How do you calculate battery pack voltage, capacity and Wh?
Pack voltage is the cell voltage times the number of cells in series. Pack capacity in Ah is the cell capacity times the number of cells in parallel. Energy in Wh is voltage times Ah.
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Battery pack calculator
Pick a cell and this battery pack calculator finds the voltage, capacity, energy, maximum current and weight of a series-parallel pack. Or enter a target voltage and energy and get the S and P counts.
Start from
Examples
Sets the voltage.
Sets the capacity and current.
%
Optional: BMS, nickel strip, case and wiring on top of the cells.
3S2P pack energy
64.8 Wh
- Nominal voltage
- 10.8 V
- Full-charge voltage
- 12.6 V
- Discharge cut-off voltage
- 7.5 V
- Capacity
- 6 Ah
- Energy
- 64.8 Wh
- Max continuous current
- 30 A
- Power at that current
- 324 W at nominal voltage
- Cells
- 6
- Cell weight
- 282 g
- Energy density
- 230 Wh/kg
- Pack resistance (1 kHz limit)
- 27 mΩ
- Voltage sag at max current
- 0.81 V an estimate from a listed 1 kHz limit, not a DC figure
The retailer listing gives 15 A continuous at 25 °C with 60 % capacity at 250 cycles. Weight is the stated figure for the button-top version. Resistance is the published limit for a new cell at 1 kHz (under 30 mΩ DC).
⚠ Lithium packs need a protection circuit (BMS) that monitors each of the 3 series groups for over-voltage and under-voltage, limits current and watches temperature.
Parallel cells should be the same model, age and state of charge when joined. Connecting cells at different voltages drives a large equalizing current.
Parallel options at 3S with this cell
| Pack | Capacity | Energy | Max current | Weight |
|---|---|---|---|---|
| 3S1P | 3 Ah | 32.4 Wh | 15 A | 141 g |
| 3S2P | 6 Ah | 64.8 Wh | 30 A | 282 g |
| 3S3P | 9 Ah | 97.2 Wh | 45 A | 423 g |
| 3S4P | 12 Ah | 129.6 Wh | 60 A | 564 g |
| 3S6P | 18 Ah | 194.4 Wh | 90 A | 846 g |
| 3S8P | 24 Ah | 259.2 Wh | 120 A | 1.13 kg |
How do you calculate a battery pack’s voltage and capacity?
Multiply the cell voltage by the series count and the cell capacity by the parallel count. A 3S2P pack of 3.6 V, 3000 mAh 18650 cells is 10.8 V nominal, 12.6 V full, 6 Ah and 64.8 Wh, and can deliver up to 30 A if the cells are rated 15 A each.
Battery pack formulas for series and parallel cells
Series cells add voltage and share the same current. Parallel cells add capacity and current and share the same voltage.
Vpack = S × Vcell Ahpack = P × Ahcell Wh = Vnominal × Ahpack
- S, P
- cells in series and in parallel
- Vcell
- cell voltage: nominal, full charge or cut-off
- Ahcell
- cell capacity in Ah
Imax = P × Icell Rpack = S × Rcell ÷ P m = S × P × mcell
- Imax
- maximum continuous pack current
- Rpack
- pack resistance, from the cell resistance
- m
- mass of the cells alone
How to calculate battery pack capacity: worked examples
Example 1: 3S2P of Samsung 30Q 18650 cells
3 × 3.6 V = 10.8 V nominal, 12.6 V full and 7.5 V at cut-off. 2 × 3 Ah = 6 Ah, so 64.8 Wh. Continuous current is 2 × 15 A = 30 A, and six cells at 47 g weigh 282 g.
Example 2: a 48 V, 500 Wh e-bike pack from Samsung 50E 21700 cells
48 ÷ 3.6 V = 13.3, so 13S. Each string holds 13 × 3.6 V × 4.9 Ah = 229.3 Wh, so 500 Wh needs 3P. A 20 A load needs 3P at 9.8 A per cell. The result is 13S3P: 46.8 V, 14.7 Ah, 688 Wh, 39 cells and 2.69 kg before the BMS and case.
Example 3: a 12 V lead-acid replacement from A123 LiFePO4 cells
Four 3.3 V cells give 13.2 V nominal and 14.4 V full, close to a lead-acid battery’s working range. One string of 2.5 Ah cells is 2.5 Ah and 33 Wh, weighing 304 g.
Cells in the calculator
Transcribed from the sources below: maker specifications for the A123, HX and Energizer cells, and public retailer listings for the two Samsung cells (the 30Q’s resistance limit is the official figure HKJ quotes in his test). Weights marked max are listed maximums. Resistance at 1 kHz is lower than DC resistance; the NiMH cell uses Energizer’s listed internal resistance instead.
| Cell | Nominal | Full | Cut-off | Capacity | Max current | Weight | Resistance |
|---|---|---|---|---|---|---|---|
| 18650 Samsung 30Q | 3.6 V | 4.2 V | 2.5 V | 3000 mAh | 15 A | 47 g | 18 mΩ max at 1 kHz |
| 21700 Samsung 50E | 3.6 V | 4.2 V | 2.5 V | 4900 mAh | 9.8 A | 69 g max | 35 mΩ max at 1 kHz |
| 26650 A123 LiFePO4 | 3.3 V | 3.6 V | 2.0 V | 2500 mAh | 50 A | 76 g | 6 mΩ at 1 kHz |
| 32700 HX LiFePO4 | 3.2 V | 3.65 V | 2.0 V | 6000 mAh | 18 A | 140 g | 8 mΩ max at 1 kHz |
| AA Energizer NiMH | 1.2 V | 1.4 V | 1.0 V | 2500 mAh | 5 A | 30 g | 30 mΩ internal |
Battery pack voltage table by series count
Voltage across a pack by series count, for Li-ion (3.6 V nominal, 4.2 V full, 2.5 V cut-off) and LiFePO4 (3.2 V, 3.65 V, 2.0 V). For other chemistries, choose Custom cell in the battery pack voltage calculator above.
| Series cells | Li-ion nominal | Li-ion full | Li-ion cut-off | LiFePO4 nominal | LiFePO4 full | LiFePO4 cut-off |
|---|---|---|---|---|---|---|
| 1S | 3.6 V | 4.2 V | 2.5 V | 3.2 V | 3.65 V | 2 V |
| 2S | 7.2 V | 8.4 V | 5 V | 6.4 V | 7.3 V | 4 V |
| 3S | 10.8 V | 12.6 V | 7.5 V | 9.6 V | 10.95 V | 6 V |
| 4S | 14.4 V | 16.8 V | 10 V | 12.8 V | 14.6 V | 8 V |
| 6S | 21.6 V | 25.2 V | 15 V | 19.2 V | 21.9 V | 12 V |
| 7S | 25.2 V | 29.4 V | 17.5 V | 22.4 V | 25.55 V | 14 V |
| 10S | 36 V | 42 V | 25 V | 32 V | 36.5 V | 20 V |
| 13S | 46.8 V | 54.6 V | 32.5 V | 41.6 V | 47.45 V | 26 V |
| 14S | 50.4 V | 58.8 V | 35 V | 44.8 V | 51.1 V | 28 V |
Building a pack that behaves
- Protection. As general practice, a lithium pack needs a BMS on every series group, and the BMS’s own sleep current has to be small enough not to drain the pack in storage.
- Current limits are conditions, not free capacity. The NKON listing pairs the 30Q’s 15 A with 60 % capacity at 250 cycles, and HX limits its 32700 to 18 A for 20 minutes or less.
- Sag and heat. The sag shown uses 1 kHz resistance, which is below DC resistance: HX rates its cell at up to 8 mΩ AC and 16 mΩ DC. The HX figure and the two Samsung figures are listed limits, so treat their sag as an estimate.
- Capacity is conditional. The 50E is listed at 4900 mAh minimum at 0.2C and 4753 mAh minimum at 1C.
- Interconnects. Nickel strip, fuses and wiring add resistance and weight, so use the overhead field for the weight of the finished pack.
Glossary
- S (series)
- The number of cell groups connected end to end. It sets the pack voltage.
- P (parallel)
- The number of cells in each group. It sets the capacity and the current.
- Nominal voltage
- The representative voltage of a cell during discharge, used to compute energy.
- Cut-off voltage
- The voltage below which a cell must not be discharged.
- BMS
- Battery management system: the electronics that monitor each series group and protect the pack.
- Wh
- Watt-hours, the energy stored: volts times amp-hours.
Related guides
- Battery life calculator: runtime from the pack’s capacity.
- Battery charging time calculator: how long the pack takes to charge.
- AWG wire gauge calculator: size the pack leads for the current.
- Voltage drop calculator: how much the wiring costs you.
- Trace width calculator: the same current on a PCB.
Frequently asked questions
Does this work as an 18650 battery pack calculator?
Yes. Pick the Samsung 30Q or enter your own cell as a custom cell, then set the series and parallel counts. A 3S2P pack of 30Q cells comes to 10.8 V, 6 Ah and 64.8 Wh.
How do I size an e-bike battery pack?
Use the Target pack mode: enter the voltage, energy and continuous current. For 48 V, 500 Wh and 20 A from Samsung 50E 21700 cells it returns 13S3P: 39 cells, 46.8 V and 688 Wh.
What does 3S2P mean?
Three groups in series, each made of two cells in parallel, so six cells. With 3.6 V, 3 Ah cells a 3S2P pack is 10.8 V and 6 Ah, or 64.8 Wh.
How many 18650 cells do I need for a 48 V battery?
A 48 V Li-ion pack is normally 13 cells in series (13 × 3.6 V = 46.8 V nominal, 54.6 V full). The number in parallel depends on the energy and current you need: each parallel string of 3 Ah cells adds 3 Ah.
Does connecting batteries in series increase capacity?
Series connection increases the voltage and leaves the Ah the same, so the energy in Wh still goes up. Parallel connection increases the Ah and leaves the voltage the same.
How much current can a battery pack deliver?
The cell’s continuous rating times the number of cells in parallel, as an upper limit. Datasheet limits are measured in specific conditions, and a pack that holds heat in the middle cells needs a margin.
Do I need a BMS for a lithium battery pack?
Yes, as general practice. Each series group needs over-voltage and under-voltage monitoring, and the pack needs over-current and temperature protection.
Can I mix different cells in a pack?
Do not. In series the weakest cell limits the pack and can be over-discharged; in parallel, cells at different voltages drive equalizing currents between them. Use the same model and batch at the same state of charge.
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Sources
- NKON, Samsung INR18650-30Q product listing (retailer page: capacity, voltage limits, charge and discharge ratings, weight)
- HKJ, Test/Review of Samsung INR18650-30Q on Budget Light Forum (official resistance figures quoted in the test)
- Oomipood, Samsung INR21700-50E product listing (retailer page: capacity, voltage limits, currents, weight, resistance)
- A123 Systems, ANR26650M1-B data sheet
- Hunan Huaxing Lithium, HX-TS-066 IFR32700 product specification
- Energizer, NH15-2500 NiMH AA product datasheet
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