Peukert’s Law and Exponent Explained

What is Peukert’s Law

Battery capacity refers to the amount of energy that the battery can store. Battery manufacturers often use specifications known as Amp Hours  and Reserve Capacity to provide an indication of what a battery’s storage capacity is.

However, the problem with quantifying the storage capacity of a lead acid battery is that the amount of energy stored is dependent on the battery’s discharge rate. The greater the discharge rate, the lower the capacity.

This phenomenon is well documented and is often know as Peukert’s Law. Peukert, a German scientist, first presented this law in 1897 and provided an equation that helps to tell us what a battery capacity is based on the rate that it is being discharged.

The Equation for Peukert’s Law

You’ll see the formula for Peukert’s law expressed a few different ways, but the one battery users are most interested in, is the one that tells them how long a battery will last under particular load (or current draw).

That equation is this…

  • t - Time in hours. Its the time that the battery will last given a particular rate of discharge (the current).
  • H – The discharge time in hours that the Amp Hour specification is based on. For example, if you had a 100 Amp Hour battery at a 20 hour discharge rate, H would equal 20.
  • C – The battery capacity in Amp Hours based on the specified discharge time. For a 100 Amp Hour battery, this would be
  • I – This is the current that we’re solving for. For example, if we wanted to know how long a battery would last while drawing 7.5 amps, we would enter it here.
  • k – the Peukert Exponent. Every battery has its own Peukert exponent. Sometimes the manufacturer will provide it and other times we may need to figure it out.

 

Peukert Example on a 100 Amp Hour Battery

Let’s consider a flooded wet cell lead acid battery that has 20 hour discharge rating of 100 amp hours.

Based on this specification, we know that this battery will supply 5 amps for 20 hours while maintaining a voltage that is above 10.5 volts.

If we were to increased the discharge rate to 10 amps, we might erroneously concluded that the battery will last for 10 hours.

Using the equation for Peukert’s law as shown below, we find that the battery will last significantly less than 10 hours.

NOTE – In order to solve this equation we’re going to need to know what the Peukert’s exponent is. For a flooded battery, its typically going to be somewhere between 1.2 and 1.6. For this example, we’re going to use 1.4.

 

What is Peukert Exponent for Your Particular Battery

It’s different from battery to battery. Worse, many manufacturers do not readily publish a Peukert’s exponent. That said, there are some general ranges for the different kinds of lead acid batteries that can be used for estimation purposes.

  • AGM batteries range between 1.05 and 1.15
  • Gel batteries range between 1.1 and 1.25
  • Flooded batteries range between 1.2 and 1.6

If more accurate estimates are required, it is possible to calculate the Peukert exponent from most battery manufacturer specifications. Stay tuned for another article.

Peukerts Law Limitations

Peukert’s law is a valuable tool for estimation. However, it has limitations. Among them are…

  • The affect that temperature has on batteries is not included in the equation.
  • Battery age is not considered. The Peukert exponent increases with battery age.
  • If you’re calculating for a low discharge rate, the equation does not account for the fact that each battery has a self discharge rate.

All that said, in terms of estimation, Peukert’s law gets us much closer to estimating real world performance of a battery than simple extrapolations of the amp hour rating.