Calculating the Battery Runtime
If the battery were a perfect power source and behaved linearly, the discharge time could be calculated according to the inandout flowing currents. “What is put in should be available as an output in the same amount” goes the argument, and “a onehour charge at 5A should deliver a onehour discharge at 5A, or a 5hour discharge at 1A." This is not possible because of intrinsic losses. The output is always less than what has been put in, and the losses escalate with increasing load. High discharge currents make the battery less efficient. To learn about the coulomb counter, see Inner Workings of a Smart Battery.
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 wellperforming 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. Nickelbased batteries have low numbers and lithiumion is even better. Figure 1 illustrates the available capacity as a function of ampere drawn with different Peukert ratings.

Figure 1: Available capacity of a lead acid battery at Peukert numbers
A value close to 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 lithiumbased system, the electrochemical reaction is much faster than with lead acid. Read more about the Basics About Charging.
The runtime of batteries in portable devices relates to the specific energy marked in Ah (mAh in personal devices). Ah as a performance indicator works best at low discharge currents. At higher loads, the internal resistance begins to play a larger role in the ability to deliver power. Resistance acts as the “gatekeeper.” Energy in Ah presents the available storage capacity of a battery and is responsible for the runtime; power governs the load current. These two attributes are critical in digital devices that require long runtimes and must deliver highcurrent pulses.
Ah alone is not a reliable runtime indicator and the relationship between capacity and the ability to deliver current can best be illustrated with the Ragone Chart. Named after David V. Ragone, the Ragone chart evaluates batteries not on energy alone but also represents power.
Figure 2 illustrates the Ragone chart on a digital camera that is powered by an Alkaline, Lithium (LiFeS2) or NiMH battery drawing 1.3W. (1.3W at 3V draws 433mA.) The horizontal axis displays energy in Watt/hours and the vertical axis displays power in Watts. The scale is logarithmic to allow a wide selection of battery sizes.

Figure 2: Ragone chart illustrates battery performance with various load conditions. Digital camera loads NiMH, LiFeS2 and Alkaline with 1.3W pulses according to ANSI C18.1 (dotted line). The results are:
 Li FeS2 690 pluses
Energy = Capacity x V Courtesy of Exponent 
The dotted line represents the power demand of the digital camera. All three batteries have similar Ah rating: NiMH delivers the highest power but has the lowest specific energy. This battery works well at high loads such as power tools. The Lithium LiFeS2 offers the highest specific energy but has moderate loading conditions. Digital cameras and personal medical instruments suit the system well. Alkaline offers an economic solution for lower current drains such as flashlights, remote controls and wall clocks, but a digital camera is stretching the capability of Alkaline. Read more about the Choices of Primary Batteries.
Reference
Presentation by Quinn Horn, Ph.D., P.E. Exponent, Inc. Medical Device & Manufacturing (MD&M) West, Anaheim, CA, 15 February 2012
Comments
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.
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
Is there any empirical formula to calculate battery DEPTH of Discharge for a given lifetime?
Hi,
Can somebody tell me how to model peukart law im modelling please?
Thanks alot
Peukart (title and sidebar menu) or Peukert (article)?
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 Liion cell for paralleling by our self ?
can anyone answer question number one from pier ? can peukerts equation be used for lithium type batteries?
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. Nickelbased batteries have low numbers and lithiumion is even better.” Missing space in there. Different chemistries have different values.
Soldering directly onto a Liion cell is not recommended. They can explode.
thanks ian. i saw that on the second read thru. i have never been a good student
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
Please infrom me how to calculate the time for discharging a traction battery with 560Ah & 420
how to calculate the charging and discharging time of Liion battery with specification of 100 Ah, 12 V.and applying 2 A constant current.?????
Yes Peukert’s Equation can be used for Lithium batteries. Their exponents are closer to 1.0 than lead acid Batteries.
How exactly do you define one cycle in a LiIon cell ? I find cycle count in Lenovo thinkpads but not sure as to how they compute it !!!
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
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
My Dear friends;
I designed a solar system in which appliance load is 500 Watt and appliance watt per day is 1500.
So I used 150watt 2 solar panel, 24volt and 12 A Solar charge controller, 2 batteries of 125Ah each.
Normally 7 hours sunlight.
My problem is that I want to calculate in how much time period batteries will again recharge.
Please help me in this problem
Thanks
my cell battry is bulging , it’s a liion, and i was wondering how i make it safe(er) to dispose of, can you help with that? the phone says “use authentic battery” so i’m afraid it might explode,
im using 12v 7.4Ah SLA battery x 3 pcs.. the load 19w 12v dc.. By calculation :
(12V x 7.2Ah )/ 19W = 4.5 hour x 3 pcs battery in parallel connection can i get 13 hour ??
but by actual run i got 57 hour only. i’m i using wrong battery or my calculation wrong..
7Ah is the capacity at a rate that flattens the battery in 20 hours. Your load is much higher than that so you need to take the Peukert effect into consideration. SLA batteries have quite high Peukert effect. The Peukert calculation is much more complicated than what you have done, but you could use the top graph instead to make it easier.
If inverter efficiency is around 80%, current from 12 volts for 19W load is approx. 2 amps.
When 3 batteries are in parallel, You have a 7.2 x 3 i.e.21.6AH (@ 20 Hr. rate.)
Using Peukert equation calculation, you should get 8Hr. 30Min. approx. This makes the battery fully discharged. For better life, batteries are not discharged beyond 80%. So inverters’ cut off volts are adjusted to higher value. Probably, the inverter efficiency may be even less than 80%. If you find exact current from the batteries, Peukert formula will give you quite accurate duration. There is no much complication.
If possible, kindly share the info on making an
SMPS charger of 4000 Watts and above
Zahid wrote:
im using 12v 7.4Ah SLA battery x 3 pcs.. the load 19w 12v dc.. By calculation :
(12V x 7.2Ah )/ 19W = 4.5 hour x 3 pcs battery in parallel connection can i get 13 hour ??
but by actual run i got 57 hour only. i’m i using wrong battery or my calculation wrong..
———————————————————————————
The Peukert effect. Your 7ah battery is too small. The rate in the above chart for 120Ah compared to you 7Ah*3=21Ah battery. Lead acid is 1.3 to 1.4. Your is 19w /12v = 1.58 Amp draw. 120/21 for battery in above chart *1.58 = proportional equivalent~ 9.0 amp so look the 9 amp and it gives capacity reduction of about 50% in the Peukert chart so you will get 20 hours run time down to 10 hours just from that, and even worst as your batteries age. SLA rating is only good for long slow discharge 20AH is 1 Amp for 20 Hours. Take 10x times (10Amps) that out in 2 Hours you get only roughly half to 1/3 that amount if your lucky. That is why my project ebike will have NiMH battery instead of SLA. The higher cost 5x is justified in lifetime use and performance. LiPo4 is still too much expense and funny picky charging/discharge/ quality.
Sorry correction, your example only 13 hours use * 50% = 6.5 hours as you discovered, I was using 20 hour run for 10 hours use.
SLA rating is only for low current draw. Peukert charts are very much relevant. NiMH is twice that of SLA in rating for real world application using any kind of Medium to Heavy use draw. Medium use is >10% current rating of battery capacity. Low is less than 1<%.
Your example of three 7aH batery for 21 Ah array pulling anything more than 23 Amps is going to cut your real amp hour capacity to 50% for SLA. You really need to buy 10x more battery or get NiMH—though NiMH self discharge over time quickly over several days in a solar array.
SIR PLEASE TELL ME HOW THE HRD END CRURRENT CALCULATE
Dear sir
I have One 3.7V,600mAh Liion battery that battery have DoD is 27% but i want to DoD 70% above that. So what is Procedure for this any circuit have built or other..Please Suggest me.
Give me process for improve battery DoD.
i want to know about the normal c20 and c10 rated battery and how to calculate, how much kWh(unit) can be obtained form particular battery like C10 26Ah dc12V battery how much kWh can be obtained at 12V and for C20 Rating Battery.
how can i calculate 50%volt shutdown on a 24vdc/1400amps inverter batterry.
NB: Inverter capacity is 30kva
i Have 24 numbers of battery, each having 2V,600Ah connected in series with only 400 Watt load that means 48V of my system So can you help me how to calculate the back up time of this system.
battery full lod discharging chart