Battery Pack Configuration Calculator

Introduction to series and parallel battery pack arithmetic

Plain-text formulas: packVoltageNominal = seriesCells * cellVoltageNominal; packCapacityAh = parallelCells * cellCapacityAh; packEnergyWh = packVoltageNominal * packCapacityAh; maxContinuousCurrentA = parallelCells * cellContinuousCurrentA; maxPowerW = packVoltageNominal * maxContinuousCurrentA; packChargeVoltage = seriesCells * cellChargeVoltage; packCutoffVoltage = seriesCells * cellCutoffVoltage; packCRate = maxContinuousCurrentA / packCapacityAh.

Safety warnings: do not mix cell models, ages, capacities, chemistries, or states of charge. Use an appropriate BMS, fusing, insulation, enclosure, charger, thermal protection, conductor sizing, and fault-current planning. This is not a pack design certification.

A battery pack is described by two integers and one cell. The series count sets voltage, the parallel count sets capacity, and everything else on a spec sheet follows from multiplying those two numbers into the cell's own figures. That is genuinely all the arithmetic there is, which is why the interesting question is never "what does 10S3P give me" but "which pair of integers do I actually need", and that question is answered by the charger you own, the controller's voltage window, and the current your load draws — not by the energy figure people usually reach for first.

The reason the notation is written cells-first is that a pack is built as parallel groups wired in series. Ten groups of three cells each is a 10S3P: within a group the three cells share a common voltage and their capacities add; across groups the voltages add. Wiring it the other way, three strings of ten cells each, produces the same nominal numbers on paper and a much worse pack in practice, because a single weak cell then throttles an entire ten-cell string rather than being propped up by its two neighbours.

This calculator reports the five figures a pack build actually needs — voltage, capacity, energy, continuous current and continuous power — plus three that decide whether the pack is buildable at all: the charge voltage your charger must produce, the cutoff voltage your BMS must enforce, and the C-rate you are asking the cells to sustain. It also draws the pack as a grid so the cell count stops being an abstraction.

How to use the battery pack configuration calculator

1. Pick the chemistry. The Li-ion and LiFePO4 presets fill in the nominal, charge and cutoff voltages that separate the two chemistries; choosing manual leaves every cell field under your control for anything else, whether that is LTO, sodium-ion, NiMH or a datasheet that disagrees with the preset.
2. Copy the cell figures from the datasheet, not from a retailer listing. Nominal voltage, rated capacity in amp-hours and continuous discharge current are the three that matter. Continuous current is the one most often inflated in marketing copy; the datasheet figure is usually well under the "max" number on the wrapper.
3. Enter the series and parallel counts as whole numbers. There is no such thing as 10.5 cells in series, and the calculator refuses fractional counts rather than quietly rounding them.
4. Set a usable depth of discharge. The default of 80% is a common compromise between usable energy and cycle life. Setting it to 100% reports the pack's nameplate energy, which is a number you should never plan a runtime around.
5. Add a load in watts if you want a runtime. Runtime is computed from usable energy, not nameplate energy, so it is already the more honest of the two figures — and still optimistic, for the reasons in the limitations section.
6. Read the charge and cutoff voltages before ordering anything. They are the two numbers that decide whether the charger and BMS you were planning to use will work, and they are the numbers a pure voltage-and-capacity calculator leaves out.

The formulas, and the two that people leave out

Write for the series count, for the parallel count, and , , for a single cell's nominal voltage, capacity and continuous current. Series multiplies voltage; parallel multiplies capacity and current:

Energy and power are then products of a voltage and its matching current or capacity:

Notice that energy depends on the product , which is just the cell count. Every arrangement of the same number of identical cells stores the same energy. Rearranging series and parallel moves that energy between volts and amps; it never creates any.

The charge and cutoff voltages, which decide the charger

Nominal voltage is a label, not an operating point. A pack lives between the voltage its cells reach when full and the voltage its BMS refuses to go below, and both scale with the series count alone:

This is where the two common lithium chemistries part company. A 13S Li-ion pack is nominally 46.8 V but charges to 54.6 V and cuts off near 32.5 V. A 15S LiFePO4 pack is nominally 48 V, charges to only 54.75 V and cuts off near 37.5 V. Both are called "48 volt" and neither can safely use the other's charger.

C-rate, the number that tells you whether the cells can do it

C-rate expresses current as a multiple of capacity, so it is comparable across pack sizes:

Because C-rate is the parallel current times the parallel count divided by the parallel capacity times the same count, the counts cancel: a pack's C-rate equals its cell's C-rate, always. Adding parallel strings raises the current the pack can deliver but never the stress on an individual cell, which is exactly why paralleling is the right answer to a high-current requirement.

Worked example: a 10S3P Li-ion pack from 3.6 V, 2.5 Ah cells

Take the common 18650 case — a 3.6 V nominal cell rated 2.5 Ah with 5 A continuous discharge — arranged 10 in series and 3 in parallel, which is 30 cells.

• Voltage: 10 × 3.6 = 36.00 V nominal, charging to 10 × 4.2 = 42.00 V and cutting off at 10 × 2.5 = 25.00 V.
• Capacity: 3 × 2.5 = 7.50 Ah.
• Energy: 36.00 × 7.50 = 270.00 Wh nameplate; at 80% usable depth that is 216.00 Wh.
• Current: 3 × 5 = 15.00 A continuous, which at 36 V is 540.00 W.
• C-rate: 15.00 ÷ 7.50 = 2.0 C, identical to the single cell's 5 A ÷ 2.5 Ah.
• Runtime driving a 100 W load: 216.00 ÷ 100 = 2.16 hours.

Now change one integer at a time and watch what moves. Going to 10S6P doubles capacity to 15 Ah, energy to 540 Wh and current to 30 A, leaves the voltage and the C-rate exactly where they were, and doubles the cell count to 60. Going to 20S3P doubles the voltage to 72 V, doubles the energy to 540 Wh, leaves capacity and current alone, and doubles the cell count too — but it also doubles the charge voltage to 84 V, which almost certainly means a different charger, a different BMS and, above 60 V DC, a meaningfully different safety conversation.

Both land within a percent of the same energy and both are sold as "48 V", yet one is thirty spot-welded connections and the other is nearly nine hundred. The charge voltages are within 0.15 V of each other by coincidence, not by design, and the cutoff voltages are not remotely close — 37.5 V against 32.5 V — so the two packs still need different low-voltage protection.

Limitations and assumptions behind these numbers

Every cell is assumed identical and perfectly matched. Real cells vary in capacity and internal resistance from the factory and diverge further with age. In a parallel group the lowest-resistance cell takes more than its share of the current; in a series string the lowest-capacity cell defines when charging must stop and when discharging must stop. A pack's real capacity is set by its worst cell, not by the arithmetic here.

Continuous current is the cell's rating, not the pack's. The calculated maximum assumes every cell can sustain its rated current simultaneously and indefinitely. Whether that is true depends on the thermal design — cell spacing, airflow, heat sinking, ambient temperature — and on the interconnects. Nickel strip in particular is a very common current bottleneck, and a pack that computes to 15 A on paper can be limited to far less by the tab welding.

Runtime is optimistic even at a realistic depth of discharge. It ignores voltage sag under load, converter and inverter losses, the capacity lost at low temperature, and the Peukert effect by which high discharge rates return less capacity than the rating. Treat the figure as a ceiling.

Nominal voltage is a convention, not a measurement. Manufacturers quote 3.6 or 3.7 V for the same Li-ion cell depending on the discharge profile they averaged over. Small differences in the nominal figure move the pack voltage and energy proportionally, which is one reason two calculators can disagree about the same pack.

Nothing here checks that a design is safe or legal. Fault-current planning, fusing, conductor sizing, insulation coordination, enclosure design, creepage and clearance above 60 V DC, transport regulations and charger compatibility are all outside what voltage-times-capacity can tell you. This is not a pack design certification, and a pack that computes correctly can still be dangerous.

The chemistry presets are typical values, not your datasheet. Cutoff voltages in particular vary: Li-ion cells are specified anywhere from 2.5 V to 3.0 V, and choosing the higher figure costs usable capacity but extends cycle life. Where a datasheet disagrees with a preset, the datasheet is right — switch to manual.

Common questions about series and parallel pack builds

Sources and assumptions. The series and parallel relationships used here are the standard results for ideal sources in series and in parallel and hold for any cell chemistry. The chemistry presets use widely published typical figures: lithium-ion at 3.6 V nominal, 4.2 V charge and 2.5 V cutoff per cell, and lithium iron phosphate at 3.2 V nominal, 3.65 V charge and 2.5 V cutoff per cell. These are representative values, not a substitute for the cell datasheet, and manufacturers differ, particularly on the discharge cutoff. The default 80% usable depth of discharge is a common planning compromise rather than a manufacturer specification. This page performs arithmetic on the figures you supply and stores nothing; it is not a pack design certification and does not evaluate fusing, conductor sizing, thermal design, enclosure design or transport compliance.