Select RMS voltage, dBm power level or load resistance to calculate from the other two values. This model assumes a positive, purely resistive load and supports Ω, kΩ, MΩ, V, mV and kV.
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RMS Voltage from dBm Formula
The following formula calculates RMS voltage from dBm for a purely resistive load. For a reactive load, real power also depends on impedance phase.
Vrms = SQRT( Z/1000) * 10 ^ (dBm/20)
Variables:
- Where Vrms is the RMS Voltage from dBm (volts)
- Z is the purely resistive load resistance (ohms), not the magnitude of a reactive impedance
- dBm is power level referenced to 1 milliwatt
To calculate the RMS voltage from dBm, take the square root of the impedance over 1000, then multiply by 10 to the power of the dBm over 20.
| dBm | RMS Voltage (V) |
|---|---|
| -20 | 0.022 |
| -15 | 0.040 |
| -12 | 0.056 |
| -10 | 0.071 |
| -9 | 0.079 |
| -6 | 0.112 |
| -3 | 0.158 |
| 0 | 0.224 |
| 1 | 0.251 |
| 2 | 0.282 |
| 3 | 0.316 |
| 4 | 0.355 |
| 5 | 0.398 |
| 6 | 0.447 |
| 10 | 0.707 |
| 13 | 0.999 |
| 20 | 2.236 |
| 23 | 3.159 |
| 27 | 5.006 |
| 30 | 7.071 |
| *Assumes load impedance Z = 50 Ω. Vrms = √(P × Z), where P = 10^(dBm/10) × 0.001 W. Reference: at 0 dBm into 50 Ω, Vrms ≈ 0.224 V. | |
How to Calculate RMS Voltage from dBm?
The following two example problems outline how to calculate the RMS Voltage from dBm.
Example Problem #1:
- First, determine the impedance (ohms). In this example, the impedance (ohms) is measured to be 5000.
- Next, determine the dBm. For this problem, the dBm is calculated to be 30.
- Finally, calculate the RMS Voltage from dBm using the formula above:
Vrms = SQRT( Z/1000) * 10 ^ (dBm/20)
Inserting the values from above and solving the equation with the imputed values gives:
Vrms = SQRT( 5000/1000) * 10 ^ (30/20) = 70.71 (volts)
FAQ
What is RMS Voltage?
RMS (Root Mean Square) Voltage is a measure of the effective voltage level. It represents the equivalent steady DC (Direct Current) value which gives the same power transfer as the given AC (Alternating Current) voltage. RMS Voltage is crucial in electrical engineering for designing and analyzing circuits that operate with alternating current.
Why is impedance important in calculating RMS Voltage from dBm?
This calculator assumes a purely resistive load, so the load value is a positive real resistance. For a reactive load, real power is Vᵣₘₛ² Re(1/Z); impedance magnitude alone is insufficient. Use the appropriate impedance phase or admittance relation for such a load.
How does the dBm value influence the RMS Voltage calculation?
dBm is a logarithmic unit that measures power relative to 1 milliwatt. In the context of calculating RMS Voltage, the dBm value represents the power level that needs to be converted into a voltage level. Since the formula involves 10 raised to the power of dBm/20, higher dBm values will result in a higher calculated RMS Voltage. This reflects the logarithmic relationship between power and voltage, where a small increase in dBm can result in a significant increase in voltage.
