Battery and Solar Sizing: Off-Grid Power Math

Why You Need to Do the Math

The most common off-grid power mistake is buying panels and batteries without calculating what you actually need. The result is either a system that runs out at 7 PM or an expensive over-build.

The math is not complicated. It takes 30 minutes to do correctly and determines whether your $2,000 power system lasts the winter or fails in week three.

Step 1: Calculate Your Daily Load (Watt-Hours)

List every device you plan to run, its wattage, and daily hours of use.

Example: Minimal Prepper Power System

| Device | Watts | Hours/Day | Watt-Hours/Day | |--------|-------|-----------|----------------| | LED lighting (4 bulbs × 8W) | 32W | 4 hours | 128 Wh | | Radio/communications | 20W | 3 hours | 60 Wh | | Phone charging (2 phones) | 20W | 2 hours | 40 Wh | | Small laptop or tablet | 45W | 3 hours | 135 Wh | | Refrigerator (efficiency model) | 100W avg | 24 hours | 2,400 Wh | | CPAP (if applicable) | 30W | 8 hours | 240 Wh |

Without refrigerator total: 363 Wh/day With refrigerator total: 2,763 Wh/day

This is why the refrigerator changes everything. A chest freezer or efficient 12V DC refrigerator (EcoFlow, Alpicool) runs on 20-40W continuous versus 100W+ for a household unit.

Add 20% for inverter efficiency losses (DC to AC conversion): multiply by 1.2.

Minimal system (no fridge): 363 × 1.2 = 435 Wh/day

Step 2: Size the Battery Bank

Determine days of autonomy: how many days without sun can your system support? For a primary preparedness system: 2-3 days minimum, 5 days for serious resilience.

Formula: Battery Bank (Wh) = Daily Load (Wh) × Days of Autonomy ÷ Maximum Depth of Discharge

For minimal system, 3-day autonomy, LiFePO4 (80% DoD): Battery Bank = 435 Wh × 3 ÷ 0.8 = 1,631 Wh

At 12V nominal voltage: 1,631 Wh ÷ 12V = 136 Ah battery bank → Round to 150Ah LiFePO4

For minimal system, 3-day autonomy, Lead-Acid (50% DoD): Battery Bank = 435 × 3 ÷ 0.5 = 2,610 Wh = 218 Ah at 12V → The lead-acid bank needs to be significantly larger for the same usable capacity.

Battery Types Compared

| Type | Usable DoD | Cycle Life | Cost per Wh | Notes | |------|-----------|-----------|-------------|-------| | Flooded lead-acid | 50% | 300-500 | $0.10-0.20 | Requires maintenance, vents gas | | AGM lead-acid | 50% | 400-600 | $0.20-0.35 | Sealed, no maintenance | | LiFePO4 | 80-90% | 2000-5000 | $0.40-0.80 | Best choice if budget allows |

Step 3: Size the Solar Array

Peak sun hours: The average number of hours per day at your location where solar irradiance equals 1,000 W/m². This varies by location and season. Conservative estimates:

| Location | Peak Sun Hours (Annual Average) | |----------|-------------------------------| | Pacific Northwest (Seattle) | 3.5 hours | | Desert Southwest (Phoenix) | 6.5 hours | | Midwest (Kansas City) | 4.5 hours | | Southeast (Atlanta) | 5.0 hours | | Northeast (Boston) | 4.0 hours |

Use your specific location value from NREL's PVWatts Calculator (pvwatts.nrel.gov). For winter sizing (worst case), use winter peak sun hours which may be 50-70% of annual average.

Formula: Solar Array (Watts) = Daily Load (Wh) ÷ Peak Sun Hours × System Efficiency Factor (0.85)

For minimal system in Midwest: Solar Array = 435 Wh ÷ 4.5 hours ÷ 0.85 = 114W → Round to 200W (provides margin for winter and panel degradation over time)

For winter sizing (assume 60% of annual = 2.7 peak sun hours): Solar Array = 435 ÷ 2.7 ÷ 0.85 = 190W → 200-250W covers winter adequately in the Midwest.

Step 4: Select a Charge Controller

A charge controller manages the flow of power from solar panels to the battery bank, preventing overcharging.

Two types:

• PWM (Pulse Width Modulation): Cheaper, adequate for small systems (under 400W), less efficient (approximately 70-80%)
• MPPT (Maximum Power Point Tracking): More expensive, 93-97% efficient, required for larger systems or mismatched panel/battery voltages

For a 200W array with a 12V battery bank, a 20-amp PWM controller works. For 400W+, MPPT is worth the premium.

Step 5: Size the Inverter (if using AC devices)

Inverter size = peak simultaneous AC load × 1.25 (safety margin)

For the minimal system with no refrigerator: lighting and phone charging can all run from 12V DC directly (no inverter needed). A laptop requires AC or a 12V-specific power supply.

If running a 12V-compatible system throughout: no inverter needed, eliminates 15-20% efficiency loss.

Complete System Example: Minimal Grid-Down Power

Goal: Lights, radio, phone charging, laptop for 3 days without sun.

| Component | Specification | Approximate Cost | |-----------|-------------|-----------------| | Solar panels | 2 × 100W (200W total) | $150-200 | | Battery | 150Ah LiFePO4, 12V | $350-500 | | MPPT charge controller | 20A Victron or Renogy | $80-150 | | 400W pure sine inverter | Renogy or Victron | $80-120 | | Wiring, fuses, connectors | Various | $50-100 | | Total | | $710-1,070 |

This system runs the minimal load list above (no refrigerator) for 3 days with no sun input, then recharges to full in approximately 1.5 days of good sun.