The formula
capacity = daily use × days ÷ (depth of discharge × round-trip efficiency)
Where it comes from
The capacity on the label is not the capacity you can use. A lead-acid battery cannot be discharged past about half without shortening its life a great deal, and lithium reaches 90 %. Add the round-trip efficiency and the same requirement needs more than twice as much lead as lithium, so comparing two batteries by their nominal kilowatt hours leads straight to the wrong choice.
How to work it out by hand
- Multiply your daily consumption by the days of autonomy you want
- Divide by the depth of discharge of that chemistry
- Divide by the round-trip efficiency
- For amp hours, multiply by a thousand and divide by the system voltage
What is worth knowing
The figure that really compares two chemistries is the cost per kilowatt hour that passes through the battery over its life, and there the order reverses: lithium costs considerably more per kilowatt hour installed and considerably less per kilowatt hour stored, because it survives many more cycles and uses more of each one. Life is measured in cycles rather than years, too: a battery cycled once a day lasts its cycle count divided by 365, and one cycled twice a day lasts half that.