**Peukert's Equation**

Mr Peukert first devised a formula that showed numerically how discharging at higher rates actually removes more power (see below before thinking this is wrong) from the battery than a simple calculation would show it to do. For instance discharging at 10 amps does not remove twice as much power as discharging at 5 amps. It removes slightly more. Therefore a 100 amp hour battery (at the 20hr rating) could provide 5 amps for 20 hours, but it could not provide 10 amps for 10 hours. The available time would actually be slightly less.

Mr Peukert wrote down a formula for describing how much less time would be available. Please note that in the first paragraph I say "Mr Peukert first devised a formula for....". This is because he is generally regarded as being the man who first discovered the phenomenon. This is incorrect. The effect had been known for many years beforehand and was first noted by a certain Mr Schroder several years before Peukert devised his formula. Mr Peukert simply quantified it in a way that had never been done before. However the effect is now known as Peukert's effect, the formula for calculating it is known as Peukert's equation, and the important number, unique to each battery type, that is put into the equation in order to perform the calculation, is known as Peukert's exponent. Note that Peukert's exponent changes as the battery ages.

Please note that there are two ways of looking at this effect. We could say that discharging at higher currents reduces the total available power that can be got out of a battery. So a 100 amp hour battery might become say an 80 amp hour battery at higher discharge rates. This is technically the correct way of looking at it.

However it is easier to assume that the total available power in the battery remains identical whatever the discharge rate. But that discharging at higher rates removes more amp hours. This is the method of explanation used throughout this website and on the Peukert calculator spreadsheet.

Note that whichever method is used, the figures and effect remain identical in both cases. It's just that we consider the second method to be easier to understand and "get your head round".

Peukert's equation can be found all over place. On the internet, in battery data sheets and documents, in battery sales literature, in battery monitoring equipment manuals etc. It is usually written as I^{n} T = C

Where:

I = the discharge current in amps

T = the time in hours

C = the capacity of the battery in amp hours

n = Peukert's exponent for that particular battery type

The idea is that the time (T) that a certain battery can run a certain load for can be calculated by rearranging the equation to read T = C/I^{n}

Please note that this equation, seen all over the place, is wrong. Actually, I'd better rephrase that. The equation is not wrong. But the way people attempt to apply it to the battery capacity is wrong.