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Battery Capacity Sizer

Determine the total raw battery capacity in Amp-Hours needed to survive off-grid cloudy days, adjusting for strict chemistry safe discharge limits.

Storage Load Paramters

Daily Energy Consumption

Watt-hours (Wh)

Days of Autonomy

days

Consecutive cloudy days

System Bus

Battery Chemistry (Depth of Discharge)

Lithium batteries can safely be drained much lower than Lead-Acid batteries before suffering permanent chemical damage.

Required Battery Block

Required Rating

625

Amp-HoursAh

Total Gross

30.0

kWh

Pure Usable Energy Need	15,000 Wh
Total Gross Battery Capacity	30,000 Wh

Depth of Discharge Penalty: Because Lead-Acid batteries shouldn't be discharged below 50% of their total capacity, you must physically purchase double your required usable energy.

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What is Depth of Discharge (DoD) & Battery Chemistry Sizing?

Solar arrays generate power, but batteries store it for use when the sun is down or storms roll in. However, you cannot simply buy the exact amount of electricity you need — battery chemistries destroy themselves if fully discharged. You must strategically oversize the physical bank to protect the cell internals. The DoD factor converts your required usable energy into the gross physical capacity you must purchase, which is always larger than your actual needs.

Mathematical Foundation

Total Usable Capacity Required

\text{Usable (Wh)} = \text{Daily Load (Wh)} \times \text{Days of Autonomy}

Daily Load (Wh)

= Total energy consumed per day by all loads (lights, appliances, inverter losses, etc.)

Days of Autonomy

= Number of consecutive sunless days the system must survive without a generator. Standard off-grid residential = 3 days.

Total Gross Battery Capacity (DoD-Adjusted)

\text{Gross (Wh)} = \frac{\text{Usable Capacity (Wh)}}{\text{DoD}}

DoD

= Depth of Discharge (decimal). Lead-Acid/AGM: 0.50 maximum (50%). LiFePO4/Lithium: 0.80 maximum. Exceeding DoD permanently damages cells.

Gross (Wh)

= The physical nameplate capacity you must purchase — always larger than usable capacity by the DoD factor.

Amp-Hour Conversion (Bank Sizing)

\text{Capacity (Ah)} = \frac{\text{Gross Capacity (Wh)}}{\text{System Voltage (V)}}

System Voltage

= Nominal DC bus voltage: 12V (small systems), 24V (mid-range), or 48V (residential off-grid / commercial). Higher voltage = lower current = smaller wire gauge required.

Laws & Principles

Days of Autonomy: The industry standard for off-grid residential systems is 3 consecutive days of full load with zero solar input. This weathers most storm events without requiring a backup generator. Grid-tied systems with battery backup typically use 1 or 2 days. Critical facilities (medical, telecom) may specify 5–7 days.
The Lead-Acid Penalty: Traditional flooded lead-acid and AGM batteries cannot be safely discharged below 50% (DoD = 0.50) without causing lead sulfate crystallization (sulfation) on the plates — permanently reducing capacity. A 10 kWh lead-acid bank provides only 5 kWh of usable energy. Users pay for double the capacity they actually use.
The Lithium Advantage: LiFePO4 (lithium iron phosphate) batteries can safely discharge to 20% remaining (DoD = 0.80). The same 5 kWh of usable energy requires only a 6.25 kWh gross LiFePO4 bank versus a 10 kWh lead-acid bank — 37.5% less physical capacity. LiFePO4 also offers 2,000–4,000 cycles vs. lead-acid's 200–500 cycles, dramatically lower cost-per-kWh over the system lifetime.
Amp-Hours (Ah): The native purchasing metric for batteries. Because systems operate at different voltages (12V/24V/48V), Watt-hours are divided by system voltage to get Ah — the value on battery spec labels. A 100Ah battery at 12V stores 1,200 Wh; the same 100Ah at 48V stores 4,800 Wh.

Step-by-Step Example Walkthrough

" An off-grid cabin uses 5,000 Wh/day and requires 3 days of autonomy on a 48V lead-acid system. "

Required usable energy: 5,000 Wh × 3 days = 15,000 Wh.
DoD adjustment (Lead-Acid at 50%): 15,000 Wh ÷ 0.50 = 30,000 Wh gross physical capacity required.
Convert to Amp-Hours: 30,000 Wh ÷ 48V = 625 Ah.
Comparison: The same system with LiFePO4 (80% DoD): 15,000 ÷ 0.80 = 18,750 Wh gross; 18,750 ÷ 48 = 391 Ah — 37% fewer batteries to purchase.

Final Result: The lead-acid bank requires 625 Ah at 48V (30 kWh gross). The LiFePO4 equivalent requires only 391 Ah (18.75 kWh gross) — a meaningful cost and space savings despite higher upfront lithium cost per kWh.

Quick Answer: How many Amp-Hours of batteries do I need for off-grid solar?

The formula: Gross Bank Capacity (Ah) = (Daily Load × Days of Autonomy) ÷ DoD ÷ System Voltage. For a typical off-grid cabin running 5 kWh/day with 3 days of autonomy on a 48V LiFePO4 system at 80% DoD: (5,000 × 3) ÷ 0.80 ÷ 48 = 391 Ah. The same load on lead-acid at 50% DoD requires 625 Ah — 60% more physical battery. The Depth of Discharge limit is not optional: discharging lead-acid below 50% permanently sulfates the plates; discharging LiFePO4 below 20% accelerates lithium plating and dendrite formation. This calculator applies the correct DoD limit for each chemistry automatically.

Battery Chemistry Comparison for Off-Grid Solar

Chemistry	Max DoD	Cycle Life	Upfront Cost/kWh	Best For
Flooded Lead-Acid (FLA)	50%	200–400 cycles	$100–$150	Budget off-grid; seasonal cabins; low-cycle applications; easily serviced/refilled
AGM (Sealed Lead-Acid)	50%	300–500 cycles	$150–$250	Maintenance-free; RVs; cold climates (better cold performance than FLA); UPS backup
Gel Cell	50–60%	500–800 cycles	$200–$300	Slow discharge applications; telecom; stationary backup; sensitive to overcharging
LiFePO4 (Lithium Iron Phosphate)	80%	2,000–4,000 cycles	$400–$700	Preferred for residential off-grid; lightweight; flat discharge curve; built-in BMS; 10+ year life
NMC Lithium (Li-Ion)	80–90%	500–1,500 cycles	$300–$500	Higher energy density than LiFePO4; EV-grade repurposed cells; requires careful BMS management; thermal runaway risk if abused
Cost per cycle = (Upfront cost/kWh) ÷ Cycle life. LiFePO4 at $600/kWh ÷ 3,000 cycles = $0.20/kWh-cycle vs. FLA at $125/kWh ÷ 300 cycles = $0.42/kWh-cycle — LiFePO4 is 53% cheaper per cycle despite 4–5× higher upfront cost. Always compare cost-per-cycle, not sticker price.

Pro Tips & Battery Bank Sizing Errors

Do This

✓Use a 48V system for any bank above 5 kWh — higher voltage dramatically reduces wire gauge, fusing, and heat losses. Power (W) = Voltage × Current. For the same 5 kW of load: at 12V, current = 417A (requires 4/0 AWG cable, expensive fusing); at 48V, current = 104A (requires 4 AWG cable, standard 150A fuse). Wire resistance loss = I²R — reducing current by 4× reduces loss by 16× for the same wire run. All modern inverter/chargers (Victron, Schneider, SMA) support 48V natively. Below 3 kWh, 12V or 24V systems are still practical. Never mix 12V and 24V batteries in the same bank.
✓Derate lead-acid battery capacity by 20–30% for cold-weather installations — a 100 Ah battery at 32°F (0°C) delivers only 70–80 Ah. Lead-acid battery capacity decreases approximately 1% per °F below 77°F (25°C), reaching about 50% capacity at 0°F (−18°C). If your battery bank is in an unheated space (garage, shed) in a cold climate, add a temperature correction factor: multiply your calculated bank size by 1.2–1.4 for winter conditions. LiFePO4 batteries also lose capacity in cold (−20% at 32°F), but they recover fully when warmed — unlike lead-acid, which permanently loses capacity from repeated cold-discharge cycling. Install insulation or a battery heater (2–5W trickle) for cold installations.

Avoid This

✗Don't mix batteries of different ages, chemistries, or capacities in the same parallel bank. When batteries are connected in parallel, the stronger (newer/fuller) battery always forces current into the weaker one, causing the weaker cell to charge faster than designed, generating heat, and accelerating degradation. The “birthday problem” in battery banks: a single weak cell tanks the entire parallel group's available capacity because current redistribution creates uneven state-of-charge across cells. If replacing cells in an existing lead-acid bank, replace the entire bank at once. For LiFePO4, individual cells with matched capacity can be added if within ±5% of existing SoC at the time of connection.
✗Don't confuse C-rate when purchasing: a battery rated “100 Ah” is usually rated at the C20 rate (20-hour discharge) — at C5 (5-hour discharge), it may only deliver 75–85 Ah. Lead-acid batteries lose effective capacity significantly at high discharge rates. Peukert's Law: C_actual = C_rated × (t/T)^1−k, where k ≈ 1.1–1.3 for FLA. An inverter drawing 500W from a 100Ah/12V bank (C2.4 rate) effectively delivers only ~75Ah, not 100Ah. For inverter applications (high discharge rate), size for the C5 or actual discharge rate capacity, not the C20 spec sheet number. This calculator uses the rated capacity — always verify the C-rate your load requires against the manufacturer's rate-dependent capacity chart.

Frequently Asked Questions

How many days of autonomy should I design for?

Standard design rules by application: Off-grid residential: 3 days (weathers most storm systems; beyond 3 days, a generator is more cost-effective than additional battery capacity). Grid-tied with battery backup: 0.5–1 day (covers typical grid outages; longer outages suggest generator pairing). RV/boat: 1–2 days (frequent partial recharge from alternator, shore power, or generator). Critical infrastructure (telecom, medical): 5–14 days (mandated by regulatory standards). Beyond 5 days of pure battery autonomy, the cost and weight of additional batteries typically exceeds the cost of a propane or diesel generator for bridging long outages. The NEC Article 706 (storage systems) and UL 9540 govern residential energy storage installation requirements in most US jurisdictions.

Should I wire batteries in series or parallel?

Series wiring adds voltages while keeping Ah constant: two 12V/100Ah batteries in series = 24V/100Ah (2,400 Wh). Parallel wiring adds Ah while keeping voltage constant: two 12V/100Ah batteries in parallel = 12V/200Ah (2,400 Wh — same Wh). To build a 48V bank from 12V batteries, wire 4 batteries in series (4 × 12V = 48V). To double the capacity of that 48V bank, wire a second group of 4 in parallel with the first. The result: 48V at twice the Ah. Series-parallel rule: always use identical batteries (same brand, model, age, and SoC at connection time). For large banks, many solar designers prefer 48V batteries (marketed as single units) over series-wired 12V strings to minimize cell imbalance risk. Modern LiFePO4 packs with built-in BMS automatically handle cell balancing in series configurations.

Is LiFePO4 worth the higher upfront cost over lead-acid?

In most daily-cycle off-grid applications, yes — LiFePO4 is cheaper over its lifetime despite 3–5× higher purchase price. Cost-per-cycle analysis (see chemistry table above): LiFePO4 at ~$600/kWh ÷ 3,000 cycles ≈ $0.20/kWh-cycle; flooded lead-acid at ~$125/kWh ÷ 300 cycles ≈ $0.42/kWh-cycle. LiFePO4 wins by 53% per cycle and eliminates: monthly equalization charges, water refilling, hydrogen off-gassing ventilation requirements, temperature sensitivity, and the 2× bank oversizing penalty of lead-acid. Lead-acid remains justified for: seasonal cabins cycling <30 times per year (cycle count too low to matter), budget-constrained projects where upfront cost is the primary constraint, or cold-storage applications where LiFePO4 BMS low-temperature cutoff is a constraint.

How do I calculate my daily load in Watt-hours?

Daily load (Wh) = sum of (appliance watts × hours per day) for all loads. Practical steps: (1) List every electrical device and its wattage (check the label or use a kill-a-watt meter for measured consumption). (2) Estimate daily usage hours. (3) Multiply and sum: e.g., LED lights 50W × 5h = 250 Wh; refrigerator 150W average × 24h = 3,600 Wh; laptop 45W × 4h = 180 Wh. Sum = 4,030 Wh/day. (4) Add inverter efficiency loss: divide by inverter efficiency (typically 85–95%) to get DC load: 4,030 ÷ 0.90 ≈ 4,478 Wh/day AC equivalent at the battery. (5) Add safety factor of 10–20% for startup surges, measurement errors, and future load growth. A realistic off-grid cabin typically runs 3–8 kWh/day depending on whether it has a standard refrigerator, electric water heater (very high load — solar thermal is far more efficient), or resistance space heating (avoid on off-grid — use a propane heater instead).