The direct answer to how to calculate battery life is found in this core formula: Battery Life (hours) = (Battery Ah × Nominal Voltage × Depth of Discharge × Inverter Efficiency) / Load Watts. However, real-world bench testing reveals that ignoring Peukert's Law for lead-acid batteries or C-rate limits for lithium cells will leave your system dead hours before the math predicted.
Below is the exact sizing math, system architecture, and configuration logic used to design reliable 12V, 24V, and 48V off-grid and backup power systems.
The Source-to-Load System Block
Before calculating runtime, you must map the energy flow. A standard off-grid or backup system follows a strict source-to-load path, and every node introduces efficiency losses:
- Source: Solar array (via MPPT charge controller) or utility grid/generator (via AC battery charger).
- Storage: The battery bank (LiFePO4, AGM, or Flooded Lead-Acid).
- Conversion: Pure sine wave inverter converting DC battery voltage to 120V/240V AC.
- Load: AC appliances, lighting, and electronics.
When calculating battery life, you are specifically measuring the duration the Storage node can support the Load node through the Conversion node without dropping below the battery's minimum safe voltage cutoff.
Sizing Math: Peukert, Efficiency, and Depth of Discharge
Battery capacity is not a fixed number; it is a sliding scale dependent on chemistry, temperature, and discharge speed. To calculate accurate runtime, we must apply three derating factors: Depth of Discharge (DoD), Inverter Efficiency, and Peukert's Law.
| Chemistry | Nominal Voltage | Max Safe DoD | Typical Inverter Efficiency | Peukert Effect |
|---|---|---|---|---|
| LiFePO4 (Lithium Iron Phosphate) | 12.8V | 80% - 100% | 92% - 95% | Negligible (Flat voltage curve) |
| AGM / Gel (Sealed Lead-Acid) | 12.0V | 50% | 85% - 90% | High (Capacity drops at high draw) |
| Flooded Lead-Acid (FLA) | 12.0V | 50% | 85% - 90% | High (Requires equalization) |
Worked Example: 500W Continuous Load
Let's calculate the runtime for a 500W continuous AC load (e.g., a full-size fridge, a laptop, and LED lights) using two different 100Ah batteries.
Scenario A: 12V 100Ah LiFePO4 (e.g., Power Queen or Renogy)
- Raw Energy: 12.8V × 100Ah = 1,280Wh
- Usable Energy (80% DoD): 1,280Wh × 0.80 = 1,024Wh
- AC Delivered (93% Inverter Eff): 1,024Wh × 0.93 = 952Wh
- Calculated Battery Life: 952Wh / 500W = 1.9 hours
Scenario B: 12V 100Ah AGM Lead-Acid
- Raw Energy: 12.0V × 100Ah = 1,200Wh (Rated at a 20-hour discharge rate)
- Peukert Derating: A 500W load on a 12V system draws ~41A. This is a C/2.5 discharge rate. According to Battery University, Peukert's Law dictates that at this high draw, a 100Ah AGM yields only about 65Ah of effective capacity.
- Effective Raw Energy: 12.0V × 65Ah = 780Wh
- Usable Energy (50% DoD): 780Wh × 0.50 = 390Wh
- AC Delivered (88% Inverter Eff): 390Wh × 0.88 = 343Wh
- Calculated Battery Life: 343Wh / 500W = 0.68 hours (41 minutes)
Takeaway: The LiFePO4 battery provides nearly triple the real-world runtime of the AGM, despite sharing the same '100Ah' label on the box.
Series vs. Parallel, C-Rates, and Component Sizing
How you wire your battery bank dictates your system voltage, which cascades into your inverter and charger sizing.
Series vs. Parallel Consequences
- Series Wiring: Connects positive to negative. Consequence: Voltage adds up, Amp-hours (Ah) remain the same. Two 12V 100Ah batteries in series yield 24V 100Ah (2,560Wh). This halves the DC current draw, allowing for smaller, cheaper wire gauges and reducing I²R heat losses.
- Parallel Wiring: Connects positive to positive, negative to negative. Consequence: Ah adds up, Voltage remains the same. Two 12V 100Ah batteries in parallel yield 12V 200Ah. This maintains 12V compatibility but doubles the current draw on the busbars and fuses.
Charge and Discharge Limits (C-Rates)
The C-rate defines how fast a battery can safely charge or discharge relative to its capacity. A 1C rate for a 100Ah battery is 100A.
- LiFePO4 Discharge Limit: Typically 1C (100A continuous). BMS cutoffs usually trigger at 100A-150A.
- LiFePO4 Charge Limit: Typically 0.5C (50A max). Charging at 100A will degrade the cells and void warranties.
- Lead-Acid Discharge Limit: C/5 to C/10 (20A to 10A for a 100Ah battery) to avoid severe Peukert losses and plate sulfation.
- Lead-Acid Charge Limit: C/5 to C/8 (20A max for a 100Ah battery) to prevent electrolyte boiling and off-gassing.
Inverter and Charger Sizing Decision Tree
Your inverter must handle both the continuous load and the inductive surge (startup spike) of motors like fridges or well pumps. Your charger must replenish the bank within your available sun or generator hours without violating the battery's charge C-rate.
| Component | Sizing Rule | 12V LiFePO4 (100Ah) | 24V AGM (200Ah) |
|---|---|---|---|
| Inverter Continuous | Load Watts + 20% margin | 600W minimum | 600W minimum |
| Inverter Surge | Max motor startup spike | 1500W+ surge rating | 1500W+ surge rating |
| Recommended Inverter | Standard pure sine wave | 1000W - 2000W 12V | 1000W - 2000W 24V |
| Charger Sizing | Recharge within 4-5 hours | 30A - 50A (0.3C - 0.5C) | 20A - 25A (C/10 - C/8) |
For a deeper understanding of integrating these components with solar arrays, the National Renewable Energy Laboratory (NREL) provides excellent frameworks on solar-plus-storage dispatch strategies and component matching.
Frequently Asked Questions
How to calculate battery life for a specific appliance?
To calculate battery life for a single appliance, first locate the nameplate wattage or use a plug-in kill-a-watt meter to find the true average draw. Crucially, you must account for the duty cycle. A refrigerator might have a 400W compressor, but it only runs 30% of the time. Its average hourly draw is 120W (0.12 kWh). If your usable battery capacity (after DoD and inverter efficiency derating) is 1,000Wh, divide 1,000Wh by 120W to get 8.3 hours of runtime. Always add a 15% buffer for phantom loads and voltage sag.
How to calculate battery life in series vs parallel configurations?
The total Watt-hours (Wh) of the battery bank remains exactly the same whether you wire in series or parallel. Two 12V 100Ah batteries yield 2,560Wh in series (24V 100Ah) and 2,560Wh in parallel (12V 200Ah). Therefore, the theoretical battery life for a given AC load is identical. However, practical battery life will be longer in a series configuration. Higher system voltage (24V or 48V) cuts the DC current in half or quarters it, drastically reducing I²R heat losses in the cables and busbars, and keeping the inverter operating in its peak efficiency sweet spot (usually 85-95% load capacity).
How to calculate battery life when adding solar recharge?
When solar is actively charging the system, you must calculate the net load. First, determine your solar harvest: multiply your solar array wattage by the peak sun hours for your region, then multiply by 0.75 to account for MPPT controller and wiring losses. For example, a 400W panel in 5 peak sun hours yields 1,500Wh of daily harvest. Next, calculate your daily load consumption (e.g., 500W average draw × 24 hours = 12,000Wh). Subtract the solar harvest from the daily load (12,000Wh - 1,500Wh = 10,500Wh net deficit). Finally, divide this net deficit by your battery's usable Wh capacity to determine how many days of autonomy you have before the battery bank is depleted.
