# Calculating the Battery Runtime (Peukart Law)

Published on by www. charger-battery.ca

If the battery were a perfect power source and behaved linearly, the discharge time could be calculated according to the in-and-out current. “What has been put in can be taken out in the same form over time” is the argument, and in our example a one-hour charge at 5A should enable a one-hour discharge at 5A, or a 5-hour discharge at 1A. However, intrinsic losses impede the ideal working of a battery, and the relative discharge time becomes shorter when increasing the load. High discharge currents make the battery less efficient.

The efficiency factor of a discharging battery is expressed in the Peukert Law. W. Peukert, a German scientist (1897), was aware of this loss and devised a formula that expresses the loss at a given discharge rate in numbers. Because of sluggish behavior of lead acid, the Peukert numbers apply mostly to this battery chemistry and help in calculating the capacity when loaded at various discharge rates.

The Peukert Law takes into account the internal resistance and recovery rate of a battery. A value close to one (1) indicates a well-performing battery with good efficiency and minimal loss; a higher number reflects a less efficient battery. The Peukert Law of a battery is exponentialand the readings for lead acid are between 1.3 and 1.4. Nickel-based batteries have low numbers and lithium-ion is even better. Figure 5 illustrates the available capacity as a function of ampere drawn with different Peukert ratings.

 Figure 5: Available capacity of a lead acid battery at Peukert numbers of 1.08–1.50 A value close to 1 has the smallest losses; higher numbers deliver lower capacities. Source: von Wentzel (2008)

The lead acid battery prefers intermittent loads to a continuous heavy discharge. The rest periods allow the battery to recompose the chemical reaction and prevent exhaustion. This is why lead acid performs well in a starter application with brief 300A cranking loads and plenty of time to recharge in between. All batteries require recovery, and with nickel- and lithium-based system, the electrochemical reaction is much faster than with lead acid.