Battery Charge Time Formulas

Battery charge time formulas: ampere-hours to replace, charge efficiency, charge time from the charger current, C-rate and the energy that goes back in.

The formulas

Depth of discharge is the fraction taken out of the battery. η is the charge efficiency, about 0.80 to 0.90 for lead-acid and 0.95 to 0.99 for lithium, and I is the charge current in amperes. The formula gives the bulk charge time. Lead-acid batteries take much longer to charge the last 20% because the current falls in the absorption stage, so the real time is longer. Always keep to the maximum charge current and charge voltage given by the battery maker.

Worked example: a 100 Ah lead-acid battery, 50% discharged

A 10 A charger and an efficiency of 0.85.

1. Ah to replace = 100 × 0.5 = 50 Ah
2. t = 50 / (10 × 0.85) = 5.882 h
3. The C-rate is 10 / 100 = 0.1 C

Worked example: a 100 Ah, 51.2 V lithium battery, 80% discharged

A 20 A charger and an efficiency of 0.95.

1. Ah to replace = 100 × 0.8 = 80 Ah
2. t = 80 / (20 × 0.95) = 4.211 h
3. Energy to replace = 80 × 51.2 / 1000 = 4.096 kWh

Charge time for the lead-acid example

Frequently asked questions

Why is the charge time longer than the simple value?

The charge current falls near the end of a lead-acid charge to avoid gassing, and the efficiency is below one. The formula gives the bulk stage only.

What is the C-rate?

The current as a multiple of the capacity. A 10 A current on a 100 Ah battery is 0.1 C, and it would take about ten hours to move the whole capacity.

Can I use a bigger charger to charge faster?

Only up to the maximum charge current in the data sheet. A higher current heats the battery and shortens its life.

How much energy does the charger take from the supply?

More than the energy stored, because of the charge efficiency and the charger efficiency. Divide the energy by both.

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