Calculation methodology.

The battery bank must store enough energy to power your load for the chosen number of autonomy days — the consecutive days of little or no solar generation your system can survive without running flat.

Dividing by Depth of Discharge (DoD) accounts for the fact that not all of a battery's rated capacity is safely usable. A 100 Ah LiFePO4 battery at 80% DoD delivers 80 Ah of usable energy; the remaining 20 Ah is held in reserve to protect the cells from over-discharge and extend cycle life. Without this correction, you would be sizing for the usable portion only and inadvertently over-stressing the battery on every cycle.

Battery datasheets specify capacity in amp-hours (Ah) at a given voltage. This formula converts the watt-hour requirement from Formula 1 into the Ah figure you need when specifying or purchasing batteries, using the fundamental electrical relationship Wh = Ah × V.

System voltage has a practical engineering implication beyond the maths: a 24V system stores the same energy as a 12V system using half the current. Lower current means thinner, cheaper wiring, reduced resistive losses, and smaller fuse ratings. For systems above roughly 500W, 24V or 48V is the standard choice.

Peak Sun Hours (PSH) is the key input here. It is not the number of daylight hours — it is the equivalent number of hours per day during which solar irradiance averages 1,000 W/m², which is the standard test condition for panel wattage ratings. A 390W panel in a 4.5 PSH location produces approximately 390 × 4.5 = 1,755 Wh on a clear day before losses.

The 1.3× multiplier represents a 30% gross margin for real-world system losses that are unavoidable in practice:

• —Wiring resistance losses — current travelling through cables generates heat proportional to resistance, reducing useful power.
• —MPPT conversion efficiency — charge controllers operate at roughly 93–97% efficiency; some energy is lost in the conversion process.
• —Temperature derating — crystalline silicon panels lose approximately 0.4% of output per °C above 25°C. In warm climates, panels routinely operate at 50–65°C, reducing output by 10–16%.
• —Soiling and shading — dust, haze, bird droppings, and partial shading reduce effective panel area and output.
• —Battery charging inefficiency — lithium batteries absorb charge at roughly 95–98% efficiency; lead-acid at 80–85%.

Note that the solar array is intentionally sized to replenish one day's load. It is not scaled up to match autonomy days — that would oversize the array unnecessarily. The battery bank covers multi-day cloudy periods; the array covers the average daily replenishment requirement.

This formula derives the output-side (battery-side) continuous current rating — the amperage the charge controller must be capable of delivering into the battery bank at the chosen system voltage. This is the figure used to select a controller model (e.g., a 20A, 30A, or 40A unit).

MPPT (Maximum Power Point Tracking) controllers accept a higher panel string voltage and step it down to battery voltage, transferring as much power as possible during the conversion. Because of this, the panel-side input current is lower than the battery-side output current — the controller trades voltage for current. The formula above gives the output current, which is what the controller's amperage rating refers to.

Always round up to the next standard commercial rating. Running a controller at its maximum rated current continuously shortens its service life; a 20–25% headroom is good practice.

This metric answers: after the battery bank has been fully drawn down over the autonomy period, how many days of average sun does it take to fully recover — while the daily load continues to run?

The derivation follows from Formula 3. Because the array is sized at 1.3× the daily load, it generates 30% more energy each day than it consumes. That daily surplus of 0.3 × Load Wh is what goes toward recharging the depleted battery. The total energy to recover is Load × Autonomy Days. So:

rechargeDays = (Load × Autonomy) / (0.3 × Load) = Autonomy / 0.3

Notice that Load cancels out — recharge time depends only on the number of autonomy days and the 30% margin built into the array sizing. This is a direct consequence of the design choice in Formula 3: a larger load with a proportionally larger array recovers at the same rate as a small system.