If you are building an off-grid solar array, a camper van power system, or a home backup UPS, the most critical question you will face is: how long will my battery last under my specific load? The short answer is that you cannot simply divide the Amp-Hour (Ah) rating by your current draw. Real-world runtime is dictated by Depth of Discharge (DoD) limits, inverter conversion efficiency, and Peukert's law.
Below is the exact sizing math, system architecture, and component matching required to calculate true runtime for 12V, 24V, and 48V lithium and lead-acid battery banks.
The Core Runtime Math: Beyond Simple Amp-Hours
To calculate accurate runtime, we first need to define the power flow from source to load. A standard DC-coupled off-grid system follows this block architecture:
[Solar Array / Grid Charger] → [MPPT Charge Controller] → [Battery Bank + BMS] → [DC Disconnect / Class T Fuses] → [Inverter/Charger] → [AC Subpanel / Loads]
Energy degrades at every conversion step. The formula for calculating true AC runtime from a DC battery bank is:
Runtime (hours) = (Battery Ah × Nominal Voltage × DoD × Inverter Efficiency) / Total Load Watts
Factoring in Peukert's Law and Chemistry
Peukert's law states that as your discharge current increases, the usable capacity of the battery decreases. This effect is severe in lead-acid batteries (Peukert exponent ~1.3) but negligible in Lithium Iron Phosphate (LiFePO4) cells (exponent ~1.05). Furthermore, you must respect the chemistry's Depth of Discharge (DoD) limit to prevent permanent degradation. Lead-acid batteries should rarely be discharged past 50%, while quality LiFePO4 cells can safely cycle to 90% or even 100% DoD depending on the Battery Management System (BMS) programming.
Here is a data-dense comparison showing how these variables drastically alter real-world runtime for a 200Ah 12V battery bank under different continuous AC loads.
| Battery Chemistry | Nominal Capacity | AC Load (Watts) | Effective DoD | Inverter Eff. | Usable Energy (Wh) | Calculated Runtime |
|---|---|---|---|---|---|---|
| LiFePO4 (12.8V) | 200Ah | 500W | 90% | 93% | 2,142 Wh | 4.28 Hours |
| LiFePO4 (12.8V) | 200Ah | 1500W | 90% | 92% | 2,119 Wh | 1.41 Hours |
| AGM Lead-Acid (12.0V) | 200Ah | 500W | 50% | 90% | 1,080 Wh | 2.16 Hours |
| AGM Lead-Acid (12.0V) | 200Ah | 1500W | 50% | 88% | 1,056 Wh | 0.70 Hours |
Notice how the AGM battery effectively halves in runtime compared to the LiFePO4 equivalent at a 500W load, and the gap widens further at 1500W due to Peukert voltage sag and lower high-load inverter efficiency. For a deep dive into battery degradation curves, refer to the testing data published by Battery University.
Series vs. Parallel: Wiring for Voltage and Capacity
How you wire your cells or modules dictates your system voltage and total Amp-Hours, which directly impacts your wire sizing, inverter selection, and C-rate limits.
The Wiring Consequences
- Series Wiring: Voltage adds up, Amp-Hours remain the same. Wiring four 12V 100Ah batteries in series yields a 48V 100Ah bank. This is the preferred method for home solar because higher voltage means lower current for the same wattage, allowing you to use smaller, cheaper AWG wire between the battery and inverter.
- Parallel Wiring: Amp-Hours add up, Voltage remains the same. Wiring four 12V 100Ah batteries in parallel yields a 12V 400Ah bank. This is common in RVs and marine applications but requires massive, expensive copper cabling (like 2/0 AWG or 4/0 AWG) to handle the high DC current without dangerous voltage drop.
Never wire raw lithium cells in parallel without individual cell-level balancing, and never parallel pre-built 12V LiFePO4 batteries from different manufacturers, different ages, or different BMS firmware versions. Mismatched internal resistance causes the battery with the lowest voltage to be back-fed and overcharged by the others, bypassing its BMS protections and risking thermal runaway. If you must parallel pre-built 12V batteries, use identical models from the same batch and install a busbar balancer or individual charge controllers. Always ensure your BMS is rated for the total fault current of the parallel bank.
Understanding C-Rate and Charge/Discharge Limits
The C-rate defines how fast you can safely charge or discharge a battery relative to its total capacity. A 1C rate for a 100Ah battery is 100 Amps.
- Continuous Discharge Limit: Most 12V 100Ah LiFePO4 server-rack batteries (like the popular EG4 or SOK models) feature a BMS limited to 1C (100A) or 0.5C (50A) continuous discharge. Pulling 2000W from a 12V battery requires ~166 Amps, which will trip a 100A BMS. This is why high-wattage systems must step up to 24V or 48V.
- Charge Rate Limit: LiFePO4 cells generally accept a 0.5C charge rate safely. A 100Ah battery can be charged at 50A. Pushing a 1C charge rate (100A) generates excess heat and accelerates capacity degradation over the battery's lifecycle.
Sizing the Inverter and Charge Controller for Your Load
Your battery runtime calculator is useless if your inverter bottlenecks the power delivery or your charge controller cannot replenish the bank before the next discharge cycle.
Inverter Sizing: Continuous vs. Surge
Inverters must be sized for both the continuous running wattage of your loads and the inductive surge (Locked Rotor Amps) required to start motors, compressors, and pumps. According to NFPA 70 (National Electrical Code) guidelines regarding branch circuit and equipment sizing, you must account for continuous loads at 125% of their rated draw.
| Load Type | Running Watts | Surge Watts | Recommended Inverter Size | System Voltage Required |
|---|---|---|---|---|
| LED Lights, Laptops, Router | 300W | 300W | 1000W Pure Sine | 12V |
| Residential Fridge, TV, Microwave | 1200W | 2200W | 3000W Hybrid | 24V or 48V |
| Well Pump, AC Unit, Welder | 3500W | 9000W+ | 8000W+ Split Phase | 48V Mandatory |
Sizing the Solar Charge Controller (MPPT)
To ensure your battery actually lasts through the night, your solar array must replenish the daily consumed Amp-Hours during peak sun hours. For a 48V system, you should use a Maximum Power Point Tracking (MPPT) charge controller.
The Math: If your daily load consumes 4000Wh, and you have 4 peak sun hours, you need a minimum of 1000W of solar panels (4000Wh / 4h).
To size the MPPT amperage: Array Wattage / Battery Nominal Voltage = Charge Current.
1000W / 48V = 20.8 Amps. You would select a 30A MPPT controller (like the Victron SmartSolar 150/35) to provide a safe 20% overhead buffer, ensuring the controller does not thermally throttle during peak production.
By combining accurate DoD limits, respecting Peukert's law for your specific chemistry, and properly matching your inverter's surge capabilities to your battery's C-rate, you can reliably predict exactly how long your off-grid power system will sustain your loads.
