Power, voltage, and current are calculated the same in both DC and AC. The trick is that you typically use the RMS value of an AC voltage to substitute for the DC voltage. The power delivered formula is voltage (DC or AC RMS) x current. The entire AC waveform peaks at 170 on the positive side to 170 volts on the negative side, so an entire cycle of AC is actually 340 volts peak to peak. Through the various voltage formulas (derived from calculus), the RMS or work value of the AC is 120. So if you have 20 VDC and pull 1 amp, you can deliver 20 watts of power. If you have 120 VAC and pull an amp, you can deliver 120 watts. The early fight over power distribution was between Edisons DC and Westinghouse AC. AC won for various reasons, but its ability to be delivered cheaply and efficiently over great distances was the primary one.

So think of electricity as being similar to water. Volts is directly compared to water pressure. You can have volts and pressure without any work being done, only the potential for work. But once water flow and current begin, you can now accomplish work but only as much work as you have water or current. So the voltage wars among the cordless folks is mostly an academic exercise for now, but there are caveats which put the devil in the details. Going back to the power formulas (power = voltage x current), if you have a 50 VDC battery that can deliver 4 amps over an hour, you can do 200 watts of work before the battery gives out. If you have a 20 VDC battery that delivers the same current, you can only do 80 watts of work over the same period. But now we really dig into the weeds because the motor efficiency and design along with the power train become as important. Sheesh. Don’t get me started…Now we’re into the realm of DC and AC motor design along with the gear train to figure out definitively whose drills are more powerful and can deliver power from their battery the longest. A more telling comparison might be the horsepower delivered to the chuck and how long that HP can be delivered. The second way is to read the fine ToolGuyd reviews and make your personal choice based on your needs.

The reason your ceiling fans are going back to DC motors is that they are much simpler to control the speed of using out of the box DC converters (no specialty devices). This also allows them to better acclimate to smart-home technology. And similar to the trend to brushless motors in cordless power equipment, brushless DC fan motors are more powerful and quieter to run with little to wear out except the bearing. Since in general, less heat is produced by working brushless motors, even the bearings should have an increased life span. And of course AC motors have brushes which not only cause RFI, but wear out causing more wasted heat to be generated as the motor operates.