Battery Series + Parallel Configuration Calculator
Cell voltage + cell capacity + series count + parallel count โ pack voltage, capacity, and total energy.
Result
- Cell voltage3.7 V nominal
- Cell capacity3 Ah
- Series count S4
- Parallel count P3
- Pack voltage14.80 V
- Pack capacity9.00 Ah
- Pack energy133.2 Wh
- Total cells12
Step-by-step
- Series adds voltage: V_pack = 3.7 V ร 4 = 14.80 V.
- Parallel adds capacity: Ah_pack = 3 Ah ร 3 = 9.00 Ah.
- Total energy = V_pack ร Ah_pack = 14.80 ร 9.00 = 133.20 Wh.
How to use this calculator
- Enter the cell's nominal voltage and capacity (from the datasheet).
- Enter S (series count) for the voltage you need.
- Enter P (parallel count) for the capacity you need.
- Read pack V, Ah, and total Wh.
About this calculator
Battery pack design uses two arrangements: series adds voltage, parallel adds capacity. An S ร P pack of identical cells delivers S ร cell_V volts at P ร cell_Ah amp-hours. Total stored energy is the product, independent of how you arrange the cells โ the arrangement only changes the V/A profile. Cells in a pack must be matched in capacity, age, and internal resistance; mixing dissimilar cells causes one to overcharge or overdischarge and reduces pack lifespan.
What this calculator does
This calculator computes the pack voltage, capacity, and total energy of a battery pack built from S series cells and P parallel cells. The two parameters multiply orthogonally: series adds voltage, parallel adds capacity, and total energy depends only on the product S ร P ร cell_V ร cell_Ah. Common defaults are pre-loaded for typical lithium-ion 18650 cells (3.7 V / 3.0 Ah) in a 4S3P arrangement (14.8 V / 9.0 Ah / ~133 Wh).
How it works โ the formula
V_pack = cell_V ร S
Ah_pack = cell_Ah ร P
Wh_total = V_pack ร Ah_pack = cell_V ยท cell_Ah ยท S ยท PKirchhoff's voltage law (series cells add voltage at constant current) and Kirchhoff's current law (parallel cells split current at constant voltage) are the underlying laws. Capacity adds in parallel because parallel cells share the load. Total stored energy is the product of pack voltage and pack capacity (V ร Ah = Wh).
Worked examples
- Inputs:
- cellV=3.7, cellAh=3.0, S=3, P=3
- Output:
- 11.1 V / 9.0 Ah / 99.9 Wh / 9 cells
Typical pre-2015 laptop battery topology.
- Inputs:
- cellV=3.7, cellAh=4.0, S=96, P=74
- Output:
- 355.2 V / 296 Ah / ~105 kWh / 7104 cells
Approximate Tesla Model S Long Range pack scale.
- Inputs:
- cellV=2.0, cellAh=100, S=6, P=4
- Output:
- 12.0 V / 400 Ah / 4.8 kWh / 24 cells
Off-grid lead-acid storage โ note cells are typically built into 6-cell 12 V modules.
When to use this vs other tools
Use this for pack-topology planning. Once you know the pack voltage and capacity, the battery-from-runtime tool tells you whether they are enough for your load.
- Battery from Runtime
Use after sizing the pack to confirm runtime under your specific load and depth-of-discharge.
- Voltage Drop
Use to size the conductors between the pack and the inverter or load โ higher-V packs allow thinner conductors.
- Power (Watts)
Use to relate V, I, and W for sanity-checking pack capability against the worst-case load current.
Authority note
IEEE 1725 is the industry safety standard for multi-cell rechargeable battery packs. Battery University is the most-cited practitioner reference and uses the same S ร P ยท cell_V ยท cell_Ah identities applied here.
Limitations
- Assumes identical cells. Real packs need cell matching (capacity, IR, SoC) to operate safely โ mixing cells reduces pack life and creates safety risk.
- Total energy is nominal at full state-of-charge. Usable energy depends on DoD (see battery-from-runtime).
- High S counts require careful BMS design for cell balancing โ neglected balance leads to capacity loss and runaway risk.
- Internal resistance scales as S/P ร cell IR, which affects high-current discharge voltage sag.
Battery pack design โ especially with lithium chemistries โ carries fire and shock risk. Always include a properly rated BMS, fuses, and thermal protection.