power

Power is the pace of energy transfer — how much work gets done per unit time. Climb a flight of stairs slowly and you do the same work as climbing it quickly; the difference is the power output. For a constant force acting along the direction of motion, P = F·v. For variable forces, P(t) = F(t)·v(t), and the total work is the integral of power over time.

The SI unit is the watt, defined as one joule per second. The unit and the idea of engineering power ratings both trace back to James Watt, whose separate-condenser steam engine of 1769 transformed the technology of the industrial revolution. To sell his engines to customers who thought in horses, Watt introduced the unit of horsepower — roughly 746 watts — as a benchmark. Modern engines, generators, and appliances are still rated in watts (or kilowatts or megawatts) because power is the practically relevant quantity: it determines how quickly a task can be completed, how bright a lamp burns, how much current an outlet must supply.

Power is energy's tempo. It is why a 100 kW car engine accelerates faster than a 50 kW one even when both can do the same eventual total work; it is why an electric kettle boils water in two minutes and a gas stove takes longer; it is why solar panels are rated in peak-watts rather than total lifetime joules. Energy tells you how much. Power tells you how fast.