Cost

Prof. Dr. Thorsten Jungmann (last updated 2025-09-03)

The cost (German: Kosten) of electricity results from the energy price (per kWh) and, where applicable, a base price (per month).

1 Quantity symbol and unit

The quantity symbol and the unit depend on the type of cost:

• Total cost: $K$ in $\mathrm{EUR}$
• Energy price (price of energy): $p_E$ in $EUR/kWh$
• Base price (fixed cost): $G$ in $EUR/month$

2 Practical and worked examples

Basic formulas:

$$K=p_E\cdot W$$ $$K_{\text{year}}=p_E\cdot W_{\text{year}}+12\cdot G$$

Here, $W$ is the electrical work/energy.

2.1 Kettle (15 min)

$P=2\mathrm{kW},t=0.25\mathrm{h}\Rightarrow W=0.5\mathrm{kWh}$
$K=2\mathrm{kW}\cdot 0.25\mathrm{h}\cdot 0.29EUR/kWh\approx \underline{0.15\mathrm{EUR}}$

2.2 PC use (4 hours)

$P=80\mathrm{W}=0.08\mathrm{kW},t=4\mathrm{h}\Rightarrow W=0.32\mathrm{kWh}$
$K=0.32\mathrm{kWh}\cdot 0.29EUR/kWh\approx \underline{0.09\mathrm{EUR}}$

2.3 Household (per year with base price)

$W_{\text{year}}=2500\mathrm{kWh},p_E=0.29EUR/kWh,G=12EUR/month$
$K_{\text{year}}=0.29EUR/kWh\cdot 2500\mathrm{kWh}+12\cdot 12EUR/month=\underline{869\mathrm{EUR}}$

3 Typical orders of magnitude

• Energy price (household):
  $p_E=0.20\dots 0.50EUR/kWh$
• Annual work (household):
  $W_{\text{year}}=1500\dots 4500\mathrm{kWh}$
  If no energy price is given, use $p_E=0.29EUR/kWh$.

4 Example phrasings

• ‘The annual cost of electricity is 869 EUR.’
• ‘At an energy price of $p_E=0.29EUR/kWh$, $6\mathrm{kWh}$ cost exactly $1.74\mathrm{EUR}$.’
• ‘The annual base price is $144\mathrm{EUR}$.’

5 Related quantities

• Work from power and time: $W=P\cdot t$
• Conversion to joules: $1\mathrm{kWh}=3.6\cdot 10^6\mathrm{J}$
• Mean value: $\bar{P}=\frac{W}{t}$

6 Related components

• Energy meter