In physics, power is the rate at which work is performed or energy is converted.
If ΔW is the amount of work performed during a period of time of duration Δt, the average power P_{avg} over that period is given by the formula
It is the average amount of work done or energy converted per unit of time. The average power is often simply called "power" when the context makes it clear.
The instantaneous power is then the limiting value of the average power as the time interval Δt approaches zero.
In the case of constant power P, the amount of work performed during a period of duration T is given by:
In the context of energy conversion it is more customary to use the symbol E rather than W.
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The dimension of power is energy divided by time. The SI unit of power is the watt (W), which is equal to one joule per second. NonSI units of power include ergs per second (erg/s), horsepower (hp), metric horsepower (Pferdestärke (PS) or cheval vapeur, CV), and footpounds per minute. One horsepower is equivalent to 33,000 footpounds per minute, or the power required to lift 550 pounds by one foot in one second, and is equivalent to about 746 watts. Other units include dBm, a relative logarithmic measure with 1 milliwatt as reference; (food) calories per hour (often referred to as kilocalories per hour); Btu per hour (Btu/h); and tons of refrigeration (12,000 Btu/h).
In mechanics, the work done on an object is related to the forces acting on it by
where
This is often summarized by saying that work is equal to the force acting on an object times its displacement (how far the object moves while the force acts on it). Note that only motion that is along the same axis as the force "counts", however; motion in the same direction as force gives positive work, and motion in the opposite direction gives negative work, while motion perpendicular to the force yields zero work.
Differentiating by time gives that the instantaneous power is equal to the force times the object's velocity v(t):
The average power is then
This formula is important in characterizing engines—the power output of an engine is equal to the force it exerts multiplied by its velocity.
In rotational systems, power is related to the torque (τ) and angular velocity (ω):
Or
The average power is therefore
In systems with fluid flow, power is related to pressure, p and volumetric flow rate, Q:
where
The instantaneous electrical power P delivered to a component is given by
where
If the component is a resistor, then:
where
is the resistance, measured in ohms.
If the component is reactive (e.g. a capacitor or an inductor), then the instantaneous power is negative when the component is giving stored energy back to its environment, i.e., when the current and voltage are of opposite signs.
The average power consumed by a sinusoidallydriven linear twoterminal electrical device is a function of the root mean square (rms) values of the voltage across the terminals and the current through the device, and of the phase angle between the voltage and current sinusoids. That is,
where
The amplitudes of sinusoidal voltages and currents, such as those used almost universally in mains electrical supplies, are normally specified in terms of root mean square values. This makes the above calculation a simple matter of multiplying the two stated numbers together.
This figure can also be called the effective power, as compared to the larger apparent power which is expressed in voltamperes (VA) and does not include the cos φ term due to the current and voltage being out of phase. For simple domestic appliances or a purely resistive network, the cos φ term (called the power factor) can often be assumed to be unity, and can therefore be omitted from the equation. In this case, the effective and apparent power are assumed to be equal.
Where v(t) and i(t) are, respectively, the instantaneous voltage and current as functions of time.
For purely resistive devices, the average power is equal to the product of the rms voltage and rms current, even if the waveforms are not sinusoidal. The formula works for any waveform, periodic or otherwise, that has a mean square; that is why the rms formulation is so useful.
For devices more complex than a resistor, the average effective power can still be expressed in general as a power factor times the product of rms voltage and rms current, but the power factor is no longer as simple as the cosine of a phase angle if the drive is nonsinusoidal or the device is not linear.
In the case of a periodic signal s(t) of period T, like a train of identical pulses, the instantaneous power p(t) =  s(t)  ^{2} is also a periodic function of period T. The peak power is simply defined by:
The peak power is not always readily measurable, however, and the measurement of the average power P_{avg} is more commonly performed by an instrument. If one defines the energy per pulse as:
then the average power is:
One may define the pulse length τ such that P_{0}τ = ε_{pulse} so that the ratios
are equal. These ratios are called the duty cycle of the pulse train.
In optics, or radiometry, the term power sometimes refers to radiant flux, the average rate of energy transport by electromagnetic radiation, measured in watts. The term "power" is also, however, used to express the ability of a lens or other optical device to focus light. It is measured in dioptres (inverse metres), and equals the inverse of the focal length of the optical device.
In physics, power (symbol: P) is the rate at which work is performed or energy is transferred. In the SI system of measurement, power is measured in watts (symbol: W).
It may take a certain amount of work to effect a change in the world, like lifting a heavy weight to a higher level. It makes no difference if the weight is lifted slowly or quickly, the same amount of work will have been performed. The difference between a slow lift and a quick lift is that a quick lift requires more Power. That is the work can be done in a shorter time if there is more power available.
As a rate of change of work done or the energy of a subsystem, power is:
where
Power is also equal to force times velocity (or speed).
In optics, or radiometry, the term power sometimes refers to radiant flux, the average rate of energy transport by electromagnetic radiation, measured in watts. But the term "power" is also used to express the ability of a lens or other optical device to focus light. It is measured in dioptres (inverse metres), and is equal to one over the focal length of the optical device.
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