Power in physics is the rate at which energy is transferred or work is done. In its most general form, average power is defined as the change in energy divided by the time over which that change occurs, written as P = Delta E divided by Delta t, while instantaneous power is P = dE divided by dt. When mechanical work is being considered, power is the rate of doing work, P = W divided by t for average power.
The SI unit of power is the watt, symbol W, where one watt is equal to one joule per second. Power therefore describes how quickly an energy transfer occurs rather than how much energy is transferred in total. Two machines can perform the same amount of work but have different powers if one performs the work in a shorter time.
For example, lifting a 100 kilogram mass through the same vertical distance requires the same increase in gravitational potential energy regardless of whether it takes 10 seconds or 100 seconds, but the faster lift requires ten times the average power. Power is consequently a rate quantity and should not be confused with energy or work themselves.
Mechanical power can be expressed particularly clearly using force and velocity. Since mechanical work is related to force acting through displacement, the instantaneous power delivered by a force is P = F dot v, where F is the force vector and v is the velocity vector. The dot product means that only the component of force in the direction of motion contributes directly to mechanical power.
For straight line motion in which force and velocity are parallel, this reduces to P = Fv. If they are perpendicular, the instantaneous power is zero even though a force is present. This is important in circular motion, where a centripetal force can continuously change the direction of velocity while doing no mechanical work on an ideal object moving at constant speed.
Rotational motion has an analogous relationship, P = tau omega, when torque and angular velocity are appropriately aligned, where tau is torque and omega is angular velocity. These equations connect power directly to translational and rotational mechanics and show why the same force can correspond to very different power outputs depending on the speed at which a system moves.
Power can involve many forms of energy transfer, not only mechanical work. Electrical power is commonly expressed as P = VI, where V is potential difference and I is current. Using Ohm's law for a resistive component gives P = I squared R or P = V squared divided by R. Thermal power describes the rate at which thermal energy is transferred or generated, while radiant power describes the rate at which electromagnetic energy is emitted or transferred.
In engines, motors, turbines, generators, batteries, heaters, and biological systems, power provides a common way of quantifying the rate of energy conversion. A 1000 watt heater transfers or converts energy at a rate of 1000 joules per second under the stated operating conditions. If it operates continuously for one hour at 1000 watts, it transfers 3.6 million joules, equivalent to 1 kilowatt hour.
The distinction between power and energy is particularly important in electricity because electricity bills generally measure energy consumption in kilowatt hours rather than watts. A high power device does not necessarily consume more total energy than a lower power device if it operates for a sufficiently shorter time.
Average power and instantaneous power answer different physical questions. Average power considers an entire interval and is calculated from total energy transferred divided by elapsed time. Instantaneous power describes the transfer rate at a particular moment and can vary continuously during a process. A vehicle accelerating from rest provides a useful example because its engine power, tractive force, velocity, and energy transfer can change throughout the acceleration.
If the driving force remains constant while velocity increases, mechanical power increases because P = Fv. Conversely, if a motor supplies approximately constant power, the available driving force decreases as speed increases according to F = P divided by v, subject to other physical and engineering constraints. Power can also be negative when a force removes mechanical energy from a system, as occurs during braking or when a motor operates regeneratively. The sign of power therefore contains information about the direction of energy transfer relative to the chosen system and convention.
The concept of power is central to understanding machines because power capacity places a limit on how quickly useful work can be performed. A motor with a greater maximum power can potentially accelerate or lift a load more rapidly, provided its torque, gearing, traction, thermal limits, and other constraints permit it.
Gears can exchange torque and rotational speed while approximately conserving power apart from losses, so a gearbox can provide greater torque at lower rotational speed or lower torque at higher rotational speed. This is why comparing machines solely by torque can be misleading. A high torque motor operating at very low angular speed may have less power than a lower torque motor operating much faster. Similar principles apply to pumps, turbines, aircraft engines, electric vehicles, and industrial machinery. Real systems are never perfectly efficient, so input power normally exceeds useful output power. Efficiency is commonly defined as useful output power divided by input power, multiplied by 100 percent when expressed as a percentage.
Power is also important in thermodynamics and energy systems because it describes the rate at which energy crosses system boundaries or is converted between forms. Heat transfer rate is often expressed as power in watts, while engines are evaluated through the rate at which chemical or thermal energy is converted into mechanical output. The distinction between energy and power is particularly important when assessing infrastructure.
A power station may have a specified electrical generating capacity measured in megawatts, but the actual energy produced over a day or year depends on how long it operates and at what output level. The ratio of actual energy production to the energy that would have been produced continuously at maximum rated power is related to capacity factor. Batteries likewise have both energy capacity and power capability. A battery may store a substantial amount of energy but be unable to deliver it rapidly because of internal resistance, thermal limitations, electrochemical constraints, or power electronics. Thus energy storage and power delivery are related but distinct engineering properties.
Power also appears in fluid mechanics, biological systems, and waves. Fluid power can be associated with pressure and volumetric flow rate, with hydraulic power commonly expressed as pressure multiplied by volumetric flow rate, subject to unit conventions and efficiency. In human physiology, metabolic power describes the rate at which chemical energy is released and used by the body, while mechanical power can describe the rate at which muscles perform external mechanical work.
In wave physics, power can describe the rate of energy transport through a surface or along a propagation direction. Power density describes power per unit area or volume and is useful for comparing technologies or physical processes with different scales. These applications preserve the same fundamental idea of a rate of energy transfer even though the mechanisms differ. The dimensional definition is particularly useful because one watt has dimensions of mass times length squared divided by time cubed, showing that power combines mechanical quantities associated with energy and time.
Common misunderstandings about power arise from confusing it with force, energy, work, or strength. Force measures an interaction that can accelerate matter, energy measures the capacity for transfer or transformation, work measures energy transferred mechanically through a force acting over displacement, and power measures the rate of such transfer. A person can exert a large force without producing much mechanical power if the movement is very slow or absent.
Similarly, a device can have high power while operating for a short duration and therefore transfer less total energy than a low power device operating continuously for a long period. Power also does not by itself determine efficiency, because a high power input can accompany either a high or low useful output depending on losses. In practical physics, the most important habit is therefore to identify the energy transfer being considered, specify the time interval or instantaneous state, and use the appropriate power equation.
