Power is the amount of energy transferred or converted per unit time.

Specifying power in particular systems may require attention to other quantities; for example, the power involved in moving a ground vehicle is the product of the aerodynamic drag plus traction force on the wheels, and the velocity of the vehicle.

We will now show that the mechanical power generated by a force F on a body moving at the velocity v can be expressed as the product:

If a constant force F is applied throughout a distance x, the work done is defined as

If instead the force is variable over a three-dimensional curve C, then the work is expressed in terms of the line integral:

In older works, power is sometimes called activity.

[3][4][5] The dimension of power is energy divided by time.

Other units of power include ergs per second (erg/s), foot-pounds per minute, dBm, a logarithmic measure relative to a reference of 1 milliwatt, calories per hour, BTU per hour (BTU/h), and tons of refrigeration.

As a simple example, burning one kilogram of coal releases more energy than detonating a kilogram of TNT,[6] but because the TNT reaction releases energy more quickly, it delivers more power than the coal.

If ΔW is the amount of work performed during a period of time of duration Δt, the average power Pavg over that period is given by the formula

It is the average amount of work done or energy converted per unit of time.

When power P is constant, the amount of work performed in time period t can be calculated as

In the context of energy conversion, it is more customary to use the symbol E rather than W. Power in mechanical systems is the combination of forces and movement.

In particular, power is the product of a force on an object and the object's velocity, or the product of a torque on a shaft and the shaft's angular velocity.

Mechanical power is also described as the time derivative of work.

In mechanics, the work done by a force F on an object that travels along a curve C is given by the line integral:

If the force F is derivable from a potential (conservative), then applying the gradient theorem (and remembering that force is the negative of the gradient of the potential energy) yields:

The power at any point along the curve C is the time derivative:

In rotational systems, power is the product of the torque τ and angular velocity ω,

where ω is angular frequency, measured in radians per second.

where p is pressure in pascals or N/m2, and Q is volumetric flow rate in m3/s in SI units.

This provides a simple formula for the mechanical advantage of the system.

Let the input power to a device be a force FA acting on a point that moves with velocity vA and the output power be a force FB acts on a point that moves with velocity vB.

The similar relationship is obtained for rotating systems, where TA and ωA are the torque and angular velocity of the input and TB and ωB are the torque and angular velocity of the output.

These relations are important because they define the maximum performance of a device in terms of velocity ratios determined by its physical dimensions.

The instantaneous electrical power P delivered to a component is given by

where If the component is a resistor with time-invariant voltage to current ratio, then:

, like a train of identical pulses, the instantaneous power

These ratios are called the duty cycle of the pulse train.

; the power emitted by a source can be written as:[citation needed]