Battery Formulas: Capacity and Runtime
Battery formulas for energy in Wh, bank capacity from load and depth of discharge, runtime, C-rate and series and parallel connection, with worked examples.
The formulas
| To find | Formula |
|---|---|
| Stored energy | E (Wh) = V × Ah |
| Energy the load needs | E (kWh) = P (kW) × t (h) |
| Bank energy to install | Ebank = E / (DoD × η) |
| Bank capacity | Ah = Ebank × 1000 / V |
| Runtime | t = V × Ah × DoD × η / (P × 1000) |
| C-rate | C-rate = I / Ah, so 1C is the current that would empty the battery in one hour |
| Series connection | Voltages add, Ah stays the same |
| Parallel connection | Ah adds, voltage stays the same |
DoD is the usable fraction of the capacity (depth of discharge) and η the round-trip or inverter efficiency, both as fractions. P is in kW, V in volts. Use the DoD and efficiency from the battery data sheet.
Worked example: bank size for a 2 kW load for 5 hours
The bank is 48 V, with a usable depth of discharge of 80% and an efficiency of 90%.
- E = 2 × 5 = 10 kWh
- Ebank = 10 / (0.8 × 0.9) = 13.89 kWh
- Ah = 13.89 × 1000 / 48 = 289.4 Ah, so the next standard size up is needed
Worked example: runtime of a 48 V, 300 Ah bank
- t = 48 × 300 × 0.8 × 0.9 / (2 × 1000) = 5.184 hours at 2 kW
Bank size for 5 hours at 48 V
| Load | Bank energy | Bank capacity |
|---|---|---|
| 0.5 kW | 3.472 kWh | 72.34 Ah |
| 1 kW | 6.944 kWh | 144.7 Ah |
| 2 kW | 13.89 kWh | 289.4 Ah |
| 5 kW | 34.72 kWh | 723.4 Ah |
Frequently asked questions
Why is the bank larger than the energy I need?
You cannot use all of the stored energy. The depth of discharge limits what is taken out, and the inverter and wiring lose some of it as heat.
What depth of discharge should I use?
Take it from the data sheet. Lead-acid batteries are often limited to about 50% for a long life, and lithium iron phosphate batteries to about 80% to 90%.
Does the runtime stay the same at a higher load?
No. A heavy discharge reduces the usable capacity of most batteries, especially lead-acid. Data sheets give capacity at a stated discharge time, such as 10 or 20 hours.
Why do parallel strings need care?
Unequal cable lengths or batteries of different age make the strings share current unevenly. Keep strings identical and the connections the same length.
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