Single phase power calculator
Single-phase power is voltage times current times power factor. A 13 A load at 230 V with a power factor of 1 is 2,990 W, which is why a UK 13 A plug fuse is the practical ceiling for a domestic appliance at about 3 kW.
How to calculate single-phase power
Single phase is what almost every home has, and its ceiling is lower than people expect. A 230 V circuit protected at 16 A tops out near 3.7 kW; a 120 V circuit at 15 A stops at 1.8 kW. That is why electric showers, hobs and car chargers need their own dedicated circuits rather than a socket, and why North American homes run high-power appliances from a 240 V split-phase circuit instead. Knowing the arithmetic makes the wiring conventions stop looking arbitrary.
Questions
P = V × I × power factor. Without a power factor term you get apparent power in volt-amps.
About 2,990 W at 230 V. That is why 3 kW is the informal ceiling for a plug-in appliance in the UK.
1,800 W at 120 V, and code limits continuous loads to 80% of that, so 1,440 W for anything running over three hours.
Because they use most or all of a circuit rating on their own. Showers, hobs and EV chargers all fall into that category.
On a domestic meter, generally no. You are billed on kWh of real power. Commercial tariffs often do penalise poor power factor.