The pack designer

Choose a chemistry, a system voltage and what the pack has to deliver. The arrangement, the real cell count and the protection follow from those three.

Series sets the voltage, parallel sets the current

Cells in series add their voltages and keep one cell’s capacity; cells in parallel add capacity and current capability while keeping one cell’s voltage. Almost every pack is both, and the notation puts series first — 3s2p is six cells, not five.

The chemistry decides the cell count, not the label on the pack

A nominal 12 V pack is four cells of LiFePO4 or three of li-ion, because their cell voltages differ. That is why "12 V" on its own is not a specification, and why picking the chemistry is the first question here rather than the last.

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.

Why is the usable capacity lower than the cells add up to?

Because running a lithium cell flat every cycle destroys it quickly, and because cells lose capacity as they age. The default here is 80% depth of discharge with a 20% ageing margin, so a 12 Ah pack delivers about 7.7 Ah of real work. Both figures are inputs you can change, and the result always says which were used.

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.