EV Charging Time Formulas

Electric vehicle charging formulas: the power of a single-phase or three-phase charge point, the energy to add and the charging time with the charger losses.

The formulas

V is the phase voltage, VL the line voltage and I the charging current in amperes, limited by the lower of the charge point, the cable and the on-board charger. η is the efficiency from the socket to the battery, here 0.9 as an example, and it is lower at a low current. The time is for a steady power. A real charge slows (tapers) near a full battery, and a DC charger slows as the battery warms, so the last 20% takes longer than the formula says. The pack size, the states and the power here are examples.

Worked example: a 60 kWh pack from 20% to 80% on a 7.4 kW charge point

1. En = 60 × (0.8 − 0.2) = 36 kWh in the battery
2. Eg = 36 / 0.9 = 40 kWh from the supply
3. t = 40 / 7.4 = 5.405 h

Worked example: charge point power from the current

1. Single-phase at 230 V and 32 A: P = 230 × 32 / 1000 = 7.36 kW
2. Three-phase at 400 V and 32 A: P = √3 × 400 × 32 / 1000 = 22.17 kW

Worked example: the same 36 kWh on a 50 kW DC charger, ignoring the taper

1. t = 36 / 50 = 0.72 h

Time for the 20% to 80% charge by power, with 90% efficiency

Frequently asked questions

Why is the charging time longer than the formula says?

The battery management system lowers the current near a full battery and when the cells are hot or cold. The formula gives the time at a steady power.

What limits the power?

The smallest of the supply, the charge point, the cable and the on-board charger of the car. A car with a 7.4 kW on-board charger will not take 22 kW from an AC point.

Why include the efficiency?

The charger, the cable and the battery lose some energy as heat, so the supply gives more than the battery stores, and the bill follows the supply energy.

Is a DC charger different?

The charger sits outside the car, so the rated power goes straight to the battery, within the limits of the car. The taper then sets the time.

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