Power

Power is the rate at which work is done or energy is transferred. In physics, power P is defined as the derivative of work W with respect to time, dW/dt, and is measured in watts (W), where 1 W equals 1 joule per second. Instantaneous power can vary over time; average power over an interval is the total work divided by the interval.

In electrical circuits, power is expressed as P = VI for instantaneous values. For direct current, P can also be written as P = I^2R or P = V^2/R. In alternating current systems, real power P accounts for energy actually delivered, while reactive power Q and apparent power S describe stored energy and the overall voltage–current interaction. Power factor, the cosine of the phase angle between voltage and current, indicates how effectively power is being used.

Beyond physics, power denotes the capacity to influence or control resources and people. It can arise from coercion or force, rewards, legitimate authority, expert knowledge, or information. Power relations are central to political science, sociology, and organizational studies.

In mathematics, power also means exponentiation—the operation of raising a number to a power. In statistics, the power of a test is the probability of correctly rejecting a false null hypothesis, influenced by sample size and effect size.

Power should not be confused with energy. Energy is the total amount of work available or performed, while power is the rate at which that work is done. Practical measurements include electrical power in watts and energy use reported in kilowatt-hours.