Peukert's Law (Battery Runtime)

A battery's amp-hour rating is a promise made at one particular discharge rate, and it does not survive being pushed harder. Wilhelm Peukert measured this in 1897: capacity falls off as a power law in current, $t = H(C/IH)^k$, where H is the number of hours the rating was measured over — usually 20 for lead-acid — and k is the exponent that describes how badly the chemistry copes. A 100 Ah battery at the 20-hour rate looks like it should run 4 hours at 25 A; with a typical k of 1.3 it manages under 2.5 hours.

The exponent is a health indicator as much as a design parameter. New flooded lead-acid sits around 1.1 to 1.2, AGM slightly better, a tired or sulphated bank 1.3 and worse. Lithium iron phosphate is near 1.02 to 1.05, which is a large part of why an LFP pack of the same nameplate capacity so comprehensively outperforms lead-acid in an inverter or a trolling motor — the rated capacity is nearly all real. You can measure your own k by timing two discharges at different currents and taking a ratio of logarithms, which is what solving this page for k does.

The classic error is comparing amp-hour ratings from different rate assumptions. A "100 Ah" battery at the 20-hour rate and a "100 Ah" battery at the 100-hour rate are not the same battery, and the second is markedly worse. Always check the rate the number was measured at. Two more caveats: Peukert's law says nothing about temperature, which can cost another 20% at freezing, and it assumes a steady current, so it systematically over-predicts for the pulsed loads that inverters and radios actually present.