Why off-grid banks are sized in amp-hours
An amp-hour is a charge, not an energy, and it only becomes energy when you attach a voltage: 100 Ah at 12 V is 1.2 kWh, and the same 100 Ah at 48 V is 4.8 kWh. Off-grid systems have kept the amp-hour convention because everything else in a DC system — the charge controller, the shunt, the fuses, the cable — is rated in amps. Choosing the bank voltage first, then sizing in amp-hours, keeps the numbers on the same page as the hardware.
The sizing question is straightforward to state: how much charge must the bank hold so that a run of sunless days does not leave your loads dead or the batteries damaged. Three things stand between the nameplate capacity and the energy you can actually use.
Depth of discharge. Lead-acid batteries lose cycle life sharply the deeper you take them, which is why the long-standing practice is to size flooded and AGM banks so routine discharge never passes 50%. Lithium iron phosphate tolerates 80-100%, which is the single biggest reason a lithium bank of the same usable capacity is physically smaller and lighter — you are buying roughly half the nameplate.
Inverter efficiency. Every AC watt-hour your loads consume costs more than one watt-hour out of the battery. At 90% efficiency, a 3,000 Wh daily AC load pulls 3,333 Wh from the bank.
Temperature. Battery capacity falls as it gets colder. A lead-acid battery delivering its rated capacity at 25 °C delivers noticeably less near freezing, so an unheated shed in a northern winter needs a larger bank for the same job. Lithium has a harder constraint still: most cells must not be charged below 0 °C without integral heating.
IEEE 1013, the recommended practice for sizing lead-acid batteries in stand-alone photovoltaic systems, formalises exactly this chain of derating factors, and the same structure applies whatever the chemistry — only the numbers you put in the DoD and temperature slots change.
Working through the formula
Multiply the daily load by the days of autonomy to get the energy the bank must hold. Divide by the bank voltage to convert energy into charge. Then divide by each derating factor in turn, because each one reduces the share of nameplate you may actually use.
Days of autonomy is a design decision about risk, not a physical quantity. Two days is the usual minimum for a sunny climate where a generator can cover the exception. Three to four suits a temperate climate with real winter cloud. Five or more is for remote sites where no generator will arrive. Each extra day costs a proportional amount of battery, so autonomy is the most expensive input on the page — and it is worth checking whether a generator or a few extra solar modules buys the same reliability for less. Size the array separately; the solar output calculator tells you what a given array actually returns in the worst month.
Bank voltage is chosen from the inverter's power, not from the battery. Current equals power divided by voltage, so a 3 kW inverter draws about 250 A from a 12 V bank, 125 A from 24 V and 62 A from 48 V. The 12 V version needs enormous cable, a 300 A class-T fuse and a busbar that costs real money; the 48 V version runs on cable you can bend by hand. As a working rule, use 12 V below about 1 kW of inverter, 24 V from 1 to 3 kW, and 48 V above that.
Series and parallel. Series raises voltage and keeps amp-hours; parallel raises amp-hours and keeps voltage. A 48 V bank from 12 V batteries needs four in series per string. If the required capacity is 278 Ah and each battery is 100 Ah, you need three strings, so twelve batteries. Note the rounding: the installed 300 Ah exceeds the 278 Ah requirement, which is normal and gives useful margin.
Keep parallel strings few. Identical strings never share current perfectly, and the mismatch grows as the batteries age, so a bank of six or eight parallel strings ages unevenly and the weakest string drags the rest. Three or four strings is the usual limit; beyond that, buy higher-capacity batteries — 2 V cells at 600-1,200 Ah exist precisely for this reason.
Worked example: a 3 kWh-a-day cabin on 48 V
A cabin's load audit totals 3,000 Wh a day. The owner wants two days of autonomy, runs a 48 V bank of 100 Ah 12 V AGM batteries at $250 each, limits discharge to 50%, and has a 90% efficient inverter. The battery room stays above 25 °C, so the temperature factor is 1.00.
- Energy over the autonomy period. 3,000 × 2 = 6,000 Wh.
- Combined derating. 0.50 × 0.90 × 1.00 = 0.45. Less than half of what you buy is usable.
- Denominator. 48 V × 0.45 = 21.6.
- Capacity required. 6,000 ÷ 21.6 = 277.8 Ah at 48 V.
- Nominal energy. 277.8 × 48 ÷ 1,000 = 13.33 kWh of nameplate for 6 kWh of delivered energy.
- Series count. 48 ÷ 12 = 4 batteries per string.
- Parallel strings. 277.8 ÷ 100 = 2.78, rounded up to 3 strings.
- Total batteries. 4 × 3 = 12 batteries, giving 300 Ah installed.
- Usable energy. 300 × 48 ÷ 1,000 = 14.4 kWh nameplate, × 0.45 = 6.48 kWh delivered.
- Cost per usable kWh. 12 × $250 = $3,000 ÷ 6.48 = $463 per usable kWh.
That last figure is the one to carry into a chemistry comparison. Suppose the alternative is a 48 V lithium iron phosphate bank at 80% depth of discharge and the same 90% inverter, so the derating is 0.72 rather than 0.45. The requirement drops to 6,000 ÷ (48 × 0.72) = 173.6 Ah, and a single 200 Ah 48 V unit covers it with 6.91 kWh usable. If that unit costs $2,800, the cost per usable kWh is $405 — cheaper than the lead-acid bank before you count the lithium's three-to-five times longer cycle life, its smaller footprint and the fact that it does not need equalisation charging. Comparing headline prices per amp-hour would have given the opposite ranking.
How to read the result
Check the parallel string count first. More than three or four strings is a design smell rather than an answer. It usually means the battery you picked is too small for the job, and larger batteries — or 2 V cells — will give a longer-lived bank at similar cost.
Read the gap between nominal and usable energy as the price of the chemistry. A lead-acid bank at 50% depth of discharge with a 90% inverter delivers 45% of what it stores. That is not waste, it is what buys cycle life; but it is exactly the number to hold up when someone compares a lead-acid price per amp-hour against a lithium one.
Cost per usable kWh is the only fair price comparison, and even it is incomplete. It ignores cycle life, which is where lithium earns most of its advantage. If you want to go further, divide the bank cost by (usable kWh × rated cycles) to get a cost per kWh cycled, which is the metric that actually determines lifetime cost.
Confirm the amp-hour rating's discharge rate. Lead-acid capacity is rate-dependent: a battery rated 100 Ah at the 20-hour rate delivers materially less if you pull it flat in four hours, an effect described by Peukert's law. If your loads discharge the bank quickly, the effective capacity is below the label and the bank needs to be larger than this calculation suggests. Lithium is far less rate-sensitive over normal residential discharge rates.
Check the charge current the bank needs. A rule of thumb for flooded lead-acid is a charge current of roughly 10-13% of the bank's amp-hour capacity, so a 300 Ah bank wants about 30-40 A of charging — which sets a floor on array size and charge controller rating independent of the daily energy balance.
Depth of discharge, chemistry and what you actually get
| Chemistry | Typical max depth of discharge | Usable fraction at 90% inverter | Nameplate for 6 kWh delivered | Ah at 48 V |
|---|---|---|---|---|
| Flooded lead-acid (deep cycle) | 50% | 45% | 13.33 kWh | 278 |
| AGM lead-acid | 50% | 45% | 13.33 kWh | 278 |
| Gel lead-acid | 50% | 45% | 13.33 kWh | 278 |
| Lead-carbon | 60% | 54% | 11.11 kWh | 231 |
| Lithium iron phosphate (LiFePO₄) | 80% | 72% | 8.33 kWh | 174 |
| Lithium iron phosphate, full-depth rated | 100% | 90% | 6.67 kWh | 139 |
Depth-of-discharge limits are the values commonly recommended for good cycle life rather than absolute limits; the manufacturer's cycle-life curve for your specific product is the authority. Lithium figures assume the battery management system permits the stated depth.
Off-grid battery sizing mistakes
- Quoting amp-hours without a voltage. A 400 Ah bank means nothing until you say 12, 24 or 48 V — the energy differs by a factor of four across that range.
- Sizing lead-acid to 100% depth of discharge. It works exactly once. Deep-cycle lead-acid cycled to empty loses most of its rated life within months.
- Comparing chemistries on price per amp-hour. Compare on price per usable kWh, and preferably on price per kWh cycled over the rated life.
- Building six or more parallel strings. Current sharing degrades as the strings age and the bank fails at the pace of its weakest member. Use larger batteries instead.
- Ignoring the discharge rate the capacity was measured at. Lead-acid rated 100 Ah at the 20-hour rate delivers appreciably less at a 4-hour rate; check the manufacturer's rate table if your loads are heavy relative to the bank.
- Forgetting charge current. A bank needs a minimum charge rate to reach full charge; sizing the array purely to the daily energy balance can leave lead-acid chronically undercharged and sulfating.
- Leaving the temperature factor at 1.00 for an unheated building. A cold bank is a smaller bank, and lithium additionally refuses to charge below freezing without heaters.
How this fits the rest of the off-grid design
Battery sizing is the second step in an off-grid design, not the first. Start with the load: an appliance-by-appliance audit with the daily load audit calculator gives you the watt-hour figure this page depends on, and it is the number most worth getting right — every downstream component scales with it.
Then size the array to recharge the bank in the worst month, not the average one. An off-grid array is typically much larger relative to the load than a grid-tied one, because it must also make up for the days of autonomy it just spent and because there is no grid to lean on in December. Use the worst-month peak sun hours in the production calculator rather than the annual average.
Finally, check the charge controller and the inverter. The controller must handle the array's short-circuit current with the code-required multipliers, and the inverter must handle the largest simultaneous load and the motor surges. Those are power calculations, not energy ones, and a bank sized correctly in amp-hours can still fail if the inverter is too small.
If your system is grid-tied and the battery exists for outage backup rather than daily autonomy, use the home battery backup sizing calculator instead — the arithmetic is related but the design objective, and therefore the answer, is different.