Battery Bank Sizing

Q = (E_daily × days) / (DOD × V)

Quick answer

This calculator solves Q = (E_daily × days_autonomy) / (DOD × V_battery) for Battery Capacity. With Daily Energy 0.5 kWh, Days of Autonomy 0.5, Depth of Discharge 1.1, Battery Voltage 12 V, the result is 18.94 Ah.

Calculator

Battery Capacity (Ah)
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Formula

Q = (E_daily × days_autonomy) / (DOD × V_battery)

Description

Battery bank sizing for off-grid solar systems ensures enough stored energy to power the load through cloudy days without solar input. The required capacity depends on daily energy consumption, the number of days of autonomy (typically 2-5 for residential systems), the maximum allowable depth of discharge, and the battery bank voltage. Deeper discharge shortens battery life exponentially: lead-acid batteries at 50% DOD last roughly twice as long as at 80% DOD, while lithium-ion batteries tolerate deeper cycling.

Variables

  • Q — Required battery capacity (Ah)
  • E_daily — Daily energy consumption (Wh)
  • days — Number of days of backup autonomy
  • DOD — Maximum depth of discharge (0-1)
  • V — Nominal battery bank voltage (V)

Practical Notes

Common battery bank voltages are 12V, 24V, and 48V; higher voltage reduces current and wiring losses. Lead-acid batteries should use DOD of 0.5 or less for longevity, while LiFePO4 batteries can use 0.8-0.9 DOD. Temperature significantly affects capacity: lead-acid batteries lose about 1% capacity per degree below 25°C.

Symbols and units

Symbol Meaning Default unit Accepted units
Q Battery Capacity Ah mAh, Ah
E_daily Daily Energy Wh Wh, kWh
days Days of Autonomy — —
DOD Depth of Discharge — —, %
V Battery Voltage V pV, nV, µV, mV, V, kV

Step by step

  1. 1. What you know: Daily Energy 0.5 kWh, Days of Autonomy 0.5, Depth of Discharge 1.1, Battery Voltage 12 V
  2. 2. The relation: Q = (E_daily × days_autonomy) / (DOD × V_battery)
  3. 3. Substitute: E_daily = 0.5 kWh, days = 0.5, DOD = 1.1, V = 12 V
  4. 4. Result: Battery Capacity = 18.94 Ah

Worked examples

Minimum range

Given: Daily Energy 1 Wh, Days of Autonomy 0.025, Depth of Discharge 5.5 %, Battery Voltage 0.33 V

Result: Battery Capacity = 1.377 Ah

Low range

Given: Daily Energy 10 Wh, Days of Autonomy 0.25, Depth of Discharge 0.55, Battery Voltage 3.3 V

Result: Battery Capacity = 1.377 Ah

Typical

Given: Daily Energy 0.5 kWh, Days of Autonomy 0.5, Depth of Discharge 1.1, Battery Voltage 12 V

Result: Battery Capacity = 18.94 Ah

High range

Given: Daily Energy 5 kWh, Days of Autonomy 0.8, Depth of Discharge 1.76, Battery Voltage 0.23 kV

Result: Battery Capacity = 9.881 Ah

Maximum range

Given: Daily Energy 50 kWh, Days of Autonomy 8, Depth of Discharge 17.6, Battery Voltage 2.3 kV

Result: Battery Capacity = 9.881 Ah

How Battery Capacity changes with Daily Energy

Daily Energy (input) Battery Capacity (result)
50 Wh 1.894 Ah
125 Wh 4.735 Ah
0.25 kWh 9.47 Ah
0.375 kWh 14.2 Ah
0.5 kWh 18.94 Ah
0.75 kWh 28.41 Ah
1 kWh 37.88 Ah
2 kWh 75.76 Ah
3.5 kWh 132.6 Ah
5 kWh 189.4 Ah

The same result in other units

Unit Value
mAh 18940
Ah 18.94

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Frequently asked questions

How do you calculate Battery Bank Sizing?

Use Q = (E_daily × days_autonomy) / (DOD × V_battery). With Daily Energy 0.5 kWh, Days of Autonomy 0.5, Depth of Discharge 1.1, Battery Voltage 12 V, Battery Capacity works out to 18.94 Ah.

What is the formula for Battery Bank Sizing?

The formula is Q = (E_daily × days_autonomy) / (DOD × V_battery). Battery bank sizing for off-grid solar systems ensures enough stored energy to power the load through cloudy days without solar input.

What units does Battery Bank Sizing use?

Battery Capacity is shown in mAh, Ah. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

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