Power calculator formulas

On this page, I detail the formula’s used in the power calulator. When you update a field in the calculator, it coverts the value you entered to the power in Watt: $P_\mathrm{W}$ . Then, from $P_\mathrm{W}$ , we compute all the other fields and update their values.

To convert from power in Watt to dBm, we use the following formula:

\begin{align*} P_\mathrm{dbm} &= 10 \log_{10} \left( P_{W} \right) + 30 \\ P_\mathrm{W} &= 10^{\frac{P_{dbm}-30}{10}} \end{align*}

When we assume that the power is dissipated in a load resistance $Z_{ref}$ , we can compute the voltage and current. Recall Ohm’s law and the fact that the power is the product of voltage and current:

V_\mathrm{rms} = I_\mathrm{rms} Z_\mathrm{ref} \qquad P_\mathrm{W} = V_\mathrm{rms} I_\mathrm{rms}

Combining these, we can compute power from voltage and current and vice-versa:

\begin{align*} P_\mathrm{W} &= \frac{V_\mathrm{rms}^2}{Z_{ref}} &P_\mathrm{W} = I_\mathrm{rms}^2 Z_\mathrm{ref} \\ V_\mathrm{rms} &= \sqrt{P_\mathrm{W} Z_\mathrm{ref}} &I_\mathrm{rms} = \sqrt{\frac{P_\mathrm{W}}{Z_\mathrm{ref}}} \end{align*}

Assuming that the voltage and current are sinusoidal, we can compute the peak voltage and currents simply:

V_\mathrm{pk} = \sqrt{2} V_\mathrm{rms} \qquad I_\mathrm{pk} = \sqrt{2} I_\mathrm{rms}