## 10. Battery capacity and Peukert exponent

Battery capacity is expressed in Amp hour (Ah) and indicates how much current a battery can supply over time. For example, if a 100Ah battery is being discharged with a constant current of 5A, the battery will be totally discharged in 20 hours.

The rate at which a battery is being discharged is expressed as the C rating. The C rating indicates how many hours a battery with a given capacity will last. 1C is the 1h rate and means that the discharge current will discharge the entire battery in 1 hour. For a battery with a capacity of 100Ah, this equates to a discharge current of 100A. A 5C rate for this battery would be 500A for 12 minutes (1/5 hours), and a C5 rate would be 20A for 5 hours.

### Tip

There are two ways of expressing the C rating of a battery. Either with a number before the C or with a number after the C.

For example:

5C is the same as C0.2

1C is the same as C1

0.2C is the same as C5

The capacity of a battery depends on the rate of discharge. The faster the rate of discharge, the less capacity will be available. The relation between slow or fast discharge can be calculated by Peukert’s law and is expressed by the Peukert exponent. Some battery chemistries suffer more from this phenomenon than others. Lead acid are more affected by this than lithium batteries are. The battery monitor takes this phenomenon into account with Peukert exponent.

**Discharge rate example**

A lead acid battery is rated at 100Ah at C20, this means that this battery can deliver a total current of 100A over 20 hours at a rate of 5A per hour. C20 = 100Ah (5 x 20 = 100).

When the same 100Ah battery is discharged completely in two hours, its capacity is greatly reduced. Because of the higher rate of discharge, it may only give C2 = 56Ah.

**Peukert’s formula**

The value which can be adjusted in Peukert’s formula is the exponent n: see the formula below.

In the battery monitor the Peukert exponent can be adjusted from 1.00 to 1.50. The higher the Peukert exponent the faster the effective capacity ‘shrinks’ with increasing discharge rate. An ideal (theoretical) battery has a Peukert exponent of 1.00 and has a fixed capacity regardless of the size of the discharge current. The default setting in the battery monitor for the Peukert exponent is 1.25. This is an acceptable average value for most lead acid batteries.

Peukert’s equation is stated below:

*Cp = I ^{n} x t * Where Peukert's exponent n is:

To calculate the Peukert exponent you will need two rated battery capacities. This is usually the 20h discharge rate and the 5h rate, but can also be the 10h and 5h, or the 20h and the 10h rate. Ideally use a low discharge rating together with a substantially higher rating. Battery capacity ratings can be found in the battery datasheet. If in doubt contact your battery supplier.

The C5 rating is 75Ah. The t1 rating is 5h and I1 is calculated: The C20 rating is 100Ah. The t2 rating is 20h and I2 is calculated: The Peukert exponent is: A Peukert calculator is available at http://www.victronenergy.com/support-and-downloads/software#peukert-calculator. |

Please note that the Peukert exponent is no more than a rough approximation of reality. In case of very high currents, the battery will give even less capacity than predicted by a fixed exponent. We do not recommend changing the default value in the battery monitor, except in the case of lithium batteries.