# Calculating your Required Battery Capacity

## Factors

The primary and certainly the most important factor is the load you anticipate your batteries will have to store.  Using the watts of load you calculated for your daily electrical loads, convert this into the measure of how storage batteries are measured.  Storage batteries are measured in Ampere hours (AHr.).

### Ampere Hours

Using the example of 157.42857 Watt hours per day from our getting started page and assuming the battery array will be 12 volts you will arrive at 13.1 Ampere hours required.  The math is the same as before, this time we divide Watt hours by the battery voltage ( 157.42857 ÷ 12V = 13.1 Ampere hours)

Each time you convert electricity as from solar voltaic panels to battery voltage and then from electricity to chemical storage (battery) and transport low voltage electricity over connections and through wire you lose some power.  Using experience, a bit of math and industry hearsay we use a 20% loss factor.  This loss factor must be taken into account within your battery storage.  We call this portion of the calculation the Loaded Daily AHr required. If we use 20% we now require 15.7 AHr ( 13.1 AHr X (1+20%) = 15.7 AHr.)

### Reserve Days

All would be fine if the sun were guaranteed to shine equally every day.  We now need to factor how many days of capacity you want your batteries to hold up until the sun comes out from the clouds or you need to turn on your generator.  Lets assume you want 2 and a half days of reserve time. This will bring your requirement up to 39.4 Ampere hours of battery (15.7 Ampere hours X 2.5 days = 39.4 Ampere hours) of battery with reserve calculated.

### Battery Aging

Your batteries if well taken care of will have many years of life.  However, batteries will age over time and lose some of their potential.  Because a battery array will work at the level of the weakest battery placing new batteries into an old battery array is a waste (see adding batteries ).  We use best to account for the loss now as it also helps you keep the DOD (soon! read on to the next point!) down.  It is not unreasonable to use a factor of 20% to account for battery aging so your battery requirement now comes to 47.2 AHr. (39.4 AHr X (1+20%) = 47.2)

### Battery Temperature

Because they are a based on an electro chemical process batteries lose power in the cold. If you are going to use your system during the winter or shoulder seasons and store them outside or in an unheated area, your batteries will need to be de-rated.  If you use your batteries all year, this is an important factor.  Most battery manufacturers supply de-rating tables based on battery temperature.  We'll leave this factor out of our example for now because many of you use your systems only in the summer and shoulder seasons (see temperature de-rating).

### Depth of Discharge (DOD) this is very important!

DOD a measure of how deeply a battery is discharged. When a battery is 100% full, the DOD is 0%. Ampere hours removed from a fully charged cell or battery, is expressed as a percentage of rated capacity. For example if 25 Ah are removed from a 100 Ah battery, it's depth of discharge is 25% and the battery is at a 75% state of charge.

OK, with the definition taken care of, why is DOD an important part of calculating battery capacity?   First another definition:

A Cycle is a period of discharge and recharge is called one cycle. A battery cycle is one complete discharge and recharge cycle. It is usually considered to be discharging from 100% to 20% DOD, and then back to 100%. One of a Battery's performance indicators is the measure of the expected number of cycles it may deliver.

The greater the average depth-of-discharge, the shorter the cycle life. Be careful when looking at ratings that list how many cycles a battery is rated for unless it also states how far down it is being discharged. A battery that is rated for a 20 year life expectancy if discharged by only 15% may have a 5 year life expectancy if discharged to 50%.  Typically batteries ratings are in AHr are published  to 100% discharge.  (Careful again! The longer the discharge time e.g. 100 hr the more Ampere hours that can be squeezed from a battery.  Ratings should be compared at 20 hr discharge rate for off-grid purposes.)

Here's the crunch; If say a 100 AHr battery that is discharged to 100% will last 100 cycles, however, it will last 400 cycles if discharged to 50% and longer yet if discharged to 35%.  Before we go further with your battery sizing lets do the math for DOD.
100 cycles at 100% = 10,000 AHr discharge over the life of the battery. (100 cycles of 100AHr = 10,000AHr.)
400 cycles at 50% = 20,000 AHr discharge over the life of the battery (400 cycles of 50AHr = 20,000 AHr.)
At 400 cycles the battery lasts 4X as long an produces 2X as much power over its life!

back to battery sizing...

Size Calculation at 50% DOD

At 50% discharge the battery size required is 94.5 AHr. (47.2 AHr ÷ 50% = 94.5 Ahr.)

### CALCULATION SUMMARY

We started off with a daily usage of 157 Watts or 13.1 AHr @ 12V and ended up with a requirement of 94.5 AHr. capacity.  I hope by this you appreciate how many systems are sized to people's pocket books not to the system configuration requirement.

A Cynical Aside: Too many clerks tend to sell what a client is be able to afford, knowing full well you'll be back later with your wallet open to buy more.  It's easy to blame client electrical usage, the weather or any number of things, then sell you more.  ...or they just don't know.  Remember, you cannot add new or different batteries to you existing battery bank.  The new ones will fail before your existing batteries.

## Saving you from Battery Math

We have developed a MS EXCEL spreadsheet to assist our Canadian clients with these calculations.  Contact us by email and we'll help you with your calculations.

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