Battery series voltage:
formula and worked example
Connecting cells in series stacks their voltages while leaving capacity unchanged, which is how packs reach the voltage a device needs.
Calcylator Editorial Team
Updated · 4 min read
Why cells are stacked in series
A single lithium-ion cell is around 3.7 V nominal, far below what most inverters, motors and e-bike controllers need. Wiring cells end to end, positive to negative, makes their voltages add. The string behaves like one tall battery with the same capacity as one cell.
This calculation gives the nominal voltage of such a string. It is the first number in designing a pack, because the load, the charger and the protection board are all chosen for a particular voltage.
The same logic applies to lead-acid batteries: two 12 V units in series make a 24 V bank, and four make 48 V.
The formula and its inputs
- cell_voltage:
- Cell voltage
- cells_series:
- Cells series
- Cell voltage in volts is the nominal value of one cell, such as 3.7 V for many lithium-ion cells or 1.2 V for nickel-metal-hydride.
- Cells in series is the number of cells joined end to end in one string.
Use only identical cells in a string, matched for capacity and age. A weaker cell in a series string limits the whole pack.
Worked example: eight 3.7 V cells in series
A builder joins eight lithium-ion cells in one string for a small power pack.
- Nominal voltage of one cell: 3.7 V.
- Number of cells in series: 8.
- Multiply: 3.7 x 8 = 29.6 V nominal.
- Check the range: eight cells at 4.2 V fully charged give 33.6 V, so the pack swings above and below the nominal value.
Cell voltage
3.7
Cells series
8
Battery series voltage
29.6 V
The 29.6 V is a nominal figure; the terminal voltage moves with state of charge and load.
The capacity in ampere-hours stays at the value of one cell, while the stored energy rises by the same factor of eight.
What 29.6 V means for the load and charger
The nominal figure is an average. A load rated for a given voltage must tolerate the pack's full range from near-empty to full, and a charger must be set to the string's full-charge voltage, which is the per-cell charge limit multiplied by the number of cells.
The nominal voltage also decides current for a given power. The higher the pack voltage, the lower the current needed for the same watts, which means thinner wires and less loss in the cables.
- Power in watts equals voltage times current, so the same load draws half the current at twice the voltage.
- A battery management system should balance and protect each cell in the string.
What a 10% higher cell voltage does
If each cell were at 4.07 V rather than 3.7 V, the same eight cells would give 32.56 V. The 10% rise in cell voltage passes straight through to the pack.
| Scenario | Cell voltage | Calculated result |
|---|---|---|
| Original assumptions | 3.7 | 29.6 V |
| Cell voltage increased by 10% | 4.07 | 32.56 V |
This is illustrative rather than a realistic design change, since a given chemistry sets the voltage per cell. A more practical variation is to add or remove one cell, which changes the pack by one cell's voltage.
Mistakes with series packs
- Mixing cells of different capacity or age, which causes the weakest cell to be over-discharged or overcharged.
- Assuming that series wiring raises capacity; it only raises voltage.
- Designing around the nominal voltage when the device needs a minimum voltage that the pack falls below when nearly empty.
- Charging the string with a single-cell charger rather than one that matches the number of cells and the chemistry.
Series packs without cell-level protection can be unsafe, so use a proper management board.
Choosing the series count
Start from the load's voltage window and the pack's per-cell range. Pick the number of cells so that the empty voltage stays above the load's minimum and the full voltage stays below its maximum.
Then use the parallel capacity calculation to decide how many strings or parallel cells are needed for the run time you want.
Common questions
How do you calculate battery voltage in series?
Multiply the voltage of one cell by the number of cells in the string. Eight 3.7 V cells give 29.6 V nominal. Capacity in ampere-hours does not change when cells are connected in series.
Does connecting batteries in series increase capacity?
No. Series wiring increases voltage only, while the ampere-hour capacity stays equal to that of a single cell. To raise capacity, cells have to be joined in parallel groups, or whole strings placed in parallel.
What is nominal voltage for a lithium-ion cell?
About 3.6 to 3.7 V is commonly quoted, with a full charge around 4.2 V and a discharge cut-off near 3 V. The exact values depend on the chemistry and the manufacturer's data sheet.
Why does my pack read higher than the nominal voltage?
Nominal voltage is an average over the discharge curve. A freshly charged pack sits near the full-charge voltage, which is higher, and it drops toward the nominal value and then below it as the pack discharges.
Can I put different batteries in series?
It is not advised. Cells of different capacity, age or chemistry age and discharge at different rates, so the weakest one is stressed and may fail early. Use matched cells from the same batch and a battery management system.
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