Electrical power always boils down to the same relationship expressed three different ways: P = VI, P = I²R, and P = V²/R. Whichever two of voltage, current, and resistance you happen to know, one of these forms solves directly for power — and this calculator also turns that wattage into an estimate of what it costs to run.
Why there are three formulas for the same thing
Power is fundamentally P = VI — voltage times current. But Ohm's law (V = IR) lets you substitute either variable out: replacing V with IR gives P = I²R, and replacing I with V/R gives P = V²/R. All three describe the identical physical quantity; which one is most convenient just depends on which two values you actually measured or know. A 120 V, 5 A appliance and a 5 A current through a 24 Ω element both land on exactly 600 W, because V = IR ties all three together.
From watts to what it costs
Power is a rate — energy per unit time — so to find out how much energy something actually uses, you multiply power by the hours it runs. A 600 W device left on for 3 hours uses 600 × 3 = 1,800 watt-hours, or 1.8 kilowatt-hours (kWh), since utilities bill in thousands of watt-hours. Multiply that by your electricity rate (typically $0.13–$0.16/kWh in the US) to get the actual dollar cost of running that device for that stretch of time.
When resistance is zero — and why that matters
The V²/R form breaks down when resistance is zero: dividing by zero gives an undefined (infinite) result. Physically, this is exactly what a short circuit is — near-zero resistance lets a nearly unlimited current flow for a given voltage, which is why short circuits trip breakers or blow fuses almost instantly rather than settling into a normal operating power level.