The Core Formula for Battery Life and System Architecture
If you want to know exactly how long your battery bank will run a specific load, you need the fundamental formula for battery life (runtime). Stripped of marketing fluff, the equation is:
Before applying this formula, you must understand the physical path your energy takes. A properly designed off-grid or hybrid power system follows a strict source-to-load block architecture:
- Source: Solar PV array or Grid/Generator input.
- Charge Controller: MPPT controller steps down high PV voltage to match the battery bank's absorption voltage.
- Storage (Battery Bank): The chemical buffer, protected by a Battery Management System (BMS) and Class T fuses.
- Inverter/Charger: Converts DC bus voltage to 120V/240V AC for household loads, and manages AC-to-DC charging when grid/generator power is present.
- Load: Your AC appliances and DC branch circuits.
Every connection in this chain introduces resistance and efficiency losses. The formula above accounts for the inverter's conversion loss, but you must also factor in a 2-3% wiring loss if your battery-to-inverter cable runs exceed 5 feet.
Series vs. Parallel: Voltage, Amp-Hours, and C-Rate Limits
How you wire your cells or monoblocks dictates your system voltage and total capacity. Getting this wrong is the most common cause of melted busbars and tripped BMS units.
| Wiring Configuration | Voltage Consequence | Amp-Hour (Ah) Consequence | Primary Use Case |
|---|---|---|---|
| Series | Voltages add (e.g., 4x 12V = 48V) | Ah remains the same | High-power systems (>2000W) to keep DC current low. |
| Parallel | Voltage remains the same | Ah adds (e.g., 2x 100Ah = 200Ah) | Expanding capacity on an existing 12V or 24V bank. |
| Series-Parallel | Both add (e.g., 2S2P 12V 100Ah = 24V 200Ah) | Both add | Building 24V or 48V banks from smaller 12V modules. |
Charge and Discharge Limits (C-Rates and DoD)
Your battery's chemistry dictates how fast you can pull energy from it, known as the C-rate. A 1C rate means discharging the full capacity in one hour. Most LiFePO4 (Lithium Iron Phosphate) server-rack batteries are rated for 0.5C continuous (e.g., a 100Ah battery can safely deliver 50A continuously) and 1C for short surges. Lead-acid batteries (FLA/AGM) should rarely exceed a 0.2C discharge rate to prevent severe voltage sag and plate damage.
Depth of Discharge (DoD) is equally critical. For LiFePO4, you can safely use 80% to 90% of the rated capacity. For Flooded Lead-Acid (FLA), you must limit DoD to 50% to achieve a reasonable cycle life (typically 500-800 cycles). If you put a 200Ah FLA battery into the formula for battery life, your usable multiplier is 0.50, not 1.0.
Sizing Math: Peukert’s Law, Efficiency, and Inverter Selection
The basic formula for battery life assumes a linear discharge, which is true for lithium but false for lead-acid. If you are using lead-acid, you must apply Peukert’s Law, which states that as the discharge current increases, the battery's effective capacity decreases.
The Peukert equation is: t = H × (C / (I × H))^k
- t = Actual time to discharge (hours)
- H = Rated discharge time (usually 20 hours)
- C = Rated capacity at H hours (e.g., 100Ah)
- I = Actual discharge current (Amps)
- k = Peukert exponent (typically 1.1 to 1.3 for lead-acid; ~1.0 for LiFePO4)
Worked Example: You have a 12V, 100Ah FLA battery (k=1.2) powering a 600W load through an 85% efficient inverter.
DC Current (I) = 600W / (12V × 0.85) = 58.8A.
Applying Peukert: t = 20 × (100 / (58.8 × 20))^1.2 = 20 × (0.085)^1.2 = 20 × 0.052 = 1.04 hours.
Notice that pulling 58.8A from a 100Ah battery theoretically gives you 1.7 hours (100/58.8), but Peukert's law slashes your actual runtime to just over 1 hour due to internal resistance and heat. This is exactly why high-draw systems abandon 12V lead-acid for 48V lithium.
Inverter and Charger Sizing
Your inverter must handle both the continuous load and the surge (inductive startup) of motors or compressors. If your continuous load is 2500W, you need a 3000W inverter.
Furthermore, the DC input wiring must be sized for the inverter's maximum draw, not just the continuous load. A 3000W inverter at 48V nominal (51.2V actual for LiFePO4) pulling 3000W at 93% efficiency requires:
3000W / (51.2V × 0.93) = 63 Amps continuous.
Applying the NEC 125% continuous load rule (Article 210.20), your wire and fuse must be rated for 63A × 1.25 = 78.75 Amps. This mandates 2 AWG copper wire and an 80A or 100A Class T fuse.
Lithium Fire Safety and Cell Matching Rules
When expanding a battery bank, never parallel mismatched cells. Paralleling a new 100Ah LiFePO4 battery with a 3-year-old 100Ah battery of a different brand (or even a different batch from the same brand) will result in the newer, lower-internal-resistance battery taking the brunt of the charge and discharge currents. This leads to chronic over-current events, premature BMS trips, and accelerated degradation of the newer unit. If you must parallel batteries, they must be the exact same manufacturer, model, capacity, and ideally from the same manufacturing batch, and they must be top-balanced to the exact same voltage before connecting the parallel busbars.
Decision Tree: Picking Your Exact Bank and Inverter
Stop guessing. Use this decision matrix to select your system voltage, then buy the exact parts listed below. This path terminates in a concrete, field-proven recommendation for a standard residential or large off-grid cabin setup.
| If Your Max Continuous Load Is... | And Your Daily Usage Is... | Then Choose This System Voltage | Why? |
|---|---|---|---|
| Under 1,000W | Under 2 kWh/day | 12V | Components are cheap, wiring is simple, but high current limits expansion. |
| 1,000W - 2,500W | 2 to 5 kWh/day | 24V | Cuts DC current in half compared to 12V; good for mid-size cabins and vans. |
| Over 2,500W | Over 5 kWh/day | 48V | Keeps DC current manageable (<100A), allows standard 4/0 AWG wiring, and scales easily. |
The Default Recommendation: 48V LiFePO4 Architecture
If you are building a system in 2026 and want to avoid ripping out your wiring in three years when you add a well pump or an induction cooktop, default to 48V. The copper savings alone on the DC busbars and battery interconnects pay for the voltage step-up.
Concrete Part Pick (The 'Buy This' List):
- Battery: SOK 48V 100Ah LiFePO4 Server Rack Battery (Approx. $1,299). It features a 5.12kWh capacity, a robust 100A BMS (5kW max output), and standard RS485/CAN communication ports. It is UL 1973 certified, which is increasingly required by local AHJs for indoor residential installations.
- Inverter/Charger: Victron MultiPlus-II 48/3000/35-32 (Part# PMP482305010, Approx. $1,650). This unit provides 3000VA (2400W continuous) of pure sine wave inversion, a 35A AC charger, and built-in transfer switching. Its 'PowerAssist' feature allows it to supplement grid or generator power during heavy surges, meaning a 3000W inverter can temporarily handle 5000W loads without tripping a 30A shore-power breaker.
- Wiring & Protection: 2 AWG welding cable for battery-to-inverter runs under 5 feet, paired with a Blue Sea 150A Class T Fuse (Part# 5112) mounted within 7 inches of the battery positive terminal, as mandated by NEC Article 480.8.
By plugging the SOK 48V 100Ah battery (5120Wh) into the formula for battery life with an 80% DoD (4096Wh usable) and the Victron's 93% inverter efficiency, you get exactly 3.8 hours of runtime on a continuous 1000W load. Scale the Ah by adding identical SOK units in parallel via their CAN bus, and your math scales linearly without Peukert penalties.
