A battery capacity calculator exists because batteries are labelled in a unit that cannot be compared. A power bank says 20,000 mAh, a laptop battery says 56 Wh, a solar storage unit says 5 kWh and a cell in a pack says 3,000 mAh at 3.6 V. Those are four different quantities, and only one of them — the watt-hour — describes how much energy is actually stored. This page converts between all of them and then does the second half of the job: working out what a series-parallel arrangement of those cells adds up to.
Arb Digital keeps a free tools library for the practical arithmetic behind technical decisions. This tool is deliberately about capacity and pack configuration only. It does not tell you how long a battery will last under load, and it does not work out how long it will take to charge — two separate questions with their own pages, both linked below.
What This Battery Capacity Calculator Does
Enter the capacity printed on one cell in whichever unit the label uses, choose the nominal cell voltage, and set how many cells sit in series and in parallel. The headline result is the total energy the pack holds in watt-hours, with milliamp-hours and kilowatt-hours shown alongside. The grid gives the pack's nominal voltage, its capacity in amp-hours, the usable energy at your chosen depth of discharge, and the total number of cells.
There is also an ageing field. Cells lose capacity over their life, so a pack whose cells retain 80% of their original capacity holds 80% of the energy the label claims. Setting that figure lets you calculate what a used pack really holds rather than what it held when new.
Three pages on this site sit next to each other, and it is worth being explicit about which does what. This one converts and sizes capacity. The battery life calculator takes a capacity and a load and returns runtime in hours — the question "how long will it last". The battery charge time calculator takes a capacity and a charger and returns how long refilling takes. Capacity is the input to both of the others; it is not the same question as either.
How to Use It
- Enter one cell, not the whole pack. The series and parallel fields do the multiplication. If you only have a whole-pack figure, set both S and P to 1 and enter the pack.
- Get the nominal voltage right. Nominal is the average voltage across a discharge, not the fully charged voltage. Using 4.2 V instead of 3.6 V for a lithium cell overstates its energy by about 17%.
- Count the configuration. A pack described as 4S3P has four groups in series, each group containing three cells in parallel — twelve cells in total.
- Set a realistic depth of discharge. Very few systems use 100% of a pack. The usable figure is the one to plan around.
- Compare in watt-hours. Whenever you are comparing two batteries, compare the watt-hour figures. Milliamp-hours only compare like with like at identical voltage.
The Formula / How It's Calculated
The core relationship is energy (Wh) = capacity (Ah) × voltage (V). Milliamp-hours convert to amp-hours by dividing by 1,000, and watt-hours to kilowatt-hours the same way, which follows directly from the standard SI prefixes documented by NIST's metric (SI) prefixes reference. Pack voltage is cell voltage × S, pack capacity is cell capacity × P, and pack energy is the product of the two — which is the same as cell energy × S × P.
Worked example, using the values the page loads with. A 3,000 mAh lithium-ion cell at 3.6 V nominal holds 3.0 Ah × 3.6 V = 10.8 Wh. Arrange twelve of them as 4S3P and the pack is 4 × 3.6 = 14.4 V nominal, with 3 × 3.0 = 9.0 Ah of capacity, for a total of 14.4 × 9.0 = 129.6 Wh, or 0.130 kWh. At an 80% depth of discharge the usable energy is 103.7 Wh.
Note that the twelve cells hold 129.6 Wh regardless of how they are wired. Rearranged as 3S4P they would be 10.8 V and 12.0 Ah — the same energy in a different shape. Series and parallel change the voltage and current a pack can deliver, not the total energy it stores.
Why mAh Is a Misleading Number
Milliamp-hours measure charge, not energy. A power bank advertised at 20,000 mAh is usually quoting the capacity of its internal lithium cells at around 3.7 V, which is about 74 Wh. But it delivers power at 5 V over USB, and 74 Wh at 5 V is only about 14,800 mAh before any conversion losses — so the phone you charge from it sees far less than the number on the box implies. Nothing dishonest has happened; two different voltages are being quoted in the same unit.
This is the single most common source of confusion in consumer battery specifications, and it is why regulators and better manufacturers increasingly quote watt-hours. Airline cabin-baggage rules for lithium batteries are written in watt-hours for exactly this reason: it is the only figure that describes stored energy independently of the chemistry and cell arrangement.
The practical rule is simple. Compare mAh figures only between batteries at the same voltage — two AA cells, or two phone batteries of the same chemistry. The moment voltages differ, convert to watt-hours first. The energy converter handles watt-hours against joules, calories and BTU if you need to go further, and the electric charge converter covers charge units themselves.
Series, Parallel and What Each One Buys You
Cells in series stack their voltages while the amp-hour capacity stays put: four 3.6 V cells in series make 14.4 V at the same amp-hours as one cell. Cells in parallel do the opposite — the voltage stays at one cell's value and the capacities add. Total energy is identical either way, which surprises people who expect series wiring to be somehow "more".
The choice is driven by what the load needs. A motor rated at 36 V has to see 36 V, so you need enough cells in series to reach it, no matter how much capacity you have. Higher voltage also means lower current for the same power, which means thinner cable and lower resistive losses — the reason electric vehicles and solar storage systems run at hundreds of volts rather than twelve. Parallel groups exist to supply the current the load draws and to extend runtime.
One real constraint: cells wired in parallel must be closely matched in voltage and capacity, because any difference between them drives current from one cell into another. This is why packs are built from matched cells and managed by a battery management system that balances the series groups. The Ohm's law calculator covers the voltage, current and resistance relationships, and the electrical power calculator handles power on the load side.
Depth of Discharge, Ageing and Usable Capacity
Nameplate capacity and usable capacity are different numbers. Almost no system runs a battery from completely full to completely empty: lead-acid installations are commonly designed around a partial discharge, and lithium systems reserve a buffer at both ends that the user never sees. Setting a depth of discharge in this calculator gives you the figure to plan around rather than the figure on the label.
Capacity also falls with age and use, gradually and irreversibly. The US Department of Energy's explainer on batteries describes the electrochemistry involved — charge and discharge move ions through an electrolyte, and the materials change slowly as they cycle. The practical consequence for this calculator is that a pack's real capacity is its rated capacity multiplied by whatever fraction of health remains, which is what the ageing field applies.
When you are sizing a new pack for a job that must still work in five years, apply both reductions. A 129.6 Wh pack used to 80% depth and expected to retain 80% of capacity by end of life delivers about 83 Wh in its worst year. If the job needs 100 Wh, the pack is too small even though its label says 129.6.
Arb Digital's free tools library covers the energy, power and cost maths behind hardware and household projects, and our team is happy to talk through anything the tools cannot answer.
Browse Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Comparing mAh across different voltages — it measures charge, not energy. Convert both to watt-hours before comparing anything.
- Using the fully charged voltage — nominal voltage is the average across a discharge, and using the peak overstates stored energy by a sixth or more.
- Expecting series wiring to add energy — twelve cells hold the same energy as 4S3P or 3S4P. Only the voltage and current change.
- Planning around nameplate capacity — depth of discharge and ageing both cut into it, and the usable figure is often 60 to 70% of the label.
- Mixing unmatched cells in parallel — differences in voltage or capacity drive current between cells rather than into the load.
Related Free Tools From Arb Digital
Use the battery life calculator once you know the capacity and want runtime under a load, the battery charge time calculator for how long refilling takes, the energy converter for watt-hours against joules and BTU, the appliance wattage calculator to build the load a pack must supply, and the solar panel calculator when the pack is part of an off-grid system. Everything else is in the free online tools hub.
Frequently Asked Questions
Divide milliamp-hours by 1,000 to get amp-hours, then multiply by the nominal voltage. A 3,000 mAh cell at 3.6 V is 3.0 × 3.6 = 10.8 Wh. Without a voltage the conversion is impossible, which is why mAh alone tells you nothing about stored energy.
Because the 20,000 mAh is measured at the internal cell voltage of about 3.7 V, roughly 74 Wh, while the USB output is at 5 V. The same energy at 5 V is under 15,000 mAh before conversion losses, so the phone sees considerably less than the label suggests.
Four groups wired in series, each group containing three cells in parallel — twelve cells in total. Series multiplies voltage by four; parallel multiplies amp-hour capacity by three. Total energy is twelve times one cell's energy either way.
Nominal, which is the average voltage across a discharge. A lithium-ion cell nominally rated 3.6 V peaks near 4.2 V when full, and using that peak figure overstates the stored energy by about 17%.
No. Series increases voltage while amp-hour capacity stays at one cell's value. Parallel increases amp-hour capacity while voltage stays put. The total energy in watt-hours is the same for a given number of identical cells.
It is the share of a pack's capacity you actually use between charges. Few systems use all of it, so the usable energy is meaningfully less than the nameplate. Planning around the usable figure rather than the label is what stops a pack being undersized.
This page converts and sizes capacity — what a battery holds. The battery life calculator takes that capacity plus a load and returns runtime in hours. Capacity is the input to that calculation, not the answer to it.
This tool performs arithmetic on the figures you supply. It is not battery design, wiring or safety guidance, and any pack construction should follow the cell manufacturer's own documentation.
