energy transferred or converted per unit time. In the International System of Units
, the unit of power is the watt
, equal to one joule
per second. In older works, power is sometimes called activity
Power is a scalar
The output power of a motor is the product of the torque that the motor generates and the angular velocity of its output shaft. The power involved in moving a ground vehicle is the product of the traction force on the wheels and the velocity of the vehicle. The power of a jet-propelled vehicle is the product of the engine thrust and the velocity of the vehicle. The rate at which a light bulb converts electrical energy into light and heat is measured in watts – the electrical energy used per unit of time.
Power is the rate with respect to time at which work is done; it is the time derivative of work:
where P is power, W is work, and t is time.
If a constant force F is applied throughout a distance x, the work done is defined as . In this case, power can be written as:
If instead the force is variable over a three-dimensional curve C, then the work is expressed in terms of the line integral:
From the fundamental theorem of calculus, we know that . Hence the formula is valid for any general situation.
The dimension of power is energy divided by time. In the International System of Units (SI), the unit of power is the watt (W), which is equal to one joule per second. Other common and traditional measures are horsepower (hp), comparing to the power of a horse; one mechanical horsepower equals about 745.7 watts. 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 much more energy than does detonating a kilogram of TNT, but because the TNT reaction releases energy much more quickly, it delivers far 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. 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.