Battery Sizing Formula
This is the complete formula reference for battery bank sizing. Every variable is defined, every factor is explained, and a fully worked example demonstrates how the formulas apply to a real-world 48V LFP system.
Primary Sizing Formula
The primary formula calculates the total energy capacity required in watt-hours. All other sizing parameters — autonomy, discharge limits, efficiency, and temperature — are divisors that increase the required capacity to account for real-world losses and constraints.
Capacity in Watt-Hours
C_Wh — Required battery capacity in watt-hours
E_daily — Total daily energy consumption in watt-hours
N_autonomy — Number of days of autonomy (backup duration)
D_DoD — Maximum depth of discharge as a decimal (e.g., 0.80 for 80%)
η_system — Overall system efficiency as a decimal (inverter × charge controller × wiring)
K_temp — Temperature derating factor (1.0 at 25°C, lower at colder temperatures)
Capacity in Amp-Hours
Once you have the required capacity in watt-hours, convert to amp-hours by dividing by the system voltage. This is the figure you use when selecting batteries, since most batteries are rated in Ah at a specific voltage.
Capacity in Amp-Hours
For a 48V system requiring 9,600 Wh: 9,600 / 48 = 200 Ah. For a 12V system requiring 2,400 Wh: 2,400 / 12 = 200 Ah. Same energy, different Ah ratings due to voltage.
System Efficiency Breakdown
System efficiency is the product of all conversion and transmission losses between the battery and the load. Each stage multiplies together to give the total η_system value used in the sizing formula.
| Loss Stage | Typical Efficiency | Notes |
|---|---|---|
| Inverter (DC→AC) | 88–95% | Pure sine wave inverters at the higher end |
| Charge Controller | 95–98% | MPPT controllers are more efficient than PWM |
| Battery Round-Trip | 90–98% | LFP at 96–98%, lead-acid at 80–85% |
| Wiring / Connections | 97–99% | Depends on cable gauge and length |
| Combined η_system | 78–90% | Multiply all stages together |
Temperature Derating Factors
Batteries are rated at 25°C. Cold temperatures slow the chemical reactions inside the cells, reducing the energy that can be extracted. The temperature factor K_temp is applied as a divisor — a lower K_temp means you need more installed capacity.
| Temperature | LFP (K_temp) | Lead-Acid (K_temp) | NMC (K_temp) |
|---|---|---|---|
| 30°C (86°F) | 1.02 | 1.00 | 1.01 |
| 25°C (77°F) | 1.00 | 1.00 | 1.00 |
| 10°C (50°F) | 0.95 | 0.90 | 0.93 |
| 0°C (32°F) | 0.90 | 0.80 | 0.85 |
| -10°C (14°F) | 0.80 | 0.65 | 0.75 |
| -20°C (-4°F) | 0.70 | 0.50 | 0.60 |
Values are approximate and vary by manufacturer. Always consult the specific battery datasheet for precise derating curves.
Worked Example: 48V LFP Bank
Scenario: Size a 48V LFP battery bank for a home with 10 kWh/day consumption and 2 days of autonomy.
Given:
- Daily energy consumption: 10,000 Wh (10 kWh)
- Autonomy required: 2 days
- DoD limit: 80% (LFP chemistry)
- Inverter efficiency: 92%
- Charge controller efficiency: 97%
- Battery round-trip efficiency: 96%
- Wiring losses: 98%
- Temperature factor: 0.95 (mild climate, 10°C average)
- System voltage: 48V
Step 1: Calculate combined system efficiency:
Step 2: Calculate required capacity in Wh:
Step 3: Convert to Ah at 48V:
Step 4: Select practical configuration. A 48V LFP system with 16 cells in series (48V nominal) and a 280 Ah cell configuration yields approximately 13.4 kWh. For 31.3 kWh, use 4 parallel strings of 280 Ah cells: 4 × 280 Ah = 1,120 Ah at 48V = 53.8 kWh. This provides substantial margin for 10+ years of capacity fade and potential load growth.
Alternatively, a commercially available 48V 200Ah LFP battery module (9.6 kWh) can be paralleled: 4 modules = 38.4 kWh, providing 22% margin above the 31.3 kWh requirement.
Quick Reference: Ah per kWh by Voltage
| System Voltage | Ah per 1 kWh | Typical Use |
|---|---|---|
| 12V | 83.3 Ah | RV, marine, small off-grid |
| 24V | 41.7 Ah | Medium off-grid, small home |
| 48V | 20.8 Ah | Home solar, commercial, telecom |
| 400V | 2.5 Ah | Utility-scale BESS |
Higher voltage systems require fewer Ah for the same energy, reducing cable size and conduction losses.
Try It
Use the Battery Sizing Calculator to apply these formulas with your own numbers.
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Overview of the sizing process, why it matters, and key design considerations.
Read Guide →Battery Sizing Chart Guide
Visual chart showing which Ah rating fits which application and load profile.
Read Guide →Frequently Asked Questions
What is the formula for sizing a battery bank?
The standard formula is: Required Capacity (Wh) = Daily Load (Wh) × Autonomy Days / (DoD% / 100) / (Efficiency% / 100) / Temperature Factor. Convert to Ah by dividing by system voltage. This accounts for all major variables: energy demand, backup duration, discharge limits, system losses, and environmental conditions.
How does temperature affect the sizing formula?
Temperature derating factors reduce the effective capacity available from a battery. At 0°C, LFP batteries deliver about 90% of rated capacity and lead-acid about 80%. At -20°C, the numbers drop to 70% and 50% respectively. The temperature factor is a divisor in the sizing formula — a lower factor means you need more installed capacity to compensate.
What depth of discharge should I use in the formula?
It depends on your battery chemistry and cycle life requirements. LFP can use 80–90% DoD for 4,000+ cycles. NMC lithium typically uses 80% DoD. Lead-acid should be limited to 50% DoD to avoid rapid degradation. Using a lower DoD extends battery life but requires a larger bank — the formula captures this tradeoff directly.
How do I account for inverter efficiency in the formula?
Inverter efficiency is typically 85–95% and is included in the system efficiency divisor. If your inverter is 90% efficient, use 0.90 in the formula. For systems with multiple conversion stages (DC-DC converter + inverter), multiply the efficiencies of each stage for the total system efficiency figure.