Electric Power: Definition, Formula, Units & Examples

Anyone who's turned on the news is familiar with stories about electrical power stations that pit their cost and efficiency against how much they rely on renewable versus non-renewable energy sources. But what do those terms really mean? What are people talking about when discussing electric power?

In physics, ​power​ is defined as work done per unit time, or P = W/t, where ​P​ is power in watts (W) or joules per second (J/s), work ​W​ is in newton-meters (Nm) or Joules (J), and time ​t​ is in seconds (s). In the power sector, power is often measured in kilowatts, or even megawatts.

Sources of power in the real world abound. Muscles make a body lift weights, combustion engines propel a car and wind turbines spin generators. The phrase ​electric power​ specifically refers to power generated by electricity, or the flow of electrons.

An electrical power station, then, is a place where energy from some source – burning coal, solar power or something else – is being converted into electricity that can be delivered to consumers via power lines. The more efficient this process, the more power consumers get from the same amount of energy, and often for the lowest cost.

Almost any energy source can be used in power plants to generate electric power. Forms of energy can be changed from their original state into electric potential energy. In this age of climate-change awareness, the most salient distinction between types is whether the source is ​renewable​ (self-replenishing) or ​non-renewable​ (a finite source that will eventually be used up).

Examples of renewable energy sources include:

•Solar
•Hydroelectric
•Geothermal
•Wind

Examples of non-renewable energy sources (fossil fuels) include:

•Coal
•Oil
•Natural gas

In addition to being longer-lasting, power generation via renewable energy sources also typically has a much smaller negative environmental impact than drilling or mining for non-renewable fossil fuels and then burning them.

The work done to move an electric charge ​q​, measured in coulombs (C), across a potential gap ​V​, measured in volts (v) is equal to the electric energy ​qV​ in Joules (J).

This means the definition of power can be rewritten for electric power specifically as:

\(P=\frac{qV}{t}\)

Then, drawing on the definition of an electric current as the flow of electrons (charges) over time, the "q/t" part of that equation can be rewritten using the variable for current ​I​, measured in amperes (A). So:

\(P=IV\)

In English, this demonstrates that electric power can also be defined as something's current times its voltage.

Students familiar with circuits in physics will also notice that applying Ohm's Law, ​V = IR​, to the power equation results in two more ways to calculate an object's electric power based on the properties of the circuit in which it operates:

\(P=IV=I^2R=\frac{V^2}{R}\)

Resistance ​R​ is measured in ohms (Ω).

​How much electrical energy does a 60-watt light bulb left on for 30 minutes use?​

The given information here are the values for power ​P​ and time ​t​. However, time is not in the correct SI unit of seconds. With 60 seconds per minute for 30 minutes, the light bulb was on for ​1,800 seconds​.

The next step is to realize that work ​W​ can be measured in newton-meters ​or Joules​, a unit of energy. So the general definition of power as work over time, or ​P = W/t​ to solve for ​W​, will yield the desired solution.

\(W=Pt=60\times 1800 = 108,000\text{ J}\)

​What is the power output of a vacuum that draws 12 amps of current from a 120-volt outlet?​

Since current ​I​ and voltage ​V​ are given, while power ​P​ is unknown, the equation that will relate all the variables is ​P = IV.​

\(P=IV=(12)(120)=1,440\text{ W}\)