Battery parallel capacity:
formula and worked example

How parallel cells extend run time

When cells are connected with positives together and negatives together, they share the load. Each supplies its own share of the current, so the pack can run a given load for longer or supply a higher current. The pack's capacity is the sum of the cells' capacities, while the voltage stays at that of a single cell.

This calculation gives the pack capacity in ampere-hours. It is the number that tells you how long a particular current can be drawn, and it is half of the energy story together with voltage.

Parallel groups are the building block of most larger packs: parallel cells set capacity, and series stacks of those groups set voltage.

The formula and its inputs

• Cell capacity in ampere-hours is the rated charge of one cell at the stated discharge rate.
• Cells in parallel is the number of identical cells whose terminals are joined side by side.

Because the cells share terminals they must be at the same voltage when connected. Joining cells at different charge levels causes a large equalising current.

Worked example: six 2.5 Ah cells in parallel

A builder joins six 2.5 Ah cells in parallel to make one group.

1. 1Capacity of one cell: 2.5 Ah.
2. 2Number of cells in parallel: 6.
3. 3Multiply: 2.5 x 6 = 15 Ah.
4. 4Energy at 3.7 V nominal: 15 x 3.7 = 55.5 Wh.

At a constant draw of 3 A the group would run for about 5 hours, ignoring losses and capacity reduction at higher rates.

What 15 Ah means for a load

Run time is capacity divided by current. 15 Ah supports 1.5 A for ten hours or 15 A for one hour in an ideal world. In real cells the delivered capacity falls as the current rises, so the high-current figure is optimistic.

Parallel connection also shares the current among cells. Each cell then works less hard, which tends to reduce heating and extend life compared with a single cell supplying the whole load.

• Match the pack's continuous current rating to the load, since the cell's own limit multiplies by the number of parallel cells.
• For energy, multiply the ampere-hours by pack voltage to get watt-hours.

What a 10% higher cell capacity does

Moving from 2.5 Ah to 2.75 Ah cells with the same six in parallel raises the pack capacity from 15 to 16.5 Ah.

The effect is exactly proportional, as for any product of two numbers. Adding a seventh cell of 2.5 Ah would do the same job: 17.5 Ah, a larger rise than the 10% in this table.

Mistakes in parallel packs

• Connecting cells at different states of charge, which produces a large inrush current between them.
• Believing parallel wiring raises voltage; it leaves it unchanged.
• Mixing cells of different capacity, so the pack's behaviour is governed by the weakest member and the sum overstates what you can use.
• Forgetting that fusing is required per cell or per group so that a shorted cell does not drain the others.

Check the rating of every connection and busbar against the total current.

Planning a pack from capacity

Begin with the energy you need in watt-hours, divide by the pack voltage to get ampere-hours, and then divide by the single-cell capacity to find the number of parallel cells. Round up, and add a margin for ageing.

The series calculation then sets the voltage; together the two give the total cell count of the whole pack.