The fundamental charge formula for electricity storage sizing is Ah = (Watts × Hours) / (System Voltage × Depth of Discharge × Inverter Efficiency). If you are building an off-grid or backup power system, guessing your battery bank size leads to either premature cell death from over-discharge or thousands of dollars wasted on unused capacity. This guide breaks down the exact sizing math, the physics of series versus parallel wiring, and the hard limits of charge and discharge rates, terminating in a concrete hardware recommendation for a standard off-grid load.
The Core Battery Charge Formula and Sizing Math
To size a battery bank, you must calculate the total watt-hours (Wh) your loads consume and divide by the usable capacity of your system. The base formula is:
Required Ah = (Total Watt-Hours) / (Nominal Voltage × DoD × η)
- Total Watt-Hours: Sum of (Watts × Hours used per day) for all AC and DC loads.
- Nominal Voltage (V): Your battery bank voltage (12V, 24V, or 48V).
- Depth of Discharge (DoD): The percentage of the battery you can safely use (e.g., 0.50 for Lead-Acid, 0.80 for LiFePO4).
- Inverter Efficiency (η): Typically 0.93 for high-frequency inverters, 0.85 for heavy low-frequency transformer inverters.
Worked Numeric Example
Assume a daily load of 4,000Wh (e.g., a fridge, lights, and a laptop). You are building a 24V system using LiFePO4 batteries (80% DoD) with a high-frequency inverter (93% efficiency).
Required Ah = 4000 / (24 × 0.80 × 0.93) = 4000 / 17.856 = 224 Ah
You need a 24V 224Ah battery bank. Since standard LiFePO4 drop-in batteries are 12V 100Ah, you would wire two in series (to make 24V) and three of those strings in parallel (to make 300Ah), giving you a safe buffer.
Series vs. Parallel: Wiring Consequences for Voltage and Amp-Hours
How you wire your cells dictates your system voltage and current, which directly impacts your wire sizing and fire risk. The golden rules of battery wiring are:
- Series Wiring: Adds voltage, Amp-hours (Ah) remain the same. (Four 12V 100Ah batteries in series = 48V 100Ah).
- Parallel Wiring: Adds Amp-hours, voltage remains the same. (Four 12V 100Ah batteries in parallel = 12V 400Ah).
Why does this matter? Because of Ohm's Law and power loss ($P = I^2R$). Higher voltage means lower current for the same wattage. If you have a 3,000W inverter load:
- On a 12V system, the battery must supply 250 Amps continuously. This requires massive, expensive 4/0 AWG welding cable and poses a severe arc-flash and melting risk if a lug loosens.
- On a 48V system, the battery supplies only 62.5 Amps. You can safely use standard 4 AWG or 2 AWG copper wire, which is cheaper, easier to terminate, and runs significantly cooler.
Charge and Discharge Limits: C-Rates and Depth of Discharge
Batteries are not infinite buckets; they have strict speed limits for energy entering and exiting, defined by the "C-rate". A 1C rate means charging or discharging the battery's total Ah capacity in one hour. For a 100Ah battery, 1C = 100 Amps.
| Chemistry | Max Charge Rate | Max Discharge Rate | Usable DoD | Cycle Life (to 80% health) |
|---|---|---|---|---|
| Flooded Lead-Acid (FLA) | 0.2C (20A per 100Ah) | 0.2C to 0.3C | 50% | 500 - 800 |
| AGM / Gel (VRLA) | 0.3C (30A per 100Ah) | 0.5C to 1C | 50% | 400 - 600 |
| LiFePO4 (Lithium Iron) | 0.5C to 1C (50-100A) | 1C to 2C (100-200A) | 80% to 90% | 3,000 - 5,000+ |
If your solar array or generator can push 80 Amps into a 100Ah AGM battery, you are violating its 0.3C charge limit. This causes outgassing, electrolyte boil-off, and permanent capacity loss. Always size your charge controller output to stay within the battery's maximum C-rate. According to Battery University charging guidelines, adhering to manufacturer C-rate limits is the single most critical factor in preventing premature cell degradation.
Sizing the Inverter and Charge Controller for Your Load
A complete off-grid power system follows a strict source-to-load block architecture: Source (PV/Generator) → MPPT Charge Controller → Battery Bank (BMS Protected) → Inverter → AC Load. Sizing the middle components requires matching the bottleneck.
Inverter Sizing
Your inverter must handle both the continuous running wattage and the surge (starting) wattage of inductive loads like fridge compressors and well pumps. A standard rule is to add 25% overhead to your maximum simultaneous continuous load. If your peak continuous load is 2,400W, you need a 3,000W inverter. Ensure the inverter's surge rating (usually 2x continuous for 5 seconds) exceeds the Locked Rotor Amps (LRA) of your largest motor.
MPPT Charge Controller Sizing
The MPPT controller converts high-voltage, low-current solar power into low-voltage, high-current battery charging. Size it by dividing your total solar array wattage by your battery bank voltage, then multiply by 1.25 for the NEC Article 690 safety margin.
Controller Amps = (Solar Watts / Battery Volts) × 1.25
For a 2,000W solar array on a 48V bank: (2000 / 48) × 1.25 = 52 Amps. You would select a 60A MPPT charge controller (like a Victron SmartSolar 150/60).
Decision Path: Picking Your Exact Bank and Inverter
Do not get paralyzed by the options. Use this decision tree to lock in your system voltage, battery configuration, and inverter size based on your maximum simultaneous AC load.
| Max Continuous AC Load | System Voltage | Battery Configuration (using 12V 100Ah LiFePO4) | Recommended Inverter/Charger |
|---|---|---|---|
| Under 1,200W | 12V | 1x to 3x in Parallel (12V 100-300Ah) | Victron Phoenix 12/1200 or similar 1200W HF Inverter |
| 1,200W to 2,500W | 24V | 2 in Series, up to 2 strings Parallel (24V 100-200Ah) | Victron MultiPlus 24/2000 Inverter/Charger |
| 2,500W to 4,500W | 48V | 4 in Series (48V 100Ah minimum) | Victron MultiPlus-II 48/3000 Inverter/Charger |
| Over 4,500W | 48V | 4 in Series, 2+ strings Parallel (48V 200Ah+) | Victron Quattro 48/5000 or split-phase dual inverters |
The Concrete Default Recommendation
If you are building a standard off-grid cabin or robust home backup system with typical appliances (fridge, LED lights, TV, microwave, laptop) and want a system that will last a decade without babying it, here is your exact parts list:
- Battery Bank: Build a 48V nominal bank using four 12V 100Ah LiFePO4 drop-in batteries wired in series. This yields 48V at 100Ah (5,120Wh total, ~4,096Wh usable at 80% DoD). Keep them in a climate-controlled space above 32°F (0°C) to allow charging.
- Inverter/Charger: Use the Victron MultiPlus-II 48/3000. It provides 3,000W continuous (roughly 24A at 120V), handles 5,500W surge for motor starts, and includes a built-in 120A battery charger for grid/generator integration.
- Wiring: Use 2 AWG THHN copper wire for the battery-to-inverter run (keep it under 5 feet). Torque all terminal lugs to the manufacturer's spec (usually 10-12 Nm) and use a calibrated torque wrench; loose high-current DC lugs are the leading cause of off-grid electrical fires.
By applying the core charge formula, respecting C-rate limits, and stepping up to 48V to minimize current, you eliminate the guesswork and build a power system grounded in electrical physics rather than internet forum rumors.
