To calculate how long a battery will last, divide the usable watt-hours (Total Capacity × Depth of Discharge) by your load in watts, then multiply by your inverter efficiency. For example, a 12V 100Ah LiFePO4 battery (1280Wh) at an 80% depth of discharge (DoD) powering a 500W load through a 90% efficient inverter will last approximately 1.84 hours. While the basic math is simple, real-world runtime is heavily dictated by battery chemistry, discharge rates, and system losses.
The Core Runtime Math: Peukert, DoD, and Efficiency
The fundamental formula for battery runtime is:
Runtime (hours) = [ (Voltage × Ah) × DoD × Inverter Efficiency ] / Load (Watts)
However, this assumes a linear discharge, which is only true for lithium iron phosphate (LiFePO4) and other lithium chemistries. If you are using lead-acid (FLA, AGM, or Gel), you must account for Peukert's Law. Peukert's law dictates that the faster you draw current from a lead-acid battery, the less total capacity it can deliver. A 100Ah lead-acid battery rated at a 20-hour discharge rate (5A draw) might only deliver 60Ah of usable capacity if you pull 50A from it.
Depth of Discharge (DoD) is the percentage of the battery you can safely use without degrading its lifespan. For flooded lead-acid, the practical DoD is 50%. For LiFePO4, it is typically 80% to 100%. Inverter efficiency usually hovers between 85% and 93%, depending on the load relative to the inverter's rated capacity.
Real-World Runtime Comparison: Lead-Acid vs. LiFePO4
The table below demonstrates how Peukert's effect crushes lead-acid runtime at high loads, while LiFePO4 maintains its rated capacity. Both batteries are nominally 12V 100Ah. We assume a 90% inverter efficiency.
| Continuous Load (W) | DC Current Draw (A) | FLA Usable Ah (50% DoD + Peukert) | FLA Runtime (Hours) | LiFePO4 Usable Ah (80% DoD) | LiFePO4 Runtime (Hours) |
|---|---|---|---|---|---|
| 100W | 9.2A | 50Ah | 4.9 | 80Ah | 7.8 |
| 300W | 27.7A | 42Ah | 1.3 | 80Ah | 2.6 |
| 600W | 55.5A | 31Ah | 0.5 | 80Ah | 1.3 |
| 1000W | 92.5A | 22Ah | 0.2 | 80Ah | 0.78 |
| 1500W | 138.8A | 15Ah (Voltage Sag Cutoff) | 0.1 | 80Ah | 0.52 |
Note: At 1500W, a single 12V 100Ah FLA battery will experience severe voltage sag, likely tripping the inverter's low-voltage disconnect (LVD) before the math reflects. LiFePO4 handles this load easily due to its flat discharge curve and lower internal resistance.
System Architecture: Source to Load and Battery Configurations
To accurately size your system, you must understand the power flow. A standard off-grid or backup power system follows this block architecture:
Battery Bank (Source) → DC Disconnect / Class T Fuse → Inverter/Charger → AC Breaker Panel → Loads.
When scaling up your energy storage, you will wire multiple batteries together. The way you wire them fundamentally changes your system voltage and amp-hour capacity.
Series vs. Parallel Consequences
- Series Wiring: Voltages add up, but Amp-hours (Ah) remain the same. Wiring four 12V 100Ah batteries in series yields a 48V 100Ah bank (5120Wh total). This is preferred for high-power systems (3kW+) because higher voltage means lower DC current, allowing you to use smaller, cheaper wire (e.g., 2 AWG THHN instead of 4/0 AWG).
- Parallel Wiring: Amp-hours add up, but voltage remains the same. Wiring four 12V 100Ah batteries in parallel yields a 12V 400Ah bank. This is common for small RVs or marine setups but becomes a cabling nightmare at high loads due to the massive DC current required.
Never wire batteries in parallel if they have different chemistries, ages, capacities, or internal resistances. Mismatched parallel batteries will create circulating currents, where the stronger battery forcefully overcharges the weaker one. This leads to severe overheating, venting, and in lithium systems, thermal runaway. If you must parallel, use identical batteries from the same manufacturing batch, and consider a parallel-capable smart BMS to monitor individual cell groups.
Charge/Discharge Limits, C-Rates, and Inverter Sizing
Battery capacity is only half the equation; the rate at which you can safely push energy in or out is governed by the C-rate. A C-rate of 1C means discharging the battery's total Ah capacity in one hour. For a 100Ah battery, 1C equals 100A.
Understanding Charge and Discharge Limits
- LiFePO4 Limits: Most commercial LiFePO4 cells safely support a 1C continuous discharge and a 0.5C charge rate. A 12V 100Ah LiFePO4 battery can safely output 100A continuously and accept 50A from a charge controller. Pushing beyond the BMS-rated C-rate will trip the internal protection or degrade the cells.
- Lead-Acid Limits: Lead-acid batteries prefer a gentle 0.2C discharge and a 0.25C charge rate. Pulling 1C from a lead-acid battery causes extreme voltage sag and physical damage to the lead plates.
Sizing the Inverter and Charger
Your inverter must be sized for the surge load, not just the continuous load. Motors, compressors, and power tools require 3 to 5 times their running wattage to start. If your continuous load is 1500W and includes a refrigerator compressor, you need an inverter rated for at least 3000W continuous to handle the 4500W startup surge.
Similarly, your solar charge controller or AC battery charger must be sized to match the battery's maximum charge C-rate. If you have a 200Ah LiFePO4 bank with a 0.5C charge limit, your charge controller must be capped at 100A. According to Battery University's charging guidelines, exceeding the manufacturer's recommended charge current accelerates capacity loss and risks lithium plating.
Lithium-ion and LiFePO4 cells store immense energy density. A short circuit or severe overcharge can trigger thermal runaway—a self-sustaining chemical fire that cannot be extinguished with standard water or ABC extinguishers. Always install a Class T fuse within 18 inches of the battery positive terminal, ensure your BMS has over-voltage and short-circuit protection enabled, and never bypass a tripped BMS without diagnosing the root cause. For detailed safety standards, refer to the UL lithium-ion battery safety resources.
Worked Example: Sizing a Bank for a 1500W Continuous Load
Let's apply this math to a real-world scenario. You are building a backup system for a home office and sump pump. Your continuous load is 1500W, and you need 3 hours of runtime during a grid outage.
- Calculate Total Watt-Hours Needed: 1500W × 3 hours = 4500Wh.
- Account for Inverter Efficiency (90%): 4500Wh / 0.90 = 5000Wh required from the battery bank.
- Apply Depth of Discharge: If using LiFePO4 at 80% DoD, you need a total bank capacity of 5000Wh / 0.80 = 6250Wh.
- Convert to Amp-Hours at 48V: 6250Wh / 48V = 130.2Ah.
The Verdict: You need a 48V battery bank with at least 135Ah of capacity. Since 48V 100Ah server-rack batteries (like the popular EG4 or SOK models) are the industry standard, you would purchase two 48V 100Ah batteries in parallel, giving you 200Ah (10,240Wh total). This provides your required 3 hours of runtime while keeping the DoD well under 80%, extending the cycle life of the cells.
Decision Tree: Matching Chemistry to Your Load Profile
| Use Case Scenario | Required Bank Wh | Recommended Chemistry | System Voltage & Inverter Size |
|---|---|---|---|
| Weekend Cabin (Lights, Laptop, Fridge) | 2000 - 4000Wh | 12V LiFePO4 (Single 100Ah-200Ah) | 12V System / 2000W Inverter |
| Home Backup (Sump pump, router, freezer) | 5000 - 10000Wh | 48V LiFePO4 (Server Rack style) | 48V System / 5000W Split-Phase Inverter |
| Full Off-Grid (Well pump, HVAC, stove) | 15000Wh+ | 48V LiFePO4 (Multiple parallel strings) | 48V System / 8000W+ Inverter (e.g., Schneider Conext) |
| Emergency UPS (Modem, CPAP machine only) | 500 - 1000Wh | 12V AGM or Small LiFePO4 | 12V System / 400W Pure Sine Inverter |
Calculating battery runtime is not just about dividing watt-hours by watts. By respecting Peukert's law for lead-acid, adhering to strict C-rate limits, and properly sizing your inverter for surge loads, you ensure your power system survives the night without tripping a BMS or sagging below the inverter's low-voltage cutoff.
