Use this calculator to convert from RMS Voltage to Power in dBm.

RMS means **root-mean-square** value or** V _{RMS}**

The default impedance is 50 Ω. It can be changed to any value.

**Formula**

**P _{dBm} = 10*Log_{10}((V_{RMS})^{2} /Z) + 30**

The formula is derived from the relationship:

**V _{RMS} = √(Z*P_{W})**

where **Z** is the impedance and **P _{W}** is the power in Watt.

and

**P _{dBm} = 10*Log_{10}(P_{mW})**

**Example Calculation**

For V_{RMS} = 1 Volt and impedance (Z) = 50 ohm, the power is 13 dBm.

If instead you would like to convert from the peak to peak voltage, **V _{peak-peak} to dBm**, use this calculator instead.

**Background**

RMS voltage is equal to the value of the constant direct current (DC) that would produce the same power dissipation in a resistive load [1].

VRMS depends on the type of waveform. (*Use this calculator to find the RMS voltage for different waveform types).*

For instance, the RMS value of a square wave is different from that of a sine wave. It’s actually higher for the same peak voltage. Looking at the two waveforms, it’s easy to see why intuitively.

The square wave has more energy relative to the sine wave as it’s 1 or -1 for longer.

The output power in dBm from a square wave will therefore be higher than a sine wave for the same peak voltage.

The RMS value for an arbitrary waveform can be computed from time domain data. This can then be converted to Power (dBm).

**Why convert from Volt to dBm?**

The maximum input level to an analog circuit is often specified in terms of a voltage.

**However the input to this circuit may be provided by an RF amplifier with its maximum output specified in dBm (specifically the P1dB).** In this case, you would want to convert the voltage value to dBm.

As an example, if the peak-to-peak voltage is + 2 Volt, the equivalent RMS voltage (*using Vpp to VRMS calculator*) is 0.707 Volt. Using the calculator on this page, the power is +10 dBm, assuming a 50 ohm input impedance.

Note the higher the input impedance, the lower the power. The same RMS voltage into a 1000 ohm circuit results in a max power of -3 dBm.

⚡ It’s really important therefore to understand and account for the input impedance. In this case, if a 50 ohm impedance was assumed then it would damage the circuit.

**Related Calculators**

**References**

[1] RMS on Wikipedia