The battery life equation for usable runtime calculates exactly how long your bank will power a load by factoring in Depth of Discharge (DoD), inverter efficiency, and Peukert’s effect. For a 2,000W continuous AC load running for 3 hours, the equation dictates a minimum 48V 160Ah Lithium Iron Phosphate (LiFePO4) bank, or an 800Ah Flooded Lead-Acid (FLA) bank. Sizing a system without this math results in either premature cell death from deep cycling or a massive overspend on unused capacity.
The Core Battery Life Equation and System Block
Before running the math, you must define the physical system block from source to load. A standard off-grid or backup power architecture flows in this exact sequence:
- Source: Solar array or AC Grid/Generator.
- Charge Path: MPPT Charge Controller (e.g., Victron SmartSolar 150/60) or Inverter-Charger AC input.
- DC Bus & Protection: Positive and negative busbars, separated by a Class T fuse on the positive main feed sized to 1.25x the max continuous inverter draw.
- Storage: The battery bank (the focus of our equation).
- Inversion: Inverter/Charger (e.g., Victron MultiPlus-II 48/3000) converting DC to AC.
- Load: AC Subpanel feeding your appliances.
The foundational battery life equation to find your required Amp-hours (Ah) is:
Required Bank Ah = (Load Watts × Runtime Hours) / (Nominal Volts × DoD × Inverter Efficiency × Peukert Factor)
Series vs. Parallel: Voltage, Amp-Hours, and C-Rate Limits
How you wire your cells drastically alters the math and the physical wire gauge required.
- Series Wiring: Voltage adds, Amp-hours remain the same. Wiring four 12V 100Ah batteries in series yields a 48V (51.2V nominal) 100Ah bank. This is the correct approach for loads over 2,000W because higher voltage drastically lowers the DC current (Amps = Watts / Volts), allowing you to use smaller, cheaper wire like 2/0 AWG instead of massive 4/0 AWG or parallel copper busbars.
- Parallel Wiring: Amp-hours add, Voltage remains the same. Four 12V 100Ah batteries in parallel yield a 12V 400Ah bank. This is strictly for 12V RV or marine systems with loads under 1,500W. High current at 12V generates severe voltage drop and heat.
C-Rate Limits: The C-rate defines how fast you can safely charge or discharge a battery relative to its capacity. A 1C discharge rate on a 100Ah battery means drawing 100A. LiFePO4 cells typically support a 1C continuous discharge and 0.5C charge. FLA batteries are severely limited to a 0.2C discharge rate; pulling more causes extreme voltage sag and physical degradation of the lead plates.
Sizing Math: Peukert’s Law, DoD, and Inverter Efficiency
Let’s run a real-world scenario. You need to run a 1,500W space heater and a 500W refrigerator compressor (2,000W total continuous draw) for 3 hours during a winter grid outage.
| Variable | LiFePO4 Calculation | Flooded Lead-Acid (FLA) Calculation |
|---|---|---|
| Base Energy Need | 2000W × 3h = 6,000Wh | 2000W × 3h = 6,000Wh |
| Inverter Efficiency | 92% (0.92) 6000 / 0.92 = 6,522Wh DC |
85% (0.85) 6000 / 0.85 = 7,058Wh DC |
| Peukert Factor | ~1.0 (Negligible voltage sag) 6,522 / 1.0 = 6,522Wh |
0.80 (High draw penalty at k=1.3) 7058 / 0.80 = 8,822Wh |
| Depth of Discharge (DoD) | 80% (Max for 5,000+ cycle life) 6522 / 0.80 = 8,152Wh Total |
50% (Max to prevent sulfation) 8822 / 0.50 = 17,644Wh Total |
| Required Ah at 48V (51.2V nom) | 8152 / 51.2V = 159.2Ah | 17644 / 48V = 367.5Ah |
Bench Insight on Peukert’s Law: Peukert’s exponent (k) measures how much capacity you lose at high discharge rates. For FLA, k is typically 1.2 to 1.3. If a golf cart battery is rated for 220Ah at a 20-hour discharge rate (11A), pulling 100A from it will effectively yield only about 130Ah. LiFePO4 chemistry maintains a flat voltage curve, keeping k near 1.05, meaning you actually get the capacity printed on the label even under heavy loads.
LITHIUM FIRE SAFETY DIRECTIVE: When building LiFePO4 banks, never parallel mismatched cells, different brands, or batteries with different cycle ages. Mismatched internal resistance causes one cell to over-charge and over-discharge the others, bypassing the BMS and risking thermal runaway. Every parallel string must have its own dedicated BMS, and the main positive terminal must be protected by a Class T fuse (not an ANL fuse, which lacks the high AIC interrupt rating required for lithium short circuits). Always apply manufacturer-specified top-down compression to prismatic cells to prevent delamination.
Inverter and Charger Sizing for Your Target Load
With a required LiFePO4 capacity of ~160Ah at 48V, we must size the inverter and the AC charger to match the chemistry limits.
Inverter Sizing: Your continuous load is 2,000W, but the refrigerator compressor requires a startup surge of roughly 3x its running wattage (1,500W surge) for a fraction of a second. A 3,000W (3kVA) inverter is the exact right fit. It handles the 2,000W continuous draw at 66% capacity (keeping internal MOSFETs cool) and easily absorbs the 1,500W surge without tripping.
Charger Sizing: To recharge a 160Ah LiFePO4 bank from a generator or the grid, apply the 0.2C to 0.5C rule. A 0.5C charge rate demands 80A of DC charging current. The Victron MultiPlus-II 48/3000 includes a built-in 35A or 50A AC charger (depending on the exact model). At 50A, you are charging at roughly 0.3C (50A / 160Ah), which is the sweet spot for lithium longevity and keeps the AC draw from a portable generator under 3,000W.
Programming the Charge Profile
Do not use the default "Gel" or "AGM" settings on your inverter-charger. You must manually program the lithium absorption and float voltages via Bluetooth or DIP switches:
- Absorption Voltage: 55.2V (13.8V per 12V module) for 48V systems.
- Float Voltage: 54.0V (13.5V per 12V module).
- Absorption Time: 1 to 2 hours (LiFePO4 does not require long absorption phases like lead-acid).
Decision Tree: Picking Your Exact Battery Bank
Use this decision matrix to select your hardware based on your calculated DC Watt-hour requirement and physical installation constraints. According to Battery University, keeping lithium cells between 20% and 80% State of Charge (SoC) dramatically extends calendar life, which informs the sizing below.
| System Profile | Calculated DC Need | Voltage Architecture | Concrete Hardware Pick |
|---|---|---|---|
| Light RV / Camper Van (1,000W max load, 2hr runtime) |
~2,500Wh | 12V (Keeps wiring simple for 12V DC appliances) | Redodo 12V 100Ah Pro LiFePO4 (Built-in 100A BMS, Bluetooth monitoring) |
| Small Off-Grid Cabin (2,000W load, 3hr runtime - our math example) |
~8,150Wh | 48V (Mandatory to keep DC current under 150A) | SOK 48V 100Ah Server Rack Battery × 2 (Yields 48V 200Ah / 10.24kWh total) |
| Whole Home Backup (5,000W load, 8hr runtime) |
~47,000Wh | 48V (High capacity parallel strings) | Epoch Batteries 48V 110Ah × 5 (Yields 48V 550Ah / 28.1kWh total) |
The Final Verdict for the 2,000W / 3-Hour Scenario
Based on the battery life equation and the math proven above, your default pick is to purchase two SOK 48V 100Ah Server Rack Batteries. Wire them in parallel on a 48V DC busbar using 2/0 AWG welding cable. This gives you 200Ah at 48V (10,240Wh total capacity). When restricted to an 80% DoD, you have 8,192Wh of usable energy—perfectly covering the 8,152Wh DC requirement for your 2,000W load over 3 hours, while leaving a 40Wh buffer for inverter idle consumption and wire losses. Do not attempt to achieve this capacity at 12V; the 680A draw would melt standard busbars and trip a 500A Class T fuse instantly.
