A battery's capacity is quoted in amp-hours, and an amp-hour is a charge: $Q = I t$, read aloud Q equals I t, with $Q$ the charge, $I$ the steady current in amperes and $t$ the time. Take it at face value and a 100 Ah pack runs a 5 A load for 20 hours, or a 50 A load for two. The first of those is true. The second is not.

The catch is that the rating was measured at ONE discharge rate — almost always the 20-hour rate. Pull harder and the plates cannot deliver charge as fast as the chemistry would like, and the pack gives up early. Peukert's law prices that: $t = H\left(\dfrac{C}{I H}\right)^{k}$, t equals H times, C over I H, to the k. $t$ is the real runtime in hours; $C$ is the rated capacity in amp-hours; $H$ is the rating's own discharge time in hours — the 20 in “100 Ah at the 20-hour rate” — $I$ is the actual load current in amperes, and $k$ is the Peukert exponent, a bare number with no units.

$k = 1$ would be a perfect battery, and it collapses the whole thing back to $t = C/I$. Real lead-acid runs 1.1 to 1.3, a tired one nearer 1.4, and lithium sits at 1.02 to 1.05 — which is most of why lithium packs feel so much bigger than their label.

The rail to carry: pulled harder than its rating, a pack ALWAYS delivers less than $Q = I t$ promises. If your arithmetic ever beats the naive figure, the exponent went in upside down.