Beginner
Battery Sizing Formula
Size battery backup systems — calculate required Ah and kWh from load, duration, depth of discharge, and efficiency.
Formulas
Ah = (P × t) / (V × DoD × η)
Required battery amp-hours
kWh = (P × t) / (DoD × η × 1000)
Required battery energy (kWh)
Variable Definitions
Ah=Battery capacity(amp-hours)
P=Load power(watts (W))
t=Backup duration(hours (h))
V=Battery system voltage(volts (V))
DoD=Depth of discharge(decimal (0.8-0.9 for lithium, 0.5 for lead-acid))
η=Inverter efficiency(decimal (typically 0.92-0.97))
Worked Example
5,000W critical load, 8 hours backup, 48V lithium battery, 90% DoD, 95% inverter efficiency.
- Ah = (5,000 × 8) / (48 × 0.90 × 0.95)
- Ah = 40,000 / 41.04 = 974.7 Ah
- kWh = 974.7 × 48 / 1000 = 46.8 kWh
Answer: 975 Ah at 48V = 46.8 kWh battery required
When to Use
- •Sizing UPS systems for data centers
- •Residential battery backup (Tesla Powerwall, Enphase)
- •Off-grid solar battery bank sizing
- •Emergency/standby power battery requirements
Standards & References
- NEC 480 — Storage Batteries
- NEC 706 — Energy Storage Systems
- UL 9540 — Energy Storage Systems