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Convert energy in kilowatt-hours (kWh) to battery capacity in amp-hours (Ah). Essential for sizing battery banks for solar systems and backup power.
Common system voltages: 12V, 24V, 36V, 48V
Where Ah is capacity in amp-hours, kWh is energy in kilowatt-hours, and V is voltage in volts.
To store 5 kWh in a 48V system:
Ah = (5 × 1000) ÷ 48 = 104.17 Ah
| Energy (kWh) | 12V | 24V | 36V | 48V |
|---|---|---|---|---|
| 0.5 kWh | 41.67 Ah | 20.83 Ah | 13.89 Ah | 10.42 Ah |
| 1 kWh | 83.33 Ah | 41.67 Ah | 27.78 Ah | 20.83 Ah |
| 2 kWh | 166.67 Ah | 83.33 Ah | 55.56 Ah | 41.67 Ah |
| 5 kWh | 416.67 Ah | 208.33 Ah | 138.89 Ah | 104.17 Ah |
| 10 kWh | 833.33 Ah | 416.67 Ah | 277.78 Ah | 208.33 Ah |
| 13.5 kWh | 1125.00 Ah | 562.50 Ah | 375.00 Ah | 281.25 Ah |
| 20 kWh | 1666.67 Ah | 833.33 Ah | 555.56 Ah | 416.67 Ah |
| 50 kWh | 4166.67 Ah | 2083.33 Ah | 1388.89 Ah | 1041.67 Ah |
The kWh to Ah conversion translates energy measured in kilowatt-hours into battery capacity measured in amp-hours at a specific voltage. This conversion is fundamental for designing battery-based energy storage systems, including off-grid solar installations, electric vehicle battery packs, and uninterruptible power supplies. A kilowatt-hour represents the energy consumed by a 1,000-watt load running for one hour, while amp-hours measure the total charge a battery can deliver at its nominal voltage. The formula Ah = (kWh × 1,000) ÷ V shows that the same energy requires different Ah capacities depending on system voltage. For instance, storing 10 kWh requires 833 Ah at 12V but only 208 Ah at 48V. This voltage-dependent relationship is why modern solar and EV systems favor higher voltages, as it reduces current flow, cable sizing, and resistive power losses per NEC Article 690 and IEEE 1547 guidelines for distributed energy resources.
Determine total daily or backup energy requirements by listing all loads with their wattage and run time. Multiply watts by hours for each device, sum them all, then divide by 1,000 to get kWh.
Select the battery bank voltage: 12V for small systems under 2 kWh, 24V for medium systems up to 5 kWh, or 48V for larger installations. Higher voltages reduce current and allow smaller wire gauges per NEC Article 690.
Convert kWh to watt-hours by multiplying by 1,000, then divide by the system voltage. For example: 5 kWh at 48V = 5,000 ÷ 48 = 104.17 Ah of raw capacity needed.
Divide the raw Ah by the maximum allowable DoD: 0.50 for lead-acid (50% DoD) or 0.80–0.90 for lithium (80–90% DoD). This gives the total installed Ah capacity. Example: 104.17 Ah ÷ 0.80 = 130.2 Ah for lithium batteries.
Batteries are rated in Ah, but energy needs are measured in kWh. Accurate conversion ensures your battery bank stores enough energy for the required backup duration without over- or under-sizing.
Off-grid and hybrid solar systems require precise kWh-to-Ah calculations to determine battery bank size, ensuring sufficient energy storage for cloudy days and nighttime loads.
Battery costs scale with Ah capacity. Knowing the exact Ah requirement prevents expensive over-purchasing while ensuring adequate performance for the system lifetime.
| Battery Type | Nominal Voltage | Max DoD | Cycle Life | Ah for 10 kWh (Usable) |
|---|---|---|---|---|
| Lead-Acid (FLA) | 12V per cell pair | 50% | 500–1,000 | 417 Ah @ 48V |
| AGM (Sealed) | 12V per battery | 50% | 300–700 | 417 Ah @ 48V |
| LiFePO4 (LFP) | 3.2V per cell | 80–90% | 3,000–6,000 | 231–260 Ah @ 48V |
| Li-ion (NMC) | 3.6V per cell | 80% | 1,000–3,000 | 260 Ah @ 48V |
| Gel (Sealed) | 12V per battery | 50% | 500–1,200 | 417 Ah @ 48V |
At 12V: 83.33 Ah. At 24V: 41.67 Ah. At 36V: 27.78 Ah. At 48V: 20.83 Ah. The relationship is inversely proportional to voltage, so higher voltage systems need fewer amp-hours to store the same amount of energy, which is why 48V systems are preferred for larger installations.
Higher voltage systems deliver the same power at lower current, which reduces I²R losses in wiring, allows smaller wire gauges (saving cost), and improves inverter and charge controller efficiency. For systems above 3 kWh, 48V is the industry standard. NEC Article 690 provides specific requirements for different voltage ranges in solar installations.
Depth of discharge (DoD) is the percentage of a battery's rated capacity that is actually used before recharging. Lead-acid batteries should not exceed 50% DoD to achieve reasonable cycle life, effectively doubling the required Ah capacity. LiFePO4 batteries tolerate 80–90% DoD, requiring significantly less installed capacity for the same usable energy.
Multiply your daily kWh consumption by the desired days of autonomy (typically 2–3 for off-grid). Convert to Ah at your system voltage, then divide by maximum DoD. Example: 8 kWh/day × 3 days = 24 kWh. At 48V with 50% DoD lead-acid: (24,000 Wh ÷ 48V) ÷ 0.5 = 1,000 Ah installed capacity.
Yes, significantly. Lead-acid batteries lose approximately 1% of capacity per degree Celsius below 25°C (77°F). At 0°C (32°F), expect about 75–80% of rated capacity. LiFePO4 batteries are less affected but still lose 10–15% at freezing temperatures. Apply temperature derating factors from the battery manufacturer when sizing for cold climates.