Battery Backup Calculator
Calculate backup runtime from battery capacity, or the battery bank size needed for a required number of backup hours.
Inputs
Formula
- Usable energy = Ah × V × DoD × η_batt × η_inv
- Backup hours = usable energy / load
- Required Ah = load × hours / (V × DoD × η_batt × η_inv)
Only part of a battery's nameplate capacity may be withdrawn: depth of discharge protects cycle life, and both round-trip battery losses and inverter conversion losses reduce what reaches the load. Lead-acid also suffers Peukert losses at high discharge rates, so a 200 Ah tubular battery delivering a heavy load supplies noticeably less than its C20 rating.
Step-by-step calculation
Nameplate energy
Ah × V
9,600 Wh
Combined factor
DoD × η_batt × η_inv
0.7866
Usable energy
nameplate × factor
7,551.4 Wh
Backup
usable / load
9.439 h
Worked example
- 200 Ah at 48 V LiFePO₄ (90% DoD, 95% efficiency), inverter 92%, load 800 W.
- Usable = 200 × 48 × 0.9 × 0.95 × 0.92 = 7 550 Wh.
- Backup = 7 550 / 800 = 9.4 hours.
Assumptions
- Constant load throughout the discharge and a battery at 100% state of health.
Tips
- Lithium delivers nearly twice the usable energy of lead-acid for the same nameplate Ah.
- Reducing the load by 20% extends runtime by 25% — cut standby loads before adding batteries.
Warnings
- Discharging lead-acid below 50% DoD roughly halves its cycle life.
- Ageing batteries lose 20–30% capacity; size with a margin for end-of-life performance.
Standards & references
- IEC 62619
- IEEE 1013 (PV battery sizing)
Frequently asked questions
How long will a 200 Ah battery last?
At 48 V with an 800 W load, about 9 hours for LiFePO₄ and about 4.5 hours for lead-acid, after depth-of-discharge and inverter losses.
How do I convert Ah to watt-hours?
Multiply amp-hours by the bank voltage: 200 Ah at 48 V is 9 600 Wh nameplate, of which only the usable fraction can be drawn.
Which chemistry gives more backup?
Lithium iron phosphate, because it allows 90% depth of discharge against 50% for lead-acid and has higher round-trip efficiency.
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