The Power bank capacity

Why a 20,000 mAh power bank does not charge a 5,000 mAh phone four times. The designer below starts from this arrangement; change anything and the numbers follow.

What this arrangement is for

Why a 20,000 mAh power bank does not charge a 5,000 mAh phone four times.

The thing people get wrong

A power bank’s mAh is quoted at cell voltage, around 3.7 V, while a phone charges at 5 V. Converting between them loses a fifth before any other inefficiency, so the honest figure is watt-hours.

Questions

What does 3s2p mean?

Three cells in series, then two of those strings in parallel — six cells in total, at three cells’ voltage and two cells’ capacity. Series multiplies voltage and keeps capacity; parallel multiplies capacity and current capability and keeps voltage. The series number always comes first.

Do I need a BMS?

For any lithium chemistry, yes, and this site will not design a pack without one. A BMS is the only thing that stops one cell being driven under-voltage on discharge or over-voltage on charge, and the divergence between cells is invisible from outside the pack. Lead-acid and NiMH can be built without one; lithium cannot.