Two questions come up with batteries: how big a bank do I need, and how long will the one I have last. The calculator answers either one. Both use the same four quantities: energy, voltage, usable depth of discharge and inverter efficiency.
Formulas
Runtime (h) = capacity (Ah) × V × DoD × efficiency / load (W)
Depth of discharge (DoD) is the fraction of the capacity you are willing to use. Repeatedly draining a lead-acid battery deeply shortens its life, so about 50 % is a common design limit. Lithium iron phosphate (LiFePO4) batteries are commonly specified for 80 to 90 % or more. Use the figure in the battery’s datasheet, not a rule of thumb, because warranty terms often depend on it.
Efficiency accounts for the loss in the inverter between the battery and an AC load. Typical inverters convert at 85 to 95 %, and the default here is 0.9. If your load is DC and connects directly, set it to 1.
Worked example: sizing
A home uses 5,000 Wh per day and wants 2 days of autonomy on a 48 V lead-acid bank limited to 50 % DoD:
Capacity = 5,000 × 2 / (0.5 × 48 × 0.9) = 463 Ah.
That is a nominal 22.2 kWh bank, of which 10 kWh is usable. With a 48 V LiFePO4 bank at 80 % DoD the same autonomy needs 5,000 × 2 / (0.8 × 48 × 0.9) = 289 Ah, which is why lithium banks are much smaller for the same duty.
Worked example: runtime
A 200 Ah, 48 V battery with 80 % usable depth and a 0.9 inverter runs a 1,000 W load for 200 × 48 × 0.8 × 0.9 / 1,000 = 6.9 hours.
Choosing system voltage
The same energy at a higher voltage means less current. A 5 kW load draws about 420 A from a 12 V bank but about 104 A from a 48 V bank, so cable sizes, fuses and connector losses shrink considerably. For anything above about 2 kW, 48 V is a standard choice. Batteries are then wired in series to reach the voltage and in parallel to reach the amp-hours: four 12 V batteries in series make 48 V, and a second string in parallel doubles the Ah.
What the calculator leaves out
- Temperature. Batteries deliver less capacity in the cold, and lead-acid more so than lithium. Size for the coldest conditions the bank will see.
- Discharge rate. A lead-acid battery gives less than its rated capacity at fast discharge, a behaviour described by Peukert’s law. The rated Ah is normally quoted at the 20-hour rate.
- Ageing. Capacity falls over the years. Some designers add 10 to 20 % to cover it.
- Charging. The bank needs a source that can recharge it between uses. See the off-grid calculator.
Common mistakes
- Comparing Ah across voltages. 100 Ah at 12 V is 1.2 kWh, while 100 Ah at 48 V is 4.8 kWh.
- Counting the full capacity as usable.
- Ignoring inverter loss.
Questions
How many batteries do I need?
Divide the required Ah by one battery’s Ah for parallel strings, and divide the bank voltage by one battery’s voltage for series count.
How many kWh is a 100 Ah battery?
At 12 V, 1.2 kWh nominal. At 24 V, 2.4 kWh. At 48 V, 4.8 kWh.
How many days of autonomy should I choose?
One to three days is common for homes. More days cost more, and a generator can be cheaper than the extra batteries.