Peukert Law and Battery Runtime Formulas

Peukert law formulas: the runtime of a battery at a given current, the capacity actually delivered and the effect of the Peukert exponent.

The formulas

C is the rated capacity in ampere-hours at the rated discharge time H in hours (for example 100 Ah at 20 hours), I the discharge current in amperes and k the Peukert exponent, which is 1 for an ideal battery and larger for a real one (about 1.1 to 1.3 for many lead-acid batteries, and close to 1.05 for lithium). A higher current than the rated one gives a shorter runtime than C / I and less capacity. The exponent is from the data sheet or from two discharge tests and the value here is an example. The law ignores the temperature and the ageing, and it does not hold at very low currents.

Worked example: 100 Ah at 20 hours, 20 A load

k = 1.2. The rated current is 100 / 20 = 5 A.

1. I × H = 20 × 20 = 400 A·h and C / (I × H) = 0.25
2. t = 20 × 0.25^1.2 = 3.789 h
3. Capacity delivered = 20 × 3.789 = 75.79 Ah, against 100 Ah rated

Runtime at 20 A for different exponents

Frequently asked questions

Why does a battery give less at a high current?

The internal resistance and the slow chemistry mean that less of the active material can be used when the current is high.

What is a typical exponent?

About 1.1 to 1.3 for lead-acid, and lower for lithium. Check the data sheet, because it differs between makes.

Does the law work for every current?

No. It is an empirical fit between the rated current and a few times that value, and it is poor at very low or very high currents.

How does this connect to the battery sizing?

The simple sizing divides the capacity by the current. Peukert shows that for high currents you need a larger battery or a larger discharge-rate capacity from the data sheet.

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