To calculate battery capacity for a continuous AC load, divide your total daily watt-hours by the system DC voltage, then divide by the allowable Depth of Discharge (DoD)—typically 80% for LiFePO4 or 50% for Lead-Acid. For example, a 1200W continuous load running for 4 hours on a 24V LiFePO4 system requires 4800Wh. Divided by 24V, that is 200Ah. Divided by the 0.80 DoD governing rule, you need a minimum 250Ah battery bank. However, inrush currents from compressors will trip your Battery Management System (BMS) before you hit capacity limits if peak C-ratings are ignored.
The Governing Rules: DoD, Peukert, and Inrush
When sizing a battery bank, amp-hours (Ah) alone are a trap. A 100Ah lead-acid battery and a 100Ah Lithium Iron Phosphate (LiFePO4) battery will yield vastly different usable capacities due to chemistry limits. Furthermore, the inverter's efficiency and the battery's internal resistance dictate how much power actually reaches your AC panel.
Three governing rules dictate your true usable capacity:
- Depth of Discharge (DoD): The percentage of the battery you can safely use. (80% LiFePO4 / 50% Lead-Acid).
- Inverter Efficiency: High-frequency inverters operate at roughly 85-90% efficiency. You must divide your AC load by 0.85 to find the true DC draw.
- Inrush Current (LRA): Inductive loads like fridge compressors and well pumps draw 3 to 7 times their running wattage for a fraction of a second to start. If your BMS continuous discharge rating cannot handle this spike, the system will shut down instantly, regardless of how many Ah you have in reserve.
Load Tally: Sizing the Bank for Real-World Devices
Let us run a practical load tally for a small off-grid cabin running a 24V DC system with a 3000W pure sine wave inverter. We must account for both the daily energy consumption (Ah) and the peak simultaneous draw (BMS Amp limit).
| Device | Running Watts | Inrush (Peak) Watts | Daily Hours | Daily Watt-Hours (Wh) |
|---|---|---|---|---|
| Energy Star Fridge | 150W | 1200W | 8.0 | 1200 Wh |
| Microwave | 1000W | 1000W | 0.2 | 200 Wh |
| Laptop Charger | 65W | 65W | 5.0 | 325 Wh |
| LED Lighting (Total) | 40W | 40W | 6.0 | 240 Wh |
| Totals | 1255W (Max Run) | 2200W (Max Peak) | - | 1965 Wh |
The Capacity Math:
1. Inverter Loss: 1965 Wh / 0.85 (efficiency) = 2311 DC Watt-Hours.
2. Amp-Hours at 24V: 2311 Wh / 24V = 96.3 Ah.
3. Apply 80% DoD Rule: 96.3 Ah / 0.80 = 120.4 Ah minimum required.
You would specify a standard 24V 150Ah or 200Ah LiFePO4 server-rack battery (like a SOK or EG4 PowerPro) to provide adequate headroom for future loads and winter solar deficits.
The BMS Peak Math:
If the microwave and fridge compressor start simultaneously, the peak draw is 2200W. At 24V, that is 91.6 Amps. A standard 100A BMS will handle this, but if you add a 1500W coffee maker to the morning routine, your peak jumps to 3700W (154A). This will instantly trip a 100A BMS. You must either upgrade to a 200A BMS battery or practice load management. For deeper insights on matching C-rates to inverter limits, refer to the Battery University guide on C-Rates.
What Drains or Trips the System Before the BMS Limit?
Beginners often assume a battery bank will deliver its rated Ah until the BMS clicks off at 0% State of Charge (SoC). In practice, physics intervenes long before the BMS limit is reached. Here is the decision tree for what actually kills your power mid-cycle.
| Symptom | The Real Culprit | The Fix |
|---|---|---|
| Inverter shuts off with 'Low Voltage' alarm while battery shows 40% SoC. | Voltage Sag: High current draw pulls the terminal voltage below the inverter's Low Voltage Disconnect (LVD), typically 21.0V on a 24V system. | Upgrade wire gauge (e.g., 2 AWG to 1/0 AWG) to reduce voltage drop, or add a parallel battery string to halve the amp draw per battery. |
| Lead-acid bank runs out in half the calculated time under heavy load. | Peukert Effect: Drawing high amps from lead-acid chemically limits usable capacity. A 200Ah FLA battery might only yield 110Ah if pulled at a 1C rate. | Switch to LiFePO4 (immune to Peukert losses) or drastically increase the FLA bank size to lower the C-rate draw. |
| BMS disconnects on a hot day despite low amp draw. | Thermal Runaway Protection: Cheap BMS boards mount temperature sensors on the FETs, not the cells. High ambient heat + continuous 60A draw triggers thermal shutdown. | Move batteries to a climate-controlled space or upgrade to a BMS with active cell-level temperature balancing. |
For comprehensive system wiring and loss mitigation, the Victron Energy battery sizing guidelines emphasize that cable resistance is often the hidden bottleneck in high-current DC systems.
When to Add Parallel Strings or Step Up Voltage
Headroom is not just about adding more Ah; it is about managing current. As your load tally grows, pushing high wattage through a 12V system becomes dangerous and inefficient. A 3000W inverter on a 12V battery pulls roughly 275 Amps at full load. That requires massive, expensive 4/0 AWG welding cable and generates significant heat at the busbars.
When to step up to 24V or 48V:
If your continuous inverter load exceeds 1500W, abandon 12V. Moving to a 24V system cuts the amperage in half (125A), and a 48V system quarters it (62.5A). This allows you to use smaller, cheaper wire (like 4 AWG or 2 AWG THHN in conduit) and drastically reduces voltage drop across the busbars.
When to add parallel battery strings:
Add parallel batteries when you need more days of autonomy (e.g., surviving 3 days of rain without solar input) or when your peak inrush current exceeds a single BMS limit. However, never parallel more than four strings of batteries. Beyond four strings, minor differences in cable length and internal resistance cause uneven charging, leading to premature cell degradation. If you need more than four parallel strings, buy a single, larger-capacity battery or step up your system voltage.
Frequently Asked Questions
How do I calculate battery capacity for a solar system with days of autonomy?
First, calculate your base daily Ah requirement using the load tally method above. Then, multiply that number by your desired 'Days of Autonomy' (typically 2 to 3 days for off-grid homes). Finally, divide by the DoD. For example, if you need 100Ah daily and want 3 days of backup on a 48V LiFePO4 system: (100Ah × 3 days) / 0.80 DoD = 375Ah minimum battery bank capacity.
How to calculate battery capacity for a 12V fridge and CPAP machine for camping?
A 12V compressor fridge draws roughly 40Ah per day (5A at 12V for 8 hours of compressor run-time). A CPAP machine without a humidifier draws about 3-4 Amps, totaling roughly 32Ah over an 8-hour sleep cycle. Your total daily draw is 72Ah. Applying the 80% DoD rule for a portable LiFePO4 power station, you need a minimum 90Ah battery (72 / 0.80). A standard 100Ah 'suitcase' LiFePO4 battery will comfortably handle one night, but you will need a 200Ah bank or a solar blanket to sustain multi-day trips.
Why does my calculated battery capacity run out faster than the math says?
The most common culprit is 'phantom loads' and inverter tare loss. A large high-frequency inverter consumes 20W to 40W just to keep its internal electronics and cooling fans running. Over 24 hours, that is up to 960Wh (40Ah at 24V) of 'ghost' consumption that never shows up on your AC load tally. Additionally, devices in standby mode (TVs, microwaves with clocks, laptop bricks) draw 2-5W continuously. Always add a 10-15% buffer to your final Wh calculation to account for inverter tare and phantom draws.
