Battery pack calculator (series and parallel cells) • The Science 360

By Shounak Das · Updated November 2026 · 6 min read

How do you calculate battery pack voltage and capacity?

Multiply the cell voltage by the number in series, and the cell capacity by the number in parallel. A 3S2P pack of 3,000 mAh, 3.6 V cells is 10.8 V and 6 Ah, or 64.8 Wh; a 13S4P e-bike pack of Molicel P42A cells is 46.8 V, 16.8 Ah and about 786 Wh. Energy is the cell count times one cell's energy, however the cells are arranged.

Cell values come from each maker's datasheet. The companion post works through the examples, LiPo C ratings explained covers current limits, and the mAh to Wh converter handles single batteries.

Key results from the calculator

Series sets the voltage: 13 Li-ion cells in series make 46.8 V nominal, 54.6 V full and 32.5 V empty, the "48 V" e-bike class.
Parallel sets capacity and current: four P42A cells in parallel give 16.8 Ah and 180 A continuous.
4S LiFePO4 is 12.8 V nominal and 14.6 V full, close to a 12 V lead acid battery.
Every series pack needs balancing: a 13S pack needs a BMS with 14 balance wires.

Six packs

Each example loads the cell, the S and P counts and a typical load.

3S2P of Samsung 30Q

Small robot or drone

Six 18650 cells: three in series for 10.8 V, two in parallel for 6 Ah. At 150 W each cell carries 6.9 A of its 15 A rating, for about 26 min.

Voltage 10.8 V Energy 64.8 Wh Max current 30 A Cell weight 288 g

10S3P of Samsung 30Q

36 V scooter

Ten in series is the usual "36 V" pack: 36 V nominal, 42 V full. Three in parallel give 9 Ah and 324 Wh.

Voltage 36 V Energy 324 Wh Capacity 9 Ah Run time at 350 W 56 min

13S4P of Molicel P42A

48 V e-bike

52 cells of 21700: 46.8 V nominal, 54.6 V full, 16.8 Ah and about 786 Wh. The cells alone weigh about 3.6 kg.

Voltage 46.8 V Energy 786 Wh Max current 180 A Cell weight 3.6 kg

13S5P of Samsung 30Q

Same voltage, smaller cells

65 smaller 18650 cells give 702 Wh, a little less than 52 P42A cells, and 75 A against 180 A.

Energy 702 Wh Cells 65 Max current 75 A Cell weight 3.1 kg

4S LiFePO4 32700

12 V lead acid replacement

Four 3.2 V LiFePO4 cells make 12.8 V, charged to 14.6 V. With 6 Ah cells that is 76.8 Wh.

Voltage 12.8 V Full 14.6 V Energy 76.8 Wh Max current 18 A

4S4P LiFePO4 32700

Camping power box

Four groups of four: 12.8 V, 24 Ah, 307 Wh. A 200 W load runs for about 1.5 h.

Energy 307 Wh Capacity 24 Ah Run time at 200 W 1.5 h Cell weight 2.3 kg

Common Li-ion pack voltages (3.6 V cells, 4.2 V full, 2.5 V empty)

Series	Nominal	Full	Empty	Sold as
3S	10.8 V	12.6 V	7.5 V	12 V class
4S	14.4 V	16.8 V	10 V	14.4 V / 14.8 V
7S	25.2 V	29.4 V	17.5 V	24 V
10S	36 V	42 V	25 V	36 V
13S	46.8 V	54.6 V	32.5 V	48 V
14S	50.4 V	58.8 V	35 V	52 V
20S	72 V	84 V	50 V	72 V

Packs are often sold at 3.7 V per cell (for example 13 × 3.7 = 48.1 V); the datasheets for the 30Q and P42A give 3.6 V. Full and empty voltages are the datasheet charge and cut-off voltages; most BMS boards cut off a little above the empty figure.

How the calculator works

Voltage: cells in series add their voltages: nominal, full (the datasheet charge voltage) and empty (the discharge cut-off).

Capacity and current: cells in parallel add their amp hours and their continuous current ratings. The pack current limit is the weakest group's, so all cells must match.

Energy: volts × amp hours, which equals the number of cells times one cell's energy. A Samsung 30Q holds 10.8 Wh; a P42A 15.1 Wh.

Load check: the load in watts divided by the nominal voltage gives the pack current, shared equally by the cells in parallel. Run time is the energy divided by the load, ignoring the lower capacity at high current.

What the model leaves out

Capacity at high current: cells deliver less than their rated mAh at heavy loads; the 30Q datasheet gives 2,700 mAh at 10 A against 3,000 mAh at 0.2C.
Voltage sag: internal resistance pulls the voltage below nominal under load.
Pack hardware weight: nickel, BMS, wiring, insulation and the case are not counted.
Temperature and ageing: both reduce capacity and the current a cell can safely give.

Common misconceptions

"Parallel cells raise the voltage." Only series does. Parallel keeps the voltage and adds capacity.

"A 48 V pack has 48 V." It swings from about 32.5 V empty to 54.6 V full for 13 Li-ion cells in series.

"Balancing is optional on small packs." Any pack with two or more groups in series can drift apart, and the highest group gets overcharged.

Frequently asked questions

How do I calculate battery pack voltage?

Multiply the cell voltage by the number of cells in series. 13 Li-ion cells at 3.6 V make 46.8 V nominal and 54.6 V when full at 4.2 V each.

How do I calculate battery pack capacity?

Multiply one cell's capacity by the number in parallel. Four 4,200 mAh cells in parallel make 16.8 Ah, whatever the number in series.

What does 3S2P mean?

Three cells in series and two in parallel, six cells in all. With 30Q cells it is 10.8 V, 6 Ah and 64.8 Wh.

Does a battery pack need a BMS?

Yes. A BMS cuts off overcharge, overdischarge, overcurrent and short circuits, and for packs with cells in series it balances the groups through one wire per junction.

Is a 4S LiFePO4 pack a 12 V battery?

Yes: four 3.2 V cells make 12.8 V nominal, close to a 12 V lead acid battery, but it charges to 14.6 V and needs a LiFePO4 charging profile.