Battery Pack Series-Parallel
Vpack = Ns × Vcell, Qpack = Np × Qcell
Quick answer
This calculator solves V_pack = Ns × V_cell, Q_pack = Np × Q_cell for Parallel Cells. With Series Cells 0.5, Cell Voltage 12 V, Cell Capacity 2.5 Ah, the result is 6.
Calculator
Formula
Description
Battery packs combine cells in series to increase voltage and in parallel to increase capacity. A pack configured as NsSnpP has Ns cells in series and Np strings in parallel. For example, a 4S3P pack of 3.7 V, 2500 mAh 18650 cells produces 14.8 V nominal with 7500 mAh capacity. The total energy is Ns × Np × Vcell × Qcell. The forward result shows the pack voltage (Ns × Vcell). Pack capacity is Np × Qcell. Every cell in a series string must be balanced to prevent overcharge or over-discharge of individual cells.
Variables
- Ns — Number of cells in series (dimensionless)
- Np — Number of parallel strings (dimensionless)
- V_cell — Single cell nominal voltage (V)
- Q_cell — Single cell capacity (Ah or mAh)
Practical Notes
Common Li-ion configurations: 1S (3.7 V, USB power banks), 3S (11.1 V, laptop), 4S (14.8 V, RC batteries), 7S (25.9 V, e-bikes), 14S (51.8 V, e-bikes), 96S (355 V, EVs). A BMS is essential for series configurations to balance cells and prevent dangerous over-charge or over-discharge conditions. Cells in parallel should be matched for capacity and internal resistance.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Ns | Series Cells | — | — |
| Np | Parallel Cells | — | — |
| Vcell | Cell Voltage | V | pV, nV, µV, mV, V, kV |
| Qcell | Cell Capacity | mAh | mAh, Ah |
Step by step
- 1. What you know: Series Cells 0.5, Cell Voltage 12 V, Cell Capacity 2.5 Ah
- 2. The relation: V_pack = Ns × V_cell, Q_pack = Np × Q_cell
- 3. Substitute: Ns = 0.5, Vcell = 12 V, Qcell = 2.5 Ah
- 4. Result: Parallel Cells = 6
Worked examples
Minimum range
Given: Series Cells 0.025, Cell Voltage 0.33 V, Cell Capacity 50 mAh
Result: Parallel Cells = 0.00825
Low range
Given: Series Cells 0.25, Cell Voltage 3.3 V, Cell Capacity 0.5 Ah
Result: Parallel Cells = 0.825
Typical
Given: Series Cells 0.5, Cell Voltage 12 V, Cell Capacity 2.5 Ah
Result: Parallel Cells = 6
High range
Given: Series Cells 0.8, Cell Voltage 0.23 kV, Cell Capacity 10 Ah
Result: Parallel Cells = 184
Maximum range
Given: Series Cells 8, Cell Voltage 2.3 kV, Cell Capacity 100 Ah
Result: Parallel Cells = 18400
How Parallel Cells changes with Series Cells
| Series Cells (input) | Parallel Cells (result) |
|---|---|
| 0.05 | 0.6 |
| 0.125 | 1.5 |
| 0.25 | 3 |
| 0.375 | 4.5 |
| 0.5 | 6 |
| 0.75 | 9 |
| 1 | 12 |
| 2 | 24 |
| 3.5 | 42 |
| 5 | 60 |
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<p><a href="https://vbatpower.com/formulas/battery-series-parallel/">Battery Pack Series-Parallel</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Battery Pack Series-Parallel?
Use V_pack = Ns × V_cell, Q_pack = Np × Q_cell. With Series Cells 0.5, Cell Voltage 12 V, Cell Capacity 2.5 Ah, Parallel Cells works out to 6.
What is the formula for Battery Pack Series-Parallel?
The formula is V_pack = Ns × V_cell, Q_pack = Np × Q_cell. Battery packs combine cells in series to increase voltage and in parallel to increase capacity.
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