# Peukert's law

## Description

Peukert’s law, presented by the German scientist Wilhelm Peukert in 1897, expresses the capacity of a battery in terms of the rate at which it is discharged. As the rate increases, the battery’s available capacity decreases.

Manufacturers rate the capacity of a battery with reference to a discharge time. For example, a battery might be rated at 100 A·h when discharged at a rate that will fully discharge the battery in 20 hours. In this example, the discharge current would be 5 amperes. If the battery is discharged in a shorter time, with a higher current, the delivered capacity is less. Peukert’s law describes a power relationship between the discharge current (normalized to some base rated current) and delivered capacity (normalized to the rated capacity) over some specified range of discharge currents. If the exponent constant k was one, the delivered capacity would be independent of the current. For a lead–acid battery, however, the value of k is typically between 1.1 and 1.3. It generally ranges from 1.05 to 1.15 for VRSLAB AGM batteries, from 1.1 to 1.25 for gel, and from 1.2 to 1.6 for flooded batteries. The Peukert constant varies according to the age of the battery, generally increasing with age. Application at low discharge rates must take into account the battery self-discharge current. At very high currents, practical batteries will give even less capacity than predicted from a fixed exponent. The equation does not account for the effect of temperature on battery capacity.

Related formulas## Variables

C_{p} | capacity at a one-ampere discharge rate (A*h) |

I | actual discharge current (i.e. current drawn from a load) (A) |

k | Peukert constant (dimensionless) |

t | actual time to discharge the battery (hour) |