To calculate how long a battery will last, divide your usable battery capacity (in Watt-hours) by your total load (in Watts), then factor in inverter efficiency. The baseline formula is: Runtime (hours) = (Battery Ah × Voltage × DoD × Inverter Efficiency) / Load (Watts). For example, a 12V 100Ah LiFePO4 battery (1280Wh nominal) at an 80% Depth of Discharge (DoD) yields 1024Wh of usable energy. Powering a continuous 500W AC load through an inverter with 90% efficiency gives you roughly 1.84 hours of runtime (1024Wh × 0.90 / 500W).
However, real-world bench testing reveals that nominal math rarely matches actual runtime. To get precise figures, you must account for system architecture, chemistry-specific discharge curves, and thermal losses. Below is the exact framework used by solar installers and off-grid engineers to size 12V, 24V, and 48V energy storage systems.
The Source-to-Load System Block
Before running the math, map the physical path your energy takes. Every connection point introduces resistance, and every conversion stage introduces loss. A standard off-grid or backup power system follows this block sequence:
- Source (Battery Bank): The chemical storage medium (e.g., four 12V 100Ah LiFePO4 modules in series for 48V).
- DC Protection: A Class T fuse or DC breaker (e.g., Blue Sea Systems 250A Class T) sized to 125% of the maximum continuous inverter draw.
- Interconnects: 2/0 AWG or 4/0 AWG flexible welding cable. Voltage drop here directly reduces the voltage reaching the inverter, forcing it to pull higher amps to meet the AC load.
- Inverter/Charger: The DC-to-AC conversion stage (e.g., Victron MultiPlus 48/3000). This is where the largest efficiency penalty occurs, typically 7% to 15%.
- AC Load: The appliances drawing power, measured in Watts (real power) and VA (apparent power).
When you calculate runtime, you are calculating the time from the load back to the source. The load dictates the current, and the system losses dictate how much extra energy the battery must supply.
Sizing Math: Peukert, Efficiency, and DoD
Nominal capacity (Ah) is usually rated at a 20-hour discharge rate (C/20). If you discharge a battery faster than 20 hours, its effective capacity shrinks. How much it shrinks depends entirely on the chemistry.
Depth of Discharge (DoD) Limits
DoD is the percentage of the battery you can safely drain before causing permanent degradation or triggering the Battery Management System (BMS) low-voltage cutoff.
- Flooded Lead-Acid (FLA) / AGM: 50% DoD. Draining below 12.0V (for a 12V nominal battery) drastically reduces cycle life.
- Lithium Iron Phosphate (LiFePO4): 80% to 95% DoD. Most quality BMS units will disconnect around 10.0V to 11.2V, allowing you to use almost the entire rated capacity.
Peukert's Law (Lead-Acid Only)
Peukert's Law describes the non-linear capacity loss in lead-acid batteries under high loads. A 100Ah FLA battery discharged at 5A (20-hour rate) yields 100Ah. But discharged at 50A (1-hour rate), it might only yield 60Ah before hitting the cutoff voltage. LiFePO4 batteries have a Peukert exponent so close to 1.0 that the effect is negligible for standard sizing.
| Parameter | 12V 100Ah AGM (Lead-Acid) | 12V 100Ah LiFePO4 (Lithium) |
|---|---|---|
| Nominal Energy | 1200 Wh | 1280 Wh |
| Safe DoD | 50% | 90% |
| Usable Energy (DoD adjusted) | 600 Wh | 1152 Wh |
| Peukert Effect at 500W Load | Reduces capacity by ~30% | Negligible (< 2% loss) |
| Real Usable Energy at 500W | ~420 Wh | ~1130 Wh |
| Runtime (90% Inverter Eff.) | 0.75 Hours (45 mins) | 2.03 Hours (122 mins) |
For deeper technical modeling on lead-acid discharge curves, Battery University's guide on Peukert's Law provides the exact exponential formulas used in battery monitoring shunts.
Series vs. Parallel and Charge/Discharge Limits
How you wire your battery bank changes the system voltage and the current requirements, which directly impacts wire sizing and inverter selection.
Series vs. Parallel Consequences
- Series Wiring: Voltages add, Amp-hours (Ah) remain the same. Wiring four 12V 100Ah batteries in series creates a 48V 100Ah bank (5120Wh). Advantage: Higher voltage means lower current for the same wattage, allowing thinner cables and smaller fuses.
- Parallel Wiring: Amp-hours add, Voltage remains the same. Wiring four 12V 100Ah batteries in parallel creates a 12V 400Ah bank (5120Wh). Advantage: Maintains 12V compatibility with standard RV and marine appliances. Disadvantage: Massive current draw requires expensive 4/0 AWG copper and heavy-duty busbars.
Charge and Discharge Limits (C-Rates)
The C-rate defines the maximum safe current relative to the battery's capacity. A 1C rate for a 100Ah battery is 100A.
- Discharge Limit: Most LiFePO4 BMS units are hardcoded to 1C (100A continuous). If your inverter pulls 150A, the BMS will trip. To support a 3000W 12V inverter (which pulls ~250A at full load), you must parallel at least three 100Ah batteries to safely distribute the current to 83A per battery.
- Charge Limit: LiFePO4 can safely accept 0.5C to 1C charge currents. Lead-acid should be limited to 0.2C (20A for a 100Ah battery) to prevent gassing and thermal damage.
Inverter and Charger Sizing for Your Load
Sizing the inverter and charger requires looking at both continuous thermal limits and millisecond surge limits.
| Load Type | Sizing Rule | Example Scenario | Required Inverter Spec |
|---|---|---|---|
| Resistive (Heaters, Lights) | 1.25x Continuous Wattage | 1000W space heater | 1250W+ Continuous Rating |
| Inductive (Fridges, Pumps) | 3x to 5x Continuous for Surge | 400W fridge compressor | 2000W+ Surge Rating |
| Capacitive (Power Supplies) | 1.5x Continuous for Inrush | 800W server rack PSU | 1200W+ Continuous Rating |
For the charger side, sizing depends on your recharge time goals and battery chemistry. The golden rule for LiFePO4 is to size the DC charge current at 10% to 20% of the total bank Ah. If you have a 48V 200Ah LiFePO4 bank, a 40A to 80A charger is ideal. Pushing 200A (1C) into the bank will generate excessive heat in the internal cell busbars and degrade cycle life. For AC-to-DC inverter/chargers like the Victron MultiPlus, you configure the maximum charge current in the software to match the battery manufacturer's spec sheet.
Frequently Asked Questions
How do I calculate how long a battery will last for a CPAP machine?
CPAP machines are highly variable depending on whether you use the heated humidifier. Without humidity, a standard CPAP draws about 30W to 40W. With humidity, it can spike to 90W to 120W. To calculate runtime, assume a 90W average draw. Using a 12V 100Ah LiFePO4 battery (1280Wh) with a 90% DoD (1152Wh usable) and a highly efficient 92% DC-to-DC converter (bypassing the AC inverter entirely), your math is: (1152Wh × 0.92) / 90W = 11.7 hours. This easily covers a full night of sleep. Always use a 12V DC adapter cable for your CPAP to avoid the 15% efficiency penalty of an AC inverter.
Does calculating how long a battery will last change in cold weather?
Yes, drastically, but the effect depends on the chemistry and whether you are charging or discharging. When discharging, a LiFePO4 battery's internal resistance increases in freezing temperatures, causing voltage sag. A 100Ah battery at 20°F (-6°C) might only yield 80% of its room-temperature capacity before hitting the low-voltage cutoff. However, the critical danger is charging. LiFePO4 cells cannot accept charge current below 32°F (0°C) without causing permanent lithium plating on the anode, which leads to internal short circuits. If your system operates in winter, your battery enclosure must be insulated and equipped with a thermostatically controlled heating pad or a BMS with built-in low-temp charge protection.
How to calculate how long a dual battery setup will last with a fridge?
A dual battery setup in a vehicle (like a van build) typically uses a DC-DC charger to isolate the starter battery from the house battery. To calculate runtime for a 12V compressor fridge (like a Dometic or Fridgefreezer), use the daily Amp-hour consumption rather than continuous wattage. A highly efficient 12V fridge averages 1.5 to 2.5 Amps per hour over a 24-hour cycle (roughly 45Ah per day). If your house bank is a single 12V 100Ah LiFePO4 (90Ah usable), it will run the fridge for exactly 2 days (48 hours) before hitting the BMS cutoff. If you are using AGM batteries, your 100Ah bank only yields 50Ah usable, meaning the fridge will run for just over 24 hours before you must start the vehicle engine to recharge via the alternator.
