Lithium Pack Builder Calculator

An S×P pack worked out from one cell’s datasheet: pack voltage full, nominal and empty, amp-hours and watt-hours, cell count and mass, the pack’s internal resistance and the voltage sag and I²R heat it produces at your load — plus the per-cell current, the BMS rating and the charge current.

Last updated 24 Sep 2026

S×P pack design

One cell's datasheet → the whole pack

Cells in series (S)Sets the voltage. 13S or 14S for a 48 V e-bike pack, 7S for 24 V nominal.

Cells in parallel (P)Sets the capacity and shares the current.

Cell nominal voltage (V)3.6 or 3.7 V for Li-ion, 3.2 V for LiFePO4. Use the figures from your part’s datasheet; typical values vary widely between manufacturers.

Cell fully-charged voltage (V)4.2 V for most Li-ion, 3.65 V for LiFePO4.

Cell cut-off voltage (V)Where the BMS should stop the discharge — 2.5 to 3.0 V for Li-ion.

Cell capacity (Ah)At the rate the datasheet quotes, usually 0.2C for a cylindrical cell.

Cell internal resistance (mΩ)Datasheets quote AC impedance at 1 kHz, which is the SMALLEST number a cell has. The DC resistance that sets sag under a steady load is typically two to three times larger — use a DC figure here if you have one.

Cell mass (g)

Load current (A)The steady current the pack has to deliver.

Cell maximum continuous current (A)From the cell datasheet. The per-cell current below must stay under it.

Charge rate (C)0.5C is a common compromise; check the cell’s own charge limit.

BMS headroom over the load current (%)

Assembly overhead on mass (%)Holders, nickel strip, wiring, BMS and case. 20–30% is typical for a well-built pack.

A geometry, not a schematic: the S x P matrix. Each column is a block of P cells wired in parallel; the S blocks are then wired in series, which is what sets the pack voltage. Only two columns and two rows are drawn, with dots standing in for the rest – the numbers beside them are the real S and P you entered. Parallel cells share the load current equally only if they are matched and equally connected, which is the assumption behind the per-cell current printed here. Nothing moves, because a geometry has no loop.

987.8WhExample

14S4P of a 21700 cell — 3.6 V nominal, 4.9 Ah, 35 mΩ, 69 g — at a 15 A load

An S×P pack from one cell

V_nom = S × V_cell · Ah_pack = P × Ah_cell · Wh = V_nom × Ah_pack
R_pack = S × R_cell ÷ P · sag = I × R_pack · heat = I² × R_pack · I_cell = I ÷ P

S: cells in series — sets voltage, and multiplies resistance
P: cells in parallel — sets capacity, divides resistance and divides the current each cell has to carry
R cell: the cell’s internal resistance. A datasheet’s AC 1 kHz figure is the lower bound; DC resistance is larger
I cell: what one cell carries. This, not the pack current, is what the datasheet’s continuous rating limits

Worked example

14S4P of a 21700 cell — 3.6 V nominal, 4.9 Ah, 35 mΩ, 69 g — at a 15 A load
V_nom = 14 × 3.6 = 50.4 V; Ah = 4 × 4.9 = 19.6 Ah; Wh = 50.4 × 19.6 = 987.8 Wh
Fully charged it reaches 58.8 V and the BMS should stop it at 35.0 V
R_pack = 14 × 35 mΩ ÷ 4 = 122.5 mΩ, so at 15 A the sag is 1.838 V and the cells make 27.56 W of heat
Each cell carries 15 ÷ 4 = 3.75 A, 38% of this cell's 9.8 A continuous rating
56 cells weigh 3.864 kg; with 25% for holders, nickel, BMS and case the pack is 4.83 kg, giving 205 Wh/kg
A BMS rated 18.8 A continuous suits the load, and charging at 0.5C means 9.8 A into the pack, 2.45 A per cell

The same 56 cells, arranged differently

Energy barely changes — it is the cell count times the cell’s own watt-hours. What changes is the voltage, the current for a given power, and the sag: a tall thin pack has more resistance and sags more at the same current, but needs less current for the same power. Every figure computed by this page’s own arithmetic.
Arrangement	Cells	Nominal	Capacity	Energy	Pack resistance	Sag at 15 A
7S8P	56	25.2 V	39.2 Ah	988 Wh	30.6 mΩ	0.46 V
10S6P	60	36.0 V	29.4 Ah	1,058 Wh	58.3 mΩ	0.88 V
13S4P	52	46.8 V	19.6 Ah	917 Wh	113.8 mΩ	1.71 V
14S4P	56	50.4 V	19.6 Ah	988 Wh	122.5 mΩ	1.84 V
20S3P	60	72.0 V	14.7 Ah	1,058 Wh	233.3 mΩ	3.50 V

Reading a cell datasheet into a pack

A lithium pack is S cells in series by P cells in parallel, and almost everything about it follows from one cell’s datasheet. Series multiplies voltage; parallel multiplies capacity. Energy is the product, and it is the same however you arrange a given number of cells: 56 cells of 3.6 V and 4.9 Ah hold about 988 Wh whether they are 14S4P or 7S8P.

Resistance is where the arrangement matters. Series adds resistance, parallel divides it: R_pack = S × R_cell ÷ P. At 14S4P with 35 mΩ cells that is 122.5 mΩ, so a 15 A load costs 1.84 V of sag and 27.6 W of heat inside the cells. Both matter more than they look. The sag is subtracted from a terminal voltage that is already falling as the pack empties, so a saggy pack hits the BMS cut-off with real capacity still in it. The heat has to leave 56 cells packed against each other, and cells that run hot age fast.

The resistance figure on the datasheet is the optimistic one. Manufacturers quote AC impedance measured at 1 kHz, because it is quick, repeatable and flattering: at 1 kHz the double layer at each electrode shunts current past the charge-transfer path, so the measurement misses most of what a steady load sees. A DC pulse measurement on the same cell at the same state of charge typically returns two to three times more. If you only have the 1 kHz number, treat the sag and heat here as a best case.

Per-cell current is the rating that binds. A cell’s continuous discharge rating is about its own heat, so what matters is the pack current divided by P. Fifteen amps from a 4P pack is 3.75 A per cell, comfortable for a 9.8 A cell; the same 15 A from a 1P pack would be right at the limit. The BMS then needs a continuous rating above the load with headroom, and its own FET resistance adds to the pack’s. For the C-rate that current represents, and the capacity actually delivered at it, see the C-rate calculator; for runtime with a depth of discharge, the battery life calculator.

What this does not model. Interconnect resistance — nickel strip, welds, wiring and connectors — which on a badly built pack can rival the cells. Cell mismatch, which makes parallel cells share unequally and series cells drift apart until the BMS balances them. Temperature, which raises resistance sharply in the cold. And the shape of the discharge curve: the terminal voltage here is the nominal voltage minus the I²R drop, not a full state-of-charge model.

Frequently asked questions

How do I calculate the voltage of a lithium battery pack?

Multiply the cell’s nominal voltage by the number of cells in series. 14 cells of 3.6 V give 50.4 V nominal, 58.8 V fully charged at 4.2 V per cell and 35 V at a 2.5 V cut-off. Cells in parallel do not change the voltage.

What does 14S4P mean?

Fourteen cells in series, four in parallel — 56 cells in all. The 14 sets the voltage, the 4 sets the capacity and shares the current four ways.

How much current can each cell take?

Whatever its datasheet says for continuous discharge, and the pack current divided by P has to stay under it. A Samsung INR21700-50E is rated 9.8 A continuous, so a 4P pack of them can supply 39.2 A on paper — less in practice, because the rating assumes good cooling.

Why does my pack sag under load?

Because every cell has internal resistance, and S cells in series by P in parallel give the pack S × R ÷ P of it. The drop is that resistance times the current. It is also why the pack gets warm: the same resistance turns I²R into heat inside the cells.

How big a BMS do I need?

Its continuous rating must exceed your steady load with margin — 20 to 30% is usual — and its peak rating must cover your surges. It also has to be the right cell count: a 14S BMS for a 14S pack, because the balance leads land on every series junction.

How heavy will the pack be?

Cell mass times cell count, plus 20 to 30% for holders, nickel strip, wiring, the BMS and the case. 56 cells of 69 g are 3.86 kg of cells and about 4.8 kg built, which works out at roughly 205 Wh/kg.

Related calculators

References

Samsung SDI. INR21700-50E cell specification, spec. no. INR21700-50E, version V1.0: 4,900 mAh nominal capacity, 3.6 V nominal, 4.2 V charge, 2.5 V discharge cut-off, 9,800 mA maximum continuous discharge, 14,700 mA non-continuous, internal impedance 35 mΩ or less at AC 1 kHz, 69 g maximum, 70.80 × 20.25 mm. The page’s defaults are this cell.
Ionworks. ACIR vs DCIR: AC and DC internal resistance compared: on one cell at one state of charge a 10-second DC pulse returned about 22 mΩ where a 1 kHz AC measurement returned 6.6 mΩ, because at 1 kHz the double-layer capacitance shunts the charge-transfer path. DCIR is always the larger of the two.
IATA. Lithium battery guidance for passengers: batteries and power banks up to 100 Wh are generally allowed in carry-on baggage, 100–160 Wh need the operator’s approval, above 160 Wh are not permitted on passenger aircraft, and spares must never go in checked baggage.
Reddy TB (ed.). Linden’s Handbook of Batteries, 4th ed. McGraw-Hill, 2011. Lithium-ion cell construction, internal resistance and the effect of temperature and rate on delivered capacity.