To size an off-grid or solar battery bank, divide your daily watt-hour (Wh) load by the system voltage, then divide by the allowable depth-of-discharge (DoD) and inverter efficiency. For example, a 3,000Wh daily load on a 48V system using LiFePO4 batteries (80% DoD) and a 93% efficient inverter requires a minimum of 84Ah (3000 ÷ 48 ÷ 0.80 ÷ 0.93). In practice, you add a 20% autonomy buffer, bringing the target to roughly 100Ah at 48V.
But raw math only gets you to the starting line. Real-world battery sizing demands accounting for voltage sag, chemistry-specific discharge curves, and the physical limits of your charge controllers. Here is the bench-tested framework for sizing 12V, 24V, and 48V banks without melting lugs or bricking your BMS.
The Source-to-Load System Block (and Where Energy Dies)
Before calculating amp-hours, you must map the system block from source to load. Every conversion step bleeds energy as heat, and ignoring these losses is the number one reason DIY solar banks fail to deliver their nameplate capacity.
- Source (PV/Wind/Grid): Generates raw DC or AC power. Solar panels rarely output their STC (Standard Test Condition) rating; expect 75-80% of nameplate in real-world NOCT (Nominal Operating Cell Temperature) conditions.
- Charge Controller/Rectifier: Steps down/up voltage to match the battery bank. MPPT controllers operate at 95-98% efficiency, while PWM controllers can drop to 70% if panel Vmp is poorly matched to battery voltage.
- Battery Bank (The Buffer): Stores chemical energy. Internal resistance causes voltage sag under load, reducing the effective energy delivered to the terminals.
- Inverter: Converts DC to AC. High-frequency inverters run 88-92% efficient at full load, but efficiency plummets to 70% or lower at idle/light loads. Low-frequency (transformer-based) inverters handle surges better but carry a constant 15-30W parasitic draw.
- Load: The actual appliances. Remember that inductive loads (fridges, well pumps) have a startup surge 3x to 5x their running wattage.
When sizing your bank, you are sizing for the load side of the inverter, working backward through the efficiency losses to the battery terminals.
Battery Sizing Math: Factoring in Peukert, DoD, and Efficiency
The fundamental formula for required battery capacity in Amp-hours (Ah) is:
Ah = (Daily Wh Load) ÷ (System Voltage × DoD × Inverter Efficiency)
However, this assumes a linear discharge, which is only true for lithium. If you are using lead-acid (Flooded, AGM, or Gel), you must apply Peukert’s Law. Peukert’s exponent describes how a battery's effective capacity shrinks as the discharge rate increases. A 100Ah flooded lead-acid (FLA) battery rated at the 20-hour rate (C/20) will only deliver about 60Ah if you pull 50A (C/2) from it. LiFePO4 batteries have a Peukert exponent near 1.05, meaning you get nearly 100Ah whether you pull 10A or 100A.
You must also respect the C-rate (charge/discharge current relative to capacity) and Depth of Discharge (DoD). Pushing a lead-acid battery past 50% DoD drastically cuts its cycle life, while LiFePO4 routinely handles 80-90% DoD.
| Chemistry | Max Recommended DoD | Peukert Exponent | Max Discharge C-Rate | Max Charge C-Rate | Typical Cycle Life (to 80% SOH) |
|---|---|---|---|---|---|
| Flooded Lead-Acid (FLA) | 50% | 1.30 - 1.40 | 0.2C (C/5) | 0.1C - 0.15C | 500 - 800 |
| AGM / Gel (VRLA) | 50% | 1.15 - 1.25 | 0.3C (C/3) | 0.2C | 400 - 600 |
| LiFePO4 (Lithium Iron Phosphate) | 80% - 90% | 1.05 | 1.0C (Continuous) | 0.5C (Standard) | 3,000 - 5,000+ |
Source data adapted from Battery University chemistry profiles and manufacturer datasheets.
Series vs. Parallel: Voltage, Ah, and the Mismatch Trap
Once you know your target Ah and system voltage, you must configure the physical cells or monoblocks. The rules of series and parallel are absolute:
- Series Wiring: Adds voltage, Ah remains the same. Wiring four 12V 100Ah batteries in series yields a 48V 100Ah bank (4,800Wh total). This is the preferred method for high-power systems because it keeps DC current low, allowing the use of smaller, cheaper wire (e.g., 2/0 AWG instead of 4/0 AWG).
- Parallel Wiring: Adds Ah, voltage remains the same. Wiring four 12V 100Ah batteries in parallel yields a 12V 400Ah bank (4,800Wh total). This requires massive cabling to handle the high current and is generally restricted to small RV or marine setups.
Never parallel mismatched cells or batteries. If you connect a new 100Ah LiFePO4 battery in parallel with an older 100Ah battery that has higher internal resistance, the newer battery will dump massive current into the older one during charging and discharging. This uncontrolled circulating current bypasses the BMS limits, leading to thermal runaway, venting, and catastrophic lithium fires. Always parallel identical batteries of the same age, chemistry, and capacity. For large banks, use a single high-capacity server-rack battery (e.g., 48V 100Ah) rather than paralleling multiple 12V lithium monoblocks. Adhere to NFPA 855 guidelines for stationary energy storage spacing and fire separation.
Matching the Inverter and Charge Controller to Your Bank
A perfectly sized battery bank is useless if your inverter draws more current than the battery's C-rate allows, or if your charge controller cannot replenish the bank before sunset. Charge and discharge limits dictate your hardware ceiling.
Inverter Sizing: Your inverter's continuous wattage must exceed your maximum simultaneous AC load by at least 25%. More critically, the DC current draw on the battery must not exceed the battery's continuous discharge C-rate. A 3,000W inverter on a 12V system pulls roughly 270A at full load (3000W ÷ 12V ÷ 0.93 efficiency). Most 12V 100Ah LiFePO4 BMS units will trip their over-current protection at 100A-150A. Therefore, a 3,000W inverter mandates a 24V or 48V system.
Charge Controller Sizing: Solar charge controllers must be limited to the battery's maximum charge C-rate. If you have a 200Ah LiFePO4 bank (0.5C max charge rate), your solar array and MPPT controller should not push more than 100A into the bank. Exceeding this degrades the lithium anode and triggers BMS over-current disconnects.
| System Voltage | Max Inverter Size (Continuous) | Max DC Current Draw (Approx) | Minimum Battery Bank Size (LiFePO4) | Required Wire Size (Battery to Inverter) |
|---|---|---|---|---|
| 12V | 1,200W | 115A | 12V 150Ah (1C discharge) | 1/0 AWG or 2/0 AWG THHN |
| 24V | 3,000W | 135A | 24V 100Ah (1C discharge) | 1/0 AWG or 2/0 AWG THHN |
| 48V | 5,000W - 8,000W | 110A - 180A | 48V 100Ah (1C discharge) | 2/0 AWG or 4/0 AWG THHN |
Wire sizing assumes a 1.5-meter one-way run with a maximum 3% voltage drop at full load. Always terminate with a hex-die hydraulic crimper, never a hammer crimper, to prevent high-resistance hot spots.
Battery Sizing FAQ
How does ambient temperature affect battery sizing calculations?
Temperature drastically alters usable capacity, particularly for lead-acid. At 32°F (0°C), a flooded lead-acid battery loses roughly 20% of its capacity; at -20°F (-29°C), it loses up to 50%. If you are sizing a lead-acid bank for a winter cabin, you must multiply your calculated Ah requirement by a temperature derating factor of 1.5 to 2.0. LiFePO4 batteries maintain excellent discharge capacity down to freezing, but their BMS will physically block charging below 32°F (0°C) to prevent lithium plating. If your battery enclosure drops below freezing, you must size in heating pads or specify low-temperature charge-protection cells.
Can I mix different battery capacities in parallel to reach my target Ah?
No. Mixing a 100Ah battery with a 200Ah battery in parallel creates an imbalance in internal resistance. The lower-resistance battery will take the brunt of the discharge current and the majority of the charge current, leading to premature aging, chronic undercharging of the weaker unit, and potential BMS failure. Always parallel identical models. If you need 300Ah, buy three 100Ah batteries or a single 300Ah unit; do not mix a 100Ah and a 200Ah.
What size wire and breaker do I need for a 48V 200Ah battery bank?
Wire and breaker sizing is based on the maximum continuous current draw of the inverter, not the battery's Ah capacity. If your 48V inverter is rated for 5,000W continuous, the max DC draw is roughly 115A (5000W ÷ 48V ÷ 0.90 efficiency). Applying the NEC 125% continuous load rule, you need wiring and overcurrent protection rated for at least 144A. A 150A Class T fuse or DC breaker paired with 1/0 AWG or 2/0 AWG copper wire (rated for 75°C or 90°C in the ampacity tables) is the correct specification.
How do I calculate battery sizing for a UPS backup instead of daily solar cycling?
UPS sizing prioritizes autonomy days over daily cycle life. First, calculate your critical load Wh (e.g., fridge, router, lights = 1,500Wh/day). Multiply by your desired autonomy days (e.g., 3 days = 4,500Wh). Divide by system voltage, DoD, and inverter efficiency. Because UPS batteries sit idle at 100% State of Charge (SoC) for months, LiFePO4 is vastly superior to lead-acid here; lead-acid will sulfated and die within two years if kept at float voltage without regular deep cycling, whereas LiFePO4 tolerates high-SoC storage much better (though storing at 50% SoC is still ideal for calendar life).
