Signal Power Converter
Free Signal power Converter for signal & frequency units. Enter a value to see equivalent measurements across systems. Get results you can export or share.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
dBm = 10 * log10(P_mW) | P = V^2 / Z
Convert between linear power (watts) and logarithmic power (dBm, dBW) using decibel formulas. dBm uses 1 mW as reference, dBW uses 1 W. Voltage = sqrt(Power * Impedance).
Worked Examples
Example 1: WiFi Router Power Conversion
Problem:A WiFi router transmits at 20 dBm. Convert to watts and find the voltage across 50 ohms.
Solution:Power = 10^((20-30)/10) = 10^(-1) = 0.1 W = 100 mW\nVoltage RMS = sqrt(0.1 * 50) = sqrt(5) = 2.236 V\nCurrent RMS = sqrt(0.1 / 50) = 0.04472 A
Result:20 dBm = 100 mW = 0.1 W | Vrms = 2.236 V at 50 ohms
Example 2: Cell Phone Signal Strength
Problem:A received signal measures -80 dBm. What is the power in watts?
Solution:Power = 10^((-80-30)/10) = 10^(-11)\nPower = 1e-11 W = 10 picowatts\ndBW = -80 - 30 = -110 dBW\nVrms = sqrt(1e-11 * 50) = 7.07e-5 V
Result:-80 dBm = 10 pW | -110 dBW | Vrms = 70.7 uV
Frequently Asked Questions
Why is impedance needed to convert between power and voltage?
Power, voltage, and current are related through impedance by the formulas P = V^2/Z and P = I^2*Z, where Z is the impedance. Without knowing the impedance, you cannot determine the voltage or current from power alone. Standard impedances in RF systems are 50 ohms (most test equipment and transmitters), 75 ohms (cable TV and video), and 600 ohms (traditional telephone lines). The choice of impedance affects signal levels significantly.
What are typical signal power levels in communications?
Signal power levels vary enormously across applications. WiFi routers transmit at about 20 dBm (100 mW). Cell phones transmit up to 23 dBm (200 mW) for 4G. FM radio stations broadcast at 50-100 kW (47-50 dBW). GPS satellite signals arrive at Earth at about -130 dBm (0.1 femtowatts). Cell tower receivers can detect signals as weak as -110 dBm. This vast range is why logarithmic units like dBm are essential in RF engineering.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy