Peukert's law — why a battery delivers less capacity at high discharge current than the Ah rating suggests

The guide on capacity testing and internal resistance of stationary batteries (IEEE 1188) covers how the condition of a stationary lead-acid battery is periodically tested. This article covers a fundamental property that underlies that capacity test: why a battery's rated Ah capacity does not scale linearly with discharge current, regardless of the battery's condition.

The rated Ah value applies only at one specific discharge current

A battery with a rated capacity of "100 Ah" delivers that 100 Ah only at the specific discharge duration for which the manufacturer specified that value — for example the 10-hour discharge (C10, discharged at 10 A for 10 hours) or the 20-hour discharge (C20). It is a common, intuitively understandable but incorrect assumption that the same 100 Ah can simply be divided by a different, higher discharge current to calculate the remaining runtime — a battery rated "100 Ah at C10" discharged at 100 A does not deliver its full 100 Ah over 1 hour.

Peukert's law

German scientist Wilhelm Peukert described an empirical relationship in 1897 between discharge current and the actually available capacity of a lead-acid cell, summarised in Peukert's equation:

t = Cp / Ik

where t is the discharge time, I the discharge current, Cp the Peukert capacity (a cell constant) and k the Peukert exponent — an empirical constant that differs by battery type and quality. For an ideal, hypothetical battery with no rate-dependence at all, k would equal 1 (capacity would then truly be independent of discharge current). In practice, k for lead-acid batteries is typically between 1.1 and 1.3 for high-quality VRLA cells, and can rise to 1.4-1.6 for older or lower-quality lead-acid cells — the higher k, the more sharply actual capacity falls off as discharge current increases.

Note: the Peukert exponent is an empirical fitting parameter, not a universal physical constant — it differs by cell chemistry, manufacturer and even production batch, and is typically derived by the manufacturer from multiple discharge tests at different currents, not from a single measurement.

Why this is more than an arithmetic curiosity

The practical consequence of Peukert's law is that the actual runtime of a battery at high discharge current — such as during a brief, heavy UPS load or an emergency-lighting installation that suddenly has to burn at full output — is shorter than a simple Ah division would suggest, and that this discrepancy grows larger the further the discharge current lies above the reference current (C10, C20) for which the rated capacity was specified. For sizing calculations of a standby battery bank, standards such as IEEE 485 (sizing of stationary lead-acid batteries) therefore typically do not use Peukert's equation directly, but the manufacturer's published discharge-time tables — a set of actually measured capacity values at different discharge currents — precisely because those tables already capture the non-linear reality without the installer having to estimate the Peukert exponent themselves.

Two separate corrections: rate effect and temperature effect

Besides the rate-dependent Peukert effect, the available capacity of a lead-acid battery is also affected by ambient temperature — a colder battery delivers less capacity than at the reference temperature (typically 20-25°C) for which the rated value applies. This temperature effect is a separate correction, with its own correction factors in manufacturer documentation (and in standards such as IEC 60896-11 for VRLA cells), and must not be merged with the Peukert effect: correctly sizing a standby battery bank must apply both corrections separately — for the actual discharge current and for the lowest expected ambient temperature — rather than accounting for only one of the two.

Lithium-ion: considerably less rate-dependent

One of the practical advantages of lithium-ion cells over lead-acid in stationary standby applications — besides the topics covered in the [guide on cell balancing (BMS) for lithium batteries](/guides/nen-3140/bms-celbalancering-actief-passief-lithium-batterij) and the [guide on thermal runaway and fire safety in lithium BESS](/guides/nen-3140/lithium-ion-bess-thermal-runaway-brandveiligheid) — is that the Peukert exponent of lithium-ion chemistry lies much closer to 1 than lead-acid. The available capacity of a lithium-ion cell therefore falls off much less steeply at increasing discharge current than a comparably rated lead-acid cell — one of the reasons lithium-ion performs relatively better than the nominal Ah comparison alone would suggest in applications with a high, brief discharge current (such as some UPS applications).

Practical relevance

When sizing or assessing a stationary lead-acid battery bank for UPS, emergency-lighting or standby-power applications, the actually expected discharge current (and duration) must be compared with the manufacturer's published discharge-time table for exactly that current — not with a linear extrapolation of the rated Ah value at C10 or C20 — and a separate correction must be applied for the lowest expected operating temperature.

Common mistakes

Dividing the rated Ah capacity linearly by the actual discharge current to estimate expected runtime, instead of using the manufacturer's discharge-time table for that specific current.
Confusing or merging the Peukert effect and the temperature effect into a single correction factor, when they are two independent physical mechanisms with their own correction values.
Assuming the Peukert exponent is the same for every lead-acid battery — the value differs by manufacturer and cell chemistry and must be taken from manufacturer data, not assumed.
Applying lead-acid's rate-dependence unchanged to lithium-ion cells when comparing both technologies for a standby-power application, when lithium-ion is in fact considerably less sensitive to it.