§ How it works

For a constant charging power the sum is short: energy needed divided by the power that actually reaches the battery.

t = \frac{C \times (SoC_{\text{end}} - SoC_{\text{start}})}{P \times \eta}

$C$ : usable battery capacity in kWh. $SoC$ : state of charge as a fraction.
$P$ : charging power in kW, the lower of what the charger offers and what the car accepts.
$\eta$ : efficiency. Some energy heats the cables, the on-board charger and the battery itself; 85 to 95 % is typical.

AC versus DC

On AC (home sockets, wallboxes, most public posts up to 22 kW) the car's on-board charger does the conversion, and its rating caps the power no matter how strong the supply is. On DC the charger station feeds the battery directly and the battery management system decides how much current it will take.

The taper

Lithium cells cannot accept full current as they fill up, so DC power falls away at high state of charge. This sheet integrates the time step by step with a typical taper $P(SoC)$ :

t = \int_{SoC_{\text{start}}}^{SoC_{\text{end}}} \frac{C}{\eta \; P(SoC)} \; d(SoC)

The result is the familiar road-trip advice: charging from 10 to 80 % is quick; the last 20 % can take as long again.

Cost and range

\text{cost} = \frac{E_{\text{battery}}}{\eta} \times p \qquad\qquad \text{range} = \frac{E_{\text{battery}}}{c} \times 100

You pay for the energy drawn from the grid, not the energy stored. $c$ is consumption in kWh per 100 km.

§ How it works

For a constant charging power the sum is short: energy needed divided by the power that actually reaches the battery.

t = \frac{C \times (SoC_{\text{end}} - SoC_{\text{start}})}{P \times \eta}

$C$ : usable battery capacity in kWh. $SoC$ : state of charge as a fraction.
$P$ : charging power in kW, the lower of what the charger offers and what the car accepts.
$\eta$ : efficiency. Some energy heats the cables, the on-board charger and the battery itself; 85 to 95 % is typical.

AC versus DC

The taper

Lithium cells cannot accept full current as they fill up, so DC power falls away at high state of charge. This sheet integrates the time step by step with a typical taper $P(SoC)$ :

t = \int_{SoC_{\text{start}}}^{SoC_{\text{end}}} \frac{C}{\eta \; P(SoC)} \; d(SoC)

The result is the familiar road-trip advice: charging from 10 to 80 % is quick; the last 20 % can take as long again.

Cost and range

\text{cost} = \frac{E_{\text{battery}}}{\eta} \times p \qquad\qquad \text{range} = \frac{E_{\text{battery}}}{c} \times 100

You pay for the energy drawn from the grid, not the energy stored. $c$ is consumption in kWh per 100 km.

EV Charging Time

Inputsdrag · tap · type

Fig. 21State of charge and power over the session

§ How it works

AC versus DC

The taper

Cost and range

EV Charging Time

Inputsdrag · tap · type

Fig. 21State of charge and power over the session

§ How it works

AC versus DC

The taper

Cost and range