This off-grid power calculator estimates battery bank runtime hours when powering household AC appliances through an inverter. When designing solar power setups, RV electrical systems, or home emergency backup banks, calculating usable watt-hours based on depth of discharge (DoD) and inverter conversion efficiency prevents unexpected blackouts and preserves battery longevity.

### Battery Bank Energy and Inverter Math The calculator computes runtime using system voltage, capacity, and conversion losses:

- **Total Gross Energy Storage ($E_{\text{gross}}$):** $E_{\text{gross}} = \text{ampHours} \times \text{voltage}\text{ (Watt-Hours, Wh)}$. - **Usable Energy Capacity ($E_{\text{usable}}$):** $E_{\text{usable}} = E_{\text{gross}} \times (\text{dod} / 100)$. Standard limits are 50% for lead-acid, 80% for AGM, and 95% for lithium (LiFePO4). - **Inverter Efficiency Allowance ($\eta_{\text{inv}}$):** DC-to-AC inverters consume power during conversion. The tool models real-world throughput with a standard efficiency factor of $88\%$ ($\eta_{\text{inv}} = 0.88$). - **Effective Usable Energy ($E_{\text{eff}}$):** $E_{\text{eff}} = E_{\text{usable}} \times 0.88$. - **Runtime in Hours:** $\text{runtimeHours} = E_{\text{eff}} / \text{loadWatts}$.

### Worked Numeric Example Suppose a cabin owner powers a 250W continuous load (mini fridge and satellite internet) using a single 12V 100Ah AGM battery bank at 80% maximum depth of discharge:

- **Battery Capacity:** 100 Ah - **Voltage:** 12V - **Continuous Load:** 250 Watts - **Depth of Discharge (DoD):** 80%

**Step-by-Step Calculation:** 1. **Gross Energy:** $100 \times 12 = 1,200\text{ Watt-Hours (Wh)}$. 2. **Usable Energy at 80% DoD:** $1,200 \times 0.80 = 960\text{ Wh}$. 3. **Effective AC Energy at 88% Inverter Efficiency:** $960 \times 0.88 = 844.8\text{ Wh}$. 4. **Runtime Duration:** $844.8 / 250 \approx 3.38\text{ hours}$ (approx **3.4 hours**, or **203 minutes**).

### Client-Side Processing Note All calculations run in client-side JavaScript. No solar system specs, appliance wattage figures, or battery models are transmitted across any network.