Power

Prof. Dr. Thorsten Jungmann (last updated 2026-05-04)

Power is work per time – this applies not only to your studies (…), but also in electrical engineering!

Electrical active power (German: Wirkleistung) is also simply called power (German: Leistung).
It represents the power actually absorbed by a load or actually delivered by a generator that is converted into another form of energy and used to do actual work.

1 Quantity symbol and unit

(Active) power has the quantity symbol $P$.
The unit of (active) power $P$ is the watt, named after James Watt, abbreviated with the unit symbol W:

$$[P]=\mathrm{W}$$

2 Practical and worked examples

2.1 Cycling

100 W is the power that the muscles in our body release during moderate cycling, which then acts on the pedals via the legs. Via the chain, the power (possibly assisted by an electric motor) is transmitted to the rear wheel of the bicycle. Via the tyre, which pushes against the surface of the road or path, the bicycle starts to move.
The whole body needs roughly four times this power to produce the muscle power (muscular efficiency). The remaining power is needed by the cardiovascular system, the nerves, the digestive tract, etc.; in addition, heat is generated in the muscles.

Relation to energy: A chocolate bar with nuts (‘Snickers’) supplies approx. 1 000 kJ (250 kcal) of energy. In theory, this energy is enough to pedal at 100 W for about three quarters of an hour.

2.2 Driving a car

104 kW is the power that the engine of a car (VW Tiguan, 2.0 L turbodiesel) releases at a rotational frequency of 4 200 per minute, which then acts on the running gear via the clutch and gearbox. Via the tyres, which push against the surface of the road, the car starts to move.

Relation to energy: With the energy from one ‘Snickers’, this car would travel just under 400 metres.
A full tank (70 L) supplies the energy of approx. 2 400 Snickers bars (700 kWh or 2 520 000 kJ).

2.3 Home

80 W is the power that a refrigerator absorbs on average. A computer in operation absorbs roughly the same amount of power. The lighting of a flat (with light emitting diode lamps) also absorbs about this power. Averaged over the year, a two-person household absorbs 250 W. Here, the average is taken over the day–night/weekly rhythm and the seasons.

Relation to energy:
In total, such a household ‘consumes’ $2190\mathrm{kWh}$ of energy from the power grid per year.

$$W=P\cdot t=250\mathrm{W}\cdot 365\mathrm{d}\cdot 24h/d=2190000\mathrm{W}\mathrm{h}=\underline{2190\mathrm{kWh}}$$

At an energy price of $0.30EUR/kWh$, this results in annual energy costs of $657\mathrm{EUR}$:

$$K=W\cdot K_{kWh}=2190\mathrm{kWh}\cdot 0.30EUR/kWh=\underline{657\mathrm{EUR}}$$

2.4 Further everyday examples

• In good weather, the photovoltaic system on a house provides a power of 12 kW, which can either be used directly or fed into the public grid.
• An electric grill in operation absorbs a power of 2 kW from the grid and converts it into heat.
• When accelerating, the electric motor of an electric vehicle absorbs a power of 250 kW from the rechargeable battery and converts it into motion.

3 Typical orders of magnitude

• Electronics (sensor/µC): $1\mathrm{mW}\dots 1\mathrm{W}$
• IT: charger $5\dots 30\mathrm{W}$, notebook/PC $45\dots 120\mathrm{W}$
• Household: kettle/fan heater $1.5\dots 2.5\mathrm{kW}$
• Drives: machine tool $1\dots 20\mathrm{kW}$, electric car $50\dots 300\mathrm{kW}$
• Generators: balcony power plant $800\mathrm{W}$, residential PV $5\dots 20\mathrm{kW}$, wind turbine $3\dots 10\mathrm{MW}$

4 Example phrasings

• ‘The device absorbs $80\mathrm{W}$ of power.’
• ‘The active power is $P=U\cdot I\cdot \cos \phi =1.2\mathrm{kW}$.’
• ‘The power loss of the resistor is $P_{\mathrm{loss}}=I^2\cdot R=0.8\mathrm{W}$.’
• ‘The inverter delivers a max. output power of $5\mathrm{kW}$.’

5 Related quantities

• In physics, power is defined as work per time.

$$P=\frac{W}{t}$$

• In electrical engineering, it is often expressed as the product of voltage and current.

$$P=U\cdot I$$

• The ratio of output power to input power determines the efficiency of a system, e.g. of a heating device or electric motor.

$$\eta =\frac{P_{out}}{P_{in}}$$

• The difference between input power and output power is called power loss.

$$P_{\mathrm{loss}}=P_{in}-P_{out}$$

• In AC circuit analysis, active power together with reactive power forms apparent power.

6 Related components

• Resistor
• Electric motor
• Heating device
• Energy meter