Voltage to Power Converter
Our free signal & frequency converter handles voltage power conversions. See tables, ratios, and examples for quick reference.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Power = Vrms^2 / Impedance
Power in watts equals the RMS voltage squared divided by impedance in ohms. For peak voltage, divide by sqrt(2) first. For peak-to-peak, divide by 2*sqrt(2). dBm = 10*log10(P_mW). Current = Vrms / Z.
Worked Examples
Example 1: US Household Outlet Power
Problem:Calculate the maximum power from a 120V RMS outlet into a 15 ohm heater element.
Solution:Power = V^2 / R\nP = 120^2 / 15 = 14,400 / 15 = 960 W\nCurrent = V / R = 120 / 15 = 8 A\nPeak voltage = 120 * 1.414 = 169.7 V
Result:120V RMS into 15 ohms = 960 W | 8 A RMS
Example 2: RF Signal Power Measurement
Problem:An oscilloscope shows a 2V peak-to-peak signal on a 50 ohm system. What is the power in dBm?
Solution:Vrms = Vpp / (2 * sqrt(2)) = 2 / 2.828 = 0.7071 V\nPower = 0.7071^2 / 50 = 0.01 W = 10 mW\ndBm = 10 * log10(10) = 10 dBm
Result:2 Vpp into 50 ohms = 10 mW = 10 dBm
Frequently Asked Questions
How do you convert voltage to power?
Power equals voltage squared divided by impedance: P = V^2 / Z, where V is the RMS voltage and Z is the impedance in ohms. This comes from combining Ohm's law (V = IR) with the power formula (P = IV). For example, 120V RMS across 50 ohms produces 120^2/50 = 288 watts. Always use RMS voltage for power calculations with AC signals, as peak voltage will give incorrect results.
What is the difference between RMS, peak, and peak-to-peak voltage?
For a sinusoidal AC signal, these three measurements are related by fixed ratios. RMS (root mean square) voltage equals peak voltage divided by the square root of 2 (approximately 1.414). Peak-to-peak voltage is twice the peak voltage. A US wall outlet at 120V RMS has a peak voltage of 169.7V and peak-to-peak of 339.4V. RMS is used for power calculations because it represents the DC equivalent voltage that would deliver the same power.
Why does impedance matter in voltage-to-power conversion?
Impedance determines how much current flows for a given voltage, and therefore how much power is dissipated. The same voltage across different impedances produces different power levels. For instance, 1V RMS across 50 ohms produces 20 mW (13 dBm), but across 600 ohms it produces only 1.67 mW (2.2 dBm). In RF systems, impedance matching is critical because maximum power transfer occurs when source and load impedances are equal.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy