Pull more current out of a battery and you get back proportionally less capacity than the nameplate promises. That’s not a flaw in any particular cell. It’s a general property of how batteries discharge, and it was pinned down mathematically well over a century before lithium-ion existed. Peukert’s law is the equation everyone reaches for to correct a rated amp-hour figure for the discharge rate actually being used, and despite being built entirely on lead-acid data from the 1890s, it’s still the reference point every more sophisticated capacity model gets measured against.
Quick facts
- Origin: Wilhelm Peukert, professor of electrical engineering at TU Braunschweig, published the relationship in 1897 based on constant-current discharge tests on lead-acid cells [1][2]
- Form: Cp=In⋅t, where n (the Peukert exponent) is greater than 1 for a real cell and equal to 1 for a theoretical, rate-independent one [3]
- Typical exponent: ~1.05–1.15 for AGM, ~1.1–1.25 for gel, ~1.2–1.6 for flooded lead-acid, ~1.0–1.05 for lithium-ion [3][4]
- Known limits: ignores temperature, ignores self-discharge, and the exponent itself drifts upward as a cell ages [3][5]
An equation built on a century-old workbench, not a theory of what’s happening inside the cell
Wilhelm Peukert was an engineer from Bohemia who ended up running the electrical engineering laboratory at what’s now TU Braunschweig from 1890 onward [2]. In 1897 he published a paper in Elektrotechnische Zeitschrift titled, translated, “On the dependency of capacity on discharge current strength in lead-acid accumulators” [1]. It’s exactly what it sounds like: a write-up of systematic discharge testing on lead-acid cells, from which Peukert extracted a power-law relationship between discharge current and the time to fully discharge the battery.
Worth being upfront about what this is and isn’t. It’s a curve fit to observed behaviour, not a derivation from first-principles electrochemistry: Peukert wasn’t modelling ion diffusion or reaction kinetics, he was fitting a line to a log-log plot of his test data and finding that it worked remarkably well across a useful range of discharge rates. That’s exactly why it’s held up: it doesn’t need anyone to agree on the underlying mechanism to be useful, and lead-acid chemistry hasn’t changed enough since 1897 to invalidate the fit.
The equation, and what the exponent is doing
In its simplest form, Peukert’s law is written:
where Cp is the theoretical capacity at a 1-amp discharge rate (in amp-hours), I is the actual discharge current, t is the time to full discharge, and n is the Peukert exponent [3]. That “capacity at 1 amp” figure isn’t something manufacturers publish, so in practice the equation gets rearranged around whatever rated capacity and rated discharge time are on the datasheet:
where H is the rated discharge time in hours and C is the rated capacity at that rate. Take a lead-acid battery rated 100 Ah at the 20-hour rate (i.e., a 5 A discharge current) with a Peukert exponent of 1.2. Push 10 A through it instead, and the equation gives a runtime of roughly 8.7 hours, meaning it delivers about 87 Ah, not 100 Ah [3]. Double the current, lose more than the proportional share of capacity: that’s the exponent doing its job. Set n to exactly 1 and the equation collapses to a battery that behaves like an ideal current source, delivering the same total amp-hours no matter how hard you push it. Real cells never get there; n is always greater than 1, and how much greater tells you how rate-sensitive that particular chemistry and construction is.
The exponent isn’t one number: it depends on chemistry, and it moves
Because n is fit to test data rather than derived from theory, every chemistry and even every construction within a chemistry gets its own value. Lead-acid, which is what the whole thing was built around, spans a surprisingly wide range depending on plate design: sealed AGM cells typically land around 1.05–1.15, gel cells around 1.1–1.25, and flooded cells anywhere from 1.2 up to 1.6 [3][4]. Lithium-ion, by contrast, usually sits much closer to the ideal case: commonly quoted as 1.0 to 1.05, or up to about 1.1 across the 0.2C–2C range some manufacturers test at [4], which is a large part of why lithium packs feel so much less “rate-punished” than a lead-acid battery of similar nominal capacity.
The exponent isn’t fixed for a given cell over its life, either. It generally climbs as the battery ages, meaning an old cell loses proportionally more capacity at a given discharge rate than the same cell did when new [3][5]. It also worsens in the cold: colder electrolyte slows the transport processes the exponent is implicitly capturing, so the same cell tested at 0°C will show a less favourable Peukert exponent than it does at 25°C [5]. Neither effect is in the basic equation: you’d need a separately fitted exponent for each temperature and age point to capture it, which is exactly what some of the extended, temperature-dependent versions of the equation try to do.
What’s actually happening, and why the “missing” capacity isn’t gone
It’s tempting to read Peukert’s law as saying that fast discharge burns energy as waste heat, but that’s not quite what’s going on, and it’s a common enough misreading that it’s worth being precise. The capacity that doesn’t show up at high discharge rates isn’t consumed or lost in any thermodynamic sense. It’s stranded. Inside a lead-acid cell, the reaction depends on sulfuric acid reaching the reaction sites buried in the porous lead plates, and that transport happens by diffusion, which runs at its own fixed pace regardless of how much current you’re demanding. Push the discharge hard enough and the terminal voltage collapses below the cut-off threshold well before the plates have actually run out of active material to react with: the battery isn’t empty, the chemistry just can’t keep up with the withdrawal rate.
That’s exactly why a battery’s voltage bounces back up if you stop drawing current and give it a rest: the concentration gradient that caused the early voltage sag has time to relax, acid diffuses back into the depleted regions of the plate, and capacity that seemed to have vanished becomes available again. You can see the same effect in reverse by tapering the current down as the cell approaches cut-off rather than cutting it off abruptly: nearly all of the “missing” capacity can still be recovered, just more slowly [3]. It’s the same basic story as the diffusion-limited concentration gradients that show up in fast-charging lithium cells, just running in the opposite direction and against a much older, slower-moving chemistry.
Where the equation breaks down
Peukert’s law earns its keep as a quick correction factor, but it was never meant to be a complete capacity model, and it shows in a few predictable places. It has no temperature term at all, despite temperature being one of the biggest swing factors in real-world capacity. It assumes the self-discharge current is negligible, which falls apart at very low discharge rates where self-discharge becomes a meaningful fraction of what’s being drawn. And at the other extreme, very high discharge currents, the equation tends to overstate the delivered capacity, because it doesn’t separately account for the extra energy dissipated across the battery’s own internal resistance at high current, a loss mechanism that’s real thermal waste on top of (not instead of) the diffusion-limited effect the exponent is capturing [3].
The most cited formal challenge to the equation is a 2006 critical review by Doerffel and Sharkh in the Journal of Power Sources, which tested the Peukert relationship against both lead-acid and lithium-ion cells and concluded it can’t reliably predict remaining capacity or state of charge unless the battery is discharged at genuinely constant current and constant temperature [5], conditions that describe a test bench far more often than they describe a battery actually in service, where load and ambient temperature both wander continuously.
Why an 1897 lead-acid equation still shows up in 2026 designs
Despite all of that, Peukert’s law hasn’t been retired. It’s just been scoped down to where it’s genuinely useful. Off-grid solar, marine, and UPS battery monitors (Victron’s SmartShunt line is a good example) still let you enter a Peukert exponent directly, because for lead-acid banks it remains a fast, good-enough way to turn a rated amp-hour figure into a realistic runtime estimate at whatever load the system actually sees, without needing a full electrochemical model [4]. For those applications the manufacturer’s default of around 1.25 is deliberately a conservative, one-size-fits-most value rather than a measured figure for any specific battery [4].
Lithium-ion battery management systems mostly sidestep the equation for day-to-day state-of-charge estimation, leaning instead on coulomb counting corrected against open-circuit voltage or a Kalman filter, precisely because lithium’s exponent sits so close to 1 that the correction is a second-order effect at moderate rates. But the underlying phenomenon Peukert described doesn’t disappear just because the exponent is small: push a lithium cell hard enough, or run it cold enough, and the same rate-dependent capacity shortfall shows up, which is why some of the more complete capacity and aging models used in EV and grid-storage BMS design still include a Peukert-style rate correction as one term among several, alongside temperature and state-of-health corrections the original 1897 equation never had to account for.
References
- W. Peukert, Über die Abhängigkeit der Kapazität von der Entladestromstärke bei Bleiakkumulatoren, Elektrotechnische Zeitschrift 20 (1897)
- Wilhelm Peukert, Wikipedia (German)
- Peukert’s law, Wikipedia
- Victron Energy, Battery capacity and Peukert exponent, SmartShunt manual
- Doerffel, D.; Sharkh, S. A., A critical review of using the Peukert equation for determining the remaining capacity of lead-acid and lithium-ion batteries, Journal of Power Sources, 155(2), 395–400, 2006