# Tutoring physics or chemistry, you might encounter Peukert’s Law, although it’s probably used more by industry.

In my March 2 post I mentioned reserve capacity and Amp*hours as two ways to measure a battery’s potential output. Numerically they are convertible backwards and forwards, but the reality is not necessarily so simple, because the speed of discharge affects the total output a battery can manage. Specifically, a higher discharge rate lessens the battery’s efficiency, so that the total output will decrease the faster the battery is discharged.

Peukert’s Law gives the equation

t=T(C/(I*T))k, where

t is the actual time the battery will deliver arbitrary current I,

T is the discharge time corresponding to the given amp*hour rating,

C is the given amp*hour rating,

k is a physical constant that depends on the type of battery (around 1.4 for lead-acid).

Because of Peukert’s Law, an amp*hour rating must be given with a specific time for which it’s valid. (My reading suggests that 20 hours might be a typical time.) Therefore, an amp*hour rating might read “120Ah over 20 hours”. Such a rating implies a discharge rate of 6A for 20 hours. How long the battery can deliver a different amperage can be calculated by Peukert’s Law.

Example: Imagine a battery rated 120Ah over 20 hours. How long can it deliver 120A?

Solution: Theoretically, a 120Ah battery can deliver 120A for 1 hour, although we already know not to expect it. Peukert’s Law gives

t=20(120/(120*20))1.4

t=20(0.05)1.4

t=0.30 hours, or about 18 minutes.