Calculating the Battery Runtime (Peukert Law)

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.
 

Available capacity of a lead acid battery at Peukert numbers of 1.08–1.50

 

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.

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Comments

On May 7, 2011 at 9:03pm
HITESH PATEL wrote:

battery full lod discharging chart

On May 25, 2011 at 12:17pm
Samuel Maher Youssef wrote:

please i want to install solar system,and i will use flood deep cycle battery,
i will use four battery 12 volt DC, can i use two battery each other 24 volt and what advantage to use 4 battery.
thanks a lot.

On June 6, 2011 at 10:06pm
Susanta Kumar Sahu wrote:

Dear Sir/Madam,
I am Susanta Kumar Sahu to inform you that i have no knowledge about battery discharge (EX: 180AH battery, connecting with load that depends on customer how much it give back up like this ).Can you tell BACK UP concept of all bettery?

Thank You.
Susanta Kumar Sahu

On June 9, 2011 at 11:42pm
Gaurav wrote:

Is there any empirical formula to calculate battery DEPTH of Discharge for a given lifetime?

On June 20, 2011 at 4:39am
CBT wrote:

Hi,
Can somebody tell me how to model peukart law im modelling please?
Thanks alot

On August 27, 2011 at 4:47am
Ian wrote:

Peukart (title and sidebar menu) or Peukert (article)?

On November 4, 2011 at 3:27am
Pier wrote:

1) Can Peukert’s constant be used across all battery chemistry’s ?

2) Is there any equation where we can determine the remaining time in a battery upon  
  knowing the discharge voltage during operation?

3) What exactly do you mean by efficiency of the battery ?

4) What is the effect of soldering on a Li-ion cell for paralleling by our self ?

On November 17, 2011 at 9:26pm
gary pione wrote:

can anyone answer question number one from pier ? can peukerts equation be used for lithium type batteries?

On November 17, 2011 at 9:33pm
Ian wrote:

You may have missed this, gary: “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.” Missing space in there. Different chemistries have different values.

Soldering directly onto a Li-ion cell is not recommended. They can explode.

On November 17, 2011 at 9:55pm
gary pione wrote:

thanks ian. i saw that on the second read thru. i have never been a good student

On November 25, 2011 at 9:53am
TAHIR HUSSAIN wrote:

Dear Sir,
I live in Pakistan and i am working in lead acid battery company.
My question is, How can i calculate Peukert’s number by theoretical or practical and each battery (size wise) has a different peukert number.

Regards,
TAHIR

On January 8, 2012 at 9:17pm
Terence Cheong wrote:

Please infrom me how to calculate the time for discharging a traction battery with 560Ah & 420

On February 8, 2012 at 4:30am
Komal wrote:

how to calculate the charging and discharging time of Li-ion battery with specification of 100 Ah, 12 V.and applying 2 A constant current.?????

On February 23, 2012 at 4:41am
Sheldon Patnett wrote:

Yes Peukert’s Equation can be used for Lithium batteries. Their exponents are closer to 1.0 than lead acid Batteries.

On February 23, 2012 at 9:42pm
Pier wrote:

How exactly do you define one cycle in a Li-Ion cell ? I find cycle count in Lenovo thinkpads but not sure as to how they compute it !!!

On May 8, 2012 at 6:13am
Syed wrote:

Hello,
How to calculate the charging and dischargin time of a Li- ion polymer battery of capacity 1230mAh, 3.7V applying 250mA constant current?
Thank You

On May 8, 2012 at 6:19am
Syed wrote:

Hello,
How do we calculate the no. of hours a battery can provide on continuous discharge of 250mA of capacity 1320mAh?
Also providing the voltage the battery can provide after every hour of discharge of 250mA would be good.
Note:
Nominal voltage of the battery is 3.7V.
max operating range is 2.75V to 4.2V.
max continuous discharge current is 1000mA
internal resistance is 150milli ohm
Thanks