Battery Capacity Calculator

Amp hours measure charge, watt hours measure energy, and voltage is what connects them:

$E = C \times V$

• $E$ — energy, watt hours (Wh); divide by $1000$ for kWh
• $C$ — capacity, amp hours (Ah)
• $V$ — nominal pack voltage, volts (V)

Rearranged, $C = E/V$.

Why the distinction matters: a $100$ Ah pack at $12.8$ V ($1280$ Wh) stores twice the energy of a $100$ Ah pack at $6.4$ V. Comparing batteries of different voltages by amp hours alone is meaningless — always compare watt hours.

The assumption people forget: nominal voltage is a label, not the terminal voltage. A 12 V lead-acid battery sits near $12.7$ V full and $11.8$ V empty; a 12 V LiFePO₄ pack (four cells) is nominally $12.8$ V. Manufacturers rate Ah at a specified discharge rate and temperature, so a rating is only valid under those conditions.

To size a battery for a load, work backwards through every loss:

$C_{\text{required}} = \frac{P \times t}{V \times \eta_{\text{inv}} \times \text{DoD}}$

• $P$ — load power, watts (W); $t$ — run time, hours (h)
• $\eta_{\text{inv}}$ — inverter efficiency, typically $0.85$–$0.95$ for an AC load; omit it for a DC load
• $\text{DoD}$ — usable depth of discharge as a fraction: about $0.5$ for lead-acid, $0.8$–$0.9$ for LiFePO₄

Charge time:

$t = \frac{C_{\text{needed}}}{I_{\text{charge}} \times \eta_{\text{chg}}}$

in hours, with $I$ in amperes and charging efficiency $\eta_{\text{chg}}$ around $0.85$ for lead-acid, $0.95$+ for lithium.

The assumption people forget: this is a first-pass estimate. Lead-acid capacity falls at high discharge rates (Peukert's law), cold cuts usable capacity sharply, and the constant-voltage absorption stage at the end of a charge is far slower than the constant-current stage. Follow the cell manufacturer's charge profile.

• Adding amp hours across different voltages — convert everything to watt hours first, then add.
• Planning to use 100% of the rated capacity — deep-cycling a lead-acid battery to empty destroys it in tens of cycles. Design to the usable depth of discharge.
• Ignoring inverter losses — an AC load draws $10$–$15\%$ more from the battery than its nameplate wattage.
• Treating charge time as capacity divided by current — efficiency losses and the tapering absorption stage make the real time longer.
• Confusing Ah with A — amperes are a rate, amp hours are a quantity.
• Mixing series and parallel wiring — series adds voltage at constant Ah; parallel adds Ah at constant voltage.