How to Calculate Battery Capacity and Number of Batteries Needed
When building an off-grid or backup power system, one of the first questions is: “How many batteries do I need to power my load for a specific number of hours?” This calculator helps you determine both the required battery capacity (Ah) and the total number of batteries needed, based on your system voltage, inverter efficiency, battery type, and depth of discharge (DoD).
1. Understanding the Basic Formula
The starting point is energy demand. Multiply your load power in watts by the desired runtime in hours to find total energy:
Energy (Wh) = Load (W) × Runtime (h)
For example, if your system needs to power a 500 W device for 5 hours, the total energy required is: 500 W × 5 h = 2,500 Wh.
2. Accounting for Inverter Efficiency and System Losses
Not all energy drawn from the battery makes it to the load due to inverter losses. A typical inverter efficiency is between 85–95%. Divide the required load energy by the inverter efficiency (in decimal form) to find how much DC energy your battery bank must provide.
Battery Energy (Wh) = Load Energy / Inverter Efficiency
3. Applying Safety Margin and Depth of Discharge (DoD)
To prolong battery lifespan, you should never discharge it completely. Lead-acid batteries are usually limited to 50% DoD, while lithium batteries like LiFePO₄ can safely reach 80–90%. A 15% safety margin is also recommended to account for aging, temperature, and efficiency changes.
The adjusted required battery capacity (in amp-hours) can be estimated as:
Required Capacity (Ah) =
(Load × Hours) / (System Voltage × Inverter Efficiency × Usable DoD)
4. Determining Series and Parallel Battery Configuration
Battery banks are built using combinations of series and parallel connections:
- Series connection: increases total voltage (V stays constant per battery × number of batteries in series).
- Parallel connection: increases total capacity (Ah adds up across strings).
The calculator automatically computes how many batteries you need in series to reach your system voltage (e.g., 4 × 12 V = 48 V), and how many parallel strings are required to meet total amp-hour capacity.
5. Example Calculation
Suppose you have a 1,000 W load running for 4 hours, with a 48 V system, 90% inverter efficiency, and 12 V 100 Ah batteries at 80% DoD.
- Energy = 1,000 W × 4 h = 4,000 Wh
- DC energy = 4,000 Wh / 0.9 = 4,444 Wh
- Required Ah at 48 V = 4,444 Wh / 48 V = 92.6 Ah
- Adjusted for 80% DoD = 92.6 / 0.8 = 116 Ah
- Series batteries = 48 V / 12 V = 4 batteries
- Parallel strings = 116 Ah / 100 Ah = 1.16 → round up to 2 parallel strings
✅ You’ll need 4 in series × 2 in parallel = 8 batteries total.
6. Practical Considerations
- Use larger system voltages (e.g., 48 V) to reduce current and cable size.
- Keep battery strings short and balanced for even charging/discharging.
- Regularly check terminal torque, voltage balance, and temperature.
- Consider environment: temperature extremes reduce capacity significantly.
7. Recommended Battery Chemistries
Lead-acid: Low cost, reliable but heavy and limited to ~50% DoD.
LiFePO₄ (Lithium Iron Phosphate): Long cycle life, 80–90% DoD, ideal for solar and backup systems.
Nickel or AGM Gel Batteries: Maintenance-free options, moderate lifespan, suitable for small systems.
8. Summary
Properly sizing your battery bank ensures your system runs efficiently without over-stressing your batteries. The SolarMathLab Battery Capacity & Count Calculator helps automate this process by accounting for inverter losses, usable DoD, and safety margins. Always round up battery counts and verify compatibility with your inverter’s voltage rating.
By optimizing battery sizing, you’ll improve performance, reduce maintenance, and extend your system’s overall lifespan.