Electrical Power Calculator

Electrical power, just like mechanical power, is the amount of work performed in a unit of time. In electrical circuits, work is performed by an electric current. The power depends on the "amount of workers available in a unit of time" – the current $I$ and the energy of "a single worker" – the voltage $V$.

In a DC circuit, the power is:

where:

• $I\ \rm [A]$ – Current in amperes;
• $V\ \rm [V]$ – Voltage in volts; and
• $P [W]$ – Power in watts.

In AC circuits, the equation is:

where the new symbol $\rm pf$ stands for power factor.

In AC currents, both the current and voltage vary periodically in time. The values $I$ or $V$ correspond to the root mean square (RMS).

RMS is a square root of the mean of squares of numbers (see the root mean square calculator for more). The commonly referred voltage of electrical outlets (230 V in the EU and Australia, 110 V in the USA and Canada, 100 V in Japan) is the RMS voltage.

In AC circuits, the current and voltage might not be in phase. The maximum value of the current might be ahead of or lag behind the maximum value of the voltage. This makes the transfer of power less effective. In the worst case, when the current and voltage are entirely out of sync, the transmitted power is zero.

The power factor tells us how synchronized the current is with the voltage. If they're in sync, the power factor is 1. Otherwise, it is less than one, reaching zero in the completely out-of-sync case.

The power factor depends on the device. For a device that is purely resistive, like an electric kettle or an electric heater, the power factor is 1. A device with inductive or capacitive elements puts the current and voltage out of the phase. This makes its power factor less than 1. Check out the power factor calculator to learn more.

To compute the electrical power, you have to specify the current, voltage, and power factor of the item. For devices connected to electrical outlets, the voltage is just the voltage of the domestic power. The current drawn by the device can usually be found either marked on a plug or somewhere on the device.

The power factor is a bit trickier to find – unless you have a power quality analyzer at hand. Check this list for power factors of a few typical household devices:

• Lamps with a standard bulb: $\rm pf = 1$;
• Fluorescent lamps: $\rm pf = 0.93$;
• Common induction motor at half load: $\rm pf = 0.73$, at full load: $\rm pf = 0.85$;
• Electric oven (with resistive heating element): $\rm pf = 1.0$; and
• Inductive oven: $\rm pf = 0.85$.

The exact value of the power factor depends on the details of the construction, so take these values with a grain of salt.