How this calculator works
Power and voltage are not independent: across a resistive load they are tied together by the impedance. Once you know any one of power, RMS voltage or current and the load impedance, the other two follow from Ohm law and the power law. The decibel forms are then just logarithms of those values against a fixed reference. dBm is power against 1 mW, dBW is power against 1 W, dBuV is voltage against 1 microvolt and dBmV is voltage against 1 millivolt. The EMF form assumes an open-circuit source whose voltage is twice the potential difference measured across a matched load, which adds 6.02 dB.
Formula
P (W) = Vrms^2 / R = I^2 x R. Vrms = sqrt(P x R) = I x R. I = Vrms / R = sqrt(P / R). Vpeak = Vrms x sqrt(2). Vpeak-to-peak = 2 x Vpeak. dBm = 10 x log10(P / 1 mW). dBW = 10 x log10(P / 1 W). dBuV = 20 x log10(Vrms / 1 uV). dBmV = 20 x log10(Vrms / 1 mV). dBuV EMF = dBuV + 20 x log10(2), about 6.02 dB higher.
Worked example
One watt into a 50 ohm load: Vrms = sqrt(1 x 50) = 7.071 V, and I = 7.071 / 50 = 0.1414 A. In decibels, 1 W is 10 x log10(1000) = 30 dBm and 10 x log10(1) = 0 dBW. The same 7.071 V is 20 x log10(7,071,000) = 137.0 dBuV, or 20 x log10(7071) = 77.0 dBmV. The peak voltage is 10.0 V and the peak-to-peak voltage is 20.0 V.
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Frequently asked questions
Should I use RMS or peak voltage?
Decibel voltage units are defined with RMS voltage for a sine wave. Enter the RMS value in this page. If you only have a peak reading from an oscilloscope, divide by the square root of two first, or read the peak output this page gives from an RMS input.
Why does 0 dBm not mean the same voltage at every impedance?
Because 1 mW is a power, and the voltage that produces 1 mW depends on the load. Into 50 ohm, 0 dBm is 223.6 mV RMS; into 75 ohm it is 273.9 mV. Always state the impedance when you quote a voltage in dBuV next to a power in dBm.
What is the difference between dBuV and dBuV EMF?
Both use 1 microvolt as the reference, but the EMF form describes an open-circuit source, while the potential-difference form describes the voltage across a load. A source with 2 microvolts of EMF delivers 1 microvolt to a matched load, so the EMF figure is 6.02 dB higher. Antenna and receiver datasheets are not always consistent about which one they mean.
Can I use this for audio or mains power?
Yes, as long as the load is resistive and you know its impedance. Audio commonly uses 600 ohm references and mains circuits are not simple resistive loads, so treat those results as approximate. For reactive loads the current and voltage are out of phase and simple V squared over R does not describe the real power.
Why do I get an error with zero power?
The logarithm of zero is negative infinity, so a decibel value does not exist. Enter a positive power, voltage or current. Real measurements below the noise floor still have a small positive value.