What the Battery Series-Parallel Calculator does
This calculator configures a battery pack. Give it a cell and a series-parallel arrangement and it returns the pack's nominal, fully charged and cut-off voltages, its capacity in amp-hours and its energy in watt-hours, the current the cells' charge and discharge C-rates allow, the pack's internal resistance and the sag that causes, and the current and volt drop in the pack cable.
It is a design tool for the pack itself, not a runtime estimator. If you already have a battery and want to know how long it will last under a load, use the Battery Backup Runtime Calculator - it answers that question properly, and this page deliberately does not duplicate it.
How to use it
- Pick the chemistry. Its nominal, charged and cut-off voltages per cell are the published conventions, and you can override all three for a specific cell.
- Enter the series and parallel counts and the capacity of one cell. Series multiplies voltage; parallel multiplies capacity.
- Enter the cell's charge and discharge C-rates from its data sheet, and its internal resistance if you know it.
- Enter your continuous load in watts to see the pack current, the current per cell and how much C-rate headroom is left.
- Set the pack cable's size and length to see the volt drop and the power it wastes - on a low-voltage, high-current pack this is often larger than people expect.
Reading the results
Energy in watt-hours does not change when you rearrange the same cells: 13S4P and 4S13P store exactly the same energy. Series and parallel trade volts for amps, nothing more.
The C-rate limit applies per cell. Four cells in parallel carry a quarter of the pack current each, which is why adding parallel groups is the way to raise a pack's current capability.
A constant-power load draws its highest current when the pack is nearly empty, because the voltage has fallen. Check the cut-off case, not just the nominal one - that is when a BMS trips.
Worked example: a 13S4P e-bike pack of 3.5 Ah cells
Thirteen cells in series at 3.6 V nominal give 46.8 V, charging to 13 x 4.2 = 54.6 V and cutting off at 13 x 3.0 = 39 V. Four in parallel give 4 x 3.5 = 14 Ah, so the energy is 46.8 x 14 = 655 Wh from 52 cells.
At a 2C discharge the pack can deliver 28 A - 7 A from each cell in a parallel group - which is 1,310 W. Charging at 0.5C is 7 A, about two hours before the constant-voltage taper. With 30 milliohm cells the pack resistance is 30 x 13 / 4 = 97.5 milliohms, so 28 A sags the terminals by 2.73 V and dissipates 76 W inside the cells.
A 500 W load at 90% controller efficiency draws 11.9 A at the nominal voltage - well inside the limit - but 14.2 A at the 39 V cut-off. Through 2 m of 6 mm2 cable that 11.9 A costs 0.14 V and 1.6 W. Rearranged as 4S13P the same 52 cells give 14.4 V and 45.5 Ah: identical energy, three times the current for the same power, and a much heavier cable.
Formulas and scoring rules
- Pack voltage
V = S x VcellSeparately for nominal, fully charged and cut-off.- Pack capacity
Ah = P x Ah(cell)- Pack energy
Wh = V(nominal) x AhUnchanged by rearranging the same cells.- C-rate current
I = C-rate x capacity[Ah]Per pack; divide by P for the current in each cell.- Pack internal resistance
R = (S / P) x R(cell)Series adds, parallel divides.- Voltage sag
V(sag) = I x R(pack), loss = I^2 R(pack)- Current for a constant-power load
I = P(load) / (V x efficiency)Highest at the cut-off voltage, not at nominal.- Cable drop
V = I x rho x 2L / AGo and return. Copper is 1.724e-8 ohm.m at 20 C.
How this differs from the Battery Backup Runtime Calculator
The runtime calculator starts from a battery you already have and a load, and estimates how long it lasts, allowing for depth of discharge and inverter losses. It answers "how long will this run?".
This page answers the earlier question: what pack do I build? It takes cells and an arrangement and produces the pack's voltages, capacity, energy, C-rate limits and interconnect requirements - the numbers you need before ordering cells, choosing a BMS or sizing the cable. Neither tool does the other's job, and the two are meant to be used in sequence.
What a BMS actually monitors
A battery management system balances series groups, not individual cells. A 13S4P pack has thirteen groups of four, so it needs thirteen balance channels and fourteen sense wires - one at each junction plus one at each end. Cells inside a parallel group cannot be balanced individually, because they are already connected together.
That is precisely why cells in a parallel group must be matched for capacity and internal resistance before assembly. A weak cell in a group is charged and discharged by its neighbours through the interconnect, ages faster, and drags the whole group down - and no BMS can see it happening, because the group reads as one cell.
Limitations: what the result does not prove
- Chemistry voltages are the widely published nominal conventions, not measurements. The specific cell's data sheet takes precedence, and this page lets you override all three figures.
- Capacity is a rated figure at a stated discharge rate and temperature. Real capacity falls at high current and in the cold, and lead-acid in particular loses a great deal (Peukert's effect).
- C-rate limits are continuous ratings from the cell maker. Pulse ratings are higher and temperature-dependent, and exceeding either is a safety matter, not just a performance one.
- The cable figure is resistance and volt drop only. It is not an ampacity rating: how much current a cable may carry depends on its insulation, routing, grouping and ambient temperature, and a qualified engineer sizes the conductor and its protection. This calculation is indicative and is not a compliance statement.
Privacy: where your data goes
Everything you paste, type or drop is processed in this browser tab. It is not uploaded, logged, stored or sent to analytics. Session recording and tag-manager scripts are switched off on this page.
Standards and sources
- IEC 61000-4-2 - Electrostatic discharge immunity test - checked 19 Sep 2026
- IEC 62133 - Safety requirements for portable sealed secondary lithium cells and batteries
- IEC 60228 - Conductors of insulated cables (copper resistivity reference)
Frequently asked questions
What does 13S4P mean?
Thirteen cells in series, four in parallel - 52 cells in total. The series count multiplies voltage and the parallel count multiplies capacity, so with 3.6 V 3.5 Ah cells it gives 46.8 V and 14 Ah, which is 655 Wh.
Does rearranging cells change the pack's energy?
No. The same cells store the same watt-hours whatever the arrangement; series and parallel only trade voltage against current. 13S4P and 4S13P both give 655 Wh from 52 cells - but the second needs three times the current for the same power, and therefore much heavier cable.
How much current can my pack deliver?
The cell's continuous discharge C-rate multiplied by the pack capacity. A 14 Ah pack of 2C cells gives 28 A, with each of the four parallel cells carrying 7 A. Adding parallel groups is how you raise a pack's current capability; adding series groups raises its voltage instead.
Can I mix cells of different capacity in a pack?
You should not. In series the smallest capacity limits the whole string and hits its cut-off first; in parallel the mismatched cells push current into each other and the weaker one ages fastest. Match capacity and internal resistance across every group, and never mix chemistries or ages.
How many balance wires does my BMS need?
One more than the series count: a 13S pack needs fourteen sense wires and thirteen balance channels, regardless of how many cells are in each parallel group. The BMS sees each parallel group as a single cell.
Why does my pack voltage sag under load?
Internal resistance. The pack's is (S/P) times the cell's, so a 13S4P pack of 30 milliohm cells is 97.5 milliohms; at 28 A that is 2.7 V of sag and 76 W of heat inside the cells. Cold cells have far higher resistance, which is why packs feel weak in winter.
What cable size does a battery pack need?
This page gives the resistance, volt drop and loss for the size you enter, which is the design question - but the cable's current rating is set by its insulation, routing and the applicable wiring standard, not by this calculation. Work out the drop here, then size the conductor and its protection against the standard.
How long will my pack run a load?
That is the Battery Backup Runtime Calculator's question, and it accounts for depth of discharge and converter losses properly. This page tells you what the pack is; that one tells you how long it lasts.
Last reviewed by the A2Z.Tools team against the sources listed above.
