to the power of ((dBm - 30) / 10). For example, 30 dBm = 10^((30-30)/10) = 10^0 = 1 watt. Each 10 dBm increase multiplies power by 10, and each 3 dBm increase approximately doubles it. So 33 dBm is about 2 watts, 40 dBm is 10 watts, and 0 dBm is 1 milliwatt. The dBm scale is logarithmic, which makes it convenient for expressing very large power ranges common in RF engineering.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy