To calculate battery life and properly size a bank, divide your total daily Watt-hours by the nominal system voltage, then adjust for inverter efficiency and Depth of Discharge (DoD). For example, a 4000Wh daily load on a 48V system with a 92% efficient inverter and an 80% DoD LiFePO4 bank requires a minimum of 113Ah nominal capacity. If you are using lead-acid, you must also apply Peukert’s Law, which drastically reduces usable capacity at high discharge rates.
The Source-to-Load Power Path
Before running the numbers, you must define your system block. A complete off-grid or UPS power path flows from the generation source, through storage, to the AC load. Here is a standard high-efficiency architecture:
- Source: Solar array (e.g., 4x 400W REC Alpha panels) or Grid/Generator input.
- Charge Path: MPPT Charge Controller (e.g., Victron SmartSolar 150/35) regulating DC voltage to the battery.
- Storage (The Battery Bank):strong> 48V LiFePO4 bank acting as the DC buffer.
- Inverter/Charger: Victron MultiPlus-II 48/3000/35-32 converting DC to AC and managing grid-tie/generator charging.
- Load: AC sub-panel feeding appliances, limited by the inverter's continuous and surge ratings.
Every connection point introduces a loss. Wire resistance, BMS (Battery Management System) voltage drops, and inverter switching losses mean your battery must supply more energy than the load strictly consumes.
The Core Battery Life Calculation Math
Let us size a bank for a remote cabin running a refrigerator (80W continuous), LED lighting (40W), and a laptop (60W) for 12 hours a day, plus a 1000W microwave used for 15 minutes.
Step 1: Calculate Total Daily Watt-Hours (Wh)
- Fridge: 80W x 24h = 1920Wh
- Lights & Laptop: 100W x 12h = 1200Wh
- Microwave: 1000W x 0.25h = 250Wh
- Total AC Load: 3370Wh per day
Step 2: Adjust for Inverter Efficiency
High-frequency pure sine wave inverters operate at roughly 90% to 93% efficiency. Assuming 90% (0.90), the DC energy required from the battery is:
3370Wh / 0.90 = 3744Wh DC draw
Step 3: Convert to Amp-Hours (Ah) at System Voltage
For a 48V nominal system (actual resting voltage is closer to 51.2V, but we use nominal for baseline sizing):
3744Wh / 48V = 78Ah required daily discharge
Step 4: Apply Depth of Discharge (DoD) Limits
Batteries cannot be drained to 0% without severe degradation. LiFePO4 chemistry safely allows an 80% to 90% DoD. Flooded Lead-Acid (FLA) or AGM should be limited to 50% DoD.
- LiFePO4 (80% DoD): 78Ah / 0.80 = 97.5Ah minimum bank size (Round up to a standard 100Ah 48V server-rack battery).
- AGM (50% DoD): 78Ah / 0.50 = 156Ah minimum bank size.
Series vs. Parallel: Voltage, Ah, and C-Rate Limits
When building a bank from individual 12V modules or raw cells, you must configure them to hit your target voltage and capacity. The physical wiring dictates the electrical behavior, and your BMS must be matched to the configuration.
| Configuration | Voltage Consequence | Amp-Hour (Ah) Consequence | C-Rate & Limits |
|---|---|---|---|
| Series (e.g., 4S) | Multiplies (12V x 4 = 48V) | Stays the same (100Ah) | Current (Amps) is identical through all batteries. Weakest cell limits the entire string. BMS must match the high series voltage. |
| Parallel (e.g., 4P) | Stays the same (12V) | Multiplies (100Ah x 4 = 400Ah) | Current divides among branches. Warning: Mismatched internal resistance causes uneven charging. Fuses on each parallel branch are mandatory to prevent reverse-current fires. |
| Series-Parallel (e.g., 4S2P) | Multiplies by series count | Multiplies by parallel count | Requires top-tier cell matching and active balancing. Avoid this in DIY builds; buy pre-assembled 48V server-rack batteries instead. |
Understanding C-Rate Limits: The C-rate defines your safe charge and discharge limits relative to capacity. A 100Ah battery with a 0.5C max continuous discharge rating can only safely output 50A (2400W at 48V). If your inverter pulls 80A to run a well pump, the BMS will trip its over-current protection, killing your power. Always check the BMS continuous current rating, not just the battery's Ah rating.
Inverter and Charger Sizing for Your Calculated Load
Your battery calculation is useless if the inverter bottlenecks the system or the charger cannot replenish the bank before the next cycle.
Inverter Sizing (Continuous vs. Surge):
Add up the continuous running watts of all devices that might operate simultaneously. Then, identify the highest surge load. Induction motors (fridges, well pumps, AC compressors) draw Locked Rotor Amps (LRA) for 1 to 3 seconds during startup, often 3x to 5x their running wattage.
Example: If your continuous load is 1500W, but a 1/2 HP well pump requires a 2500W surge to start, you need an inverter rated for at least 2500W continuous, with a 5000W surge capacity. The Victron MultiPlus-II 48/3000 handles 3000W continuous and 5500W peak, making it a safe choice here.
Charger Sizing (The 10% to 20% Rule):
To avoid sulfating lead-acid or undercharging lithium, your DC charge source (solar MPPT or AC-to-DC charger) should be able to deliver a current equal to 10% to 20% of the battery bank's total Ah.
Example: For a 200Ah 48V bank, your charge controller or inverter-charger should supply between 20A and 40A. A 40A charge rate on a 48V system requires roughly 2200W of solar input (accounting for panel derating and temperature losses, size the array at 2800W+). According to Cadex Electronics' Battery University, charging lithium at a moderate 0.2C to 0.3C prolongs cycle life significantly compared to max-rate 1C charging.
Battery Life Calculation FAQ
How does ambient temperature affect my battery life calculation?
Temperature drastically alters both usable capacity and cycle life. Lead-acid batteries lose roughly 50% of their capacity at -4°F (-20°C) and suffer accelerated grid corrosion if kept above 86°F (30°C). LiFePO4 batteries maintain excellent discharge capacity down to 14°F (-10°C), but they cannot be charged below freezing without a BMS equipped with low-temperature cutoff or internal heating elements. Attempting to charge lithium below 32°F (0°C) causes lithium metal plating on the anode, permanently damaging the cell and creating an internal short-circuit hazard. Always derate your battery bank by 20% if it will operate in unheated environments during winter.
Why is my calculated cycle life shorter than the manufacturer's spec sheet?
Manufacturer spec sheets typically claim 4000 to 6000 cycles for LiFePO4, but this assumes laboratory conditions: a 25°C ambient temperature, a gentle 0.2C discharge rate, and an 80% DoD. In real-world off-grid applications, high ambient heat (like an uninsulated shed in Texas), high-discharge C-rates from running microwaves, and occasionally draining the battery to the BMS low-voltage cutoff (100% DoD) will compress that cycle life to 2000 or 3000 cycles. Cycle life is non-linear; discharging to 100% DoD degrades the battery exponentially faster than discharging to 50% DoD.
Can I mix AGM and LiFePO4 batteries in parallel to increase my bank capacity?
No. Mixing different chemistries in parallel is a critical failure point. AGM and LiFePO4 have completely different resting voltages and charge absorption curves. A fully charged LiFePO4 battery rests at 13.6V, while a fully charged AGM rests at 12.8V. If paralleled, the lithium bank will continuously force current into the AGM bank attempting to equalize the voltage, leading to chronic overcharging of the AGM (causing thermal venting and dry-out) and undercharging of the lithium. Always build your bank using identical batteries of the same chemistry, brand, age, and capacity.
