Peukert Capacity Calculator
Calculate the true runtime of a battery at a discharge rate different from its rating using Peukert's equation. Accounts for the capacity loss that lead-acid and other chemistries exhibit at high currents.
How to Use
- Enter the rated capacity C (Ah) and the rated discharge time H (typically 20 hours for lead-acid, 10 for deep-cycle).
- Enter the actual discharge current I you plan to pull.
- Enter the Peukert exponent k — 1.1 to 1.3 for lead-acid, 1.02 to 1.05 for LiFePO4, 1.0 for an ideal battery.
- The calculator returns adjusted runtime, effective Ah delivered, and capacity loss vs. the nameplate rating.
Show Work
Formulas
History of Peukert's Law
Wilhelm Peukert, a German scientist, published his empirical formula in 1897 after measuring how lead-acid battery capacity varied with discharge current. His observation: rather than capacity remaining constant, it followed a power law — higher currents delivered dramatically less total charge than nameplate ratings suggested. His original equation Cp = Ik × t (where Cp is the "Peukert capacity" constant) has been rearranged into many practical forms since, but the core insight is unchanged.
The formula dominated battery design for most of the 20th century because lead-acid was the only large-scale rechargeable chemistry. Telegraph offices, military installations, telecommunications central offices, and early electric vehicles all relied on massive banks of lead-acid cells whose real-world runtimes had to be derated from rated capacity using Peukert. Modern off-grid solar and marine battery sizing guides still use Peukert calculations essentially unchanged from Peukert's 1897 paper.
Lithium chemistries changed the math significantly. Because lithium cells have internal resistance roughly 1/10th that of comparable lead-acid, their Peukert exponents hover near 1.0 — capacity is nearly independent of discharge rate in normal operation. That's one of the practical reasons lithium has displaced lead-acid in high-rate applications (power tools, EVs, drones) despite higher upfront cost.
About This Calculator
Enter the rated capacity C (typically on the battery's label), the rate at which that capacity was measured (H hours — 20 h is typical for deep-cycle lead-acid, 10 h for starter batteries), your planned discharge current, and a Peukert exponent k appropriate for the chemistry. The tool returns the true runtime, the effective ampere-hours you'll actually get, and the percent loss vs. the naive nameplate math.
For realistic engineering, combine Peukert with temperature derating (cold loses 10–40% more capacity), age derating (typical 20% capacity loss by end of cycle life), and inverter efficiency (5–20%). All math runs client-side; no values leave your browser.
Frequently Asked Questions
What is the Peukert exponent?
An empirical constant that captures how usable battery capacity falls as discharge current rises. For an ideal battery k = 1.0 (capacity is independent of current). Real lead-acid cells are 1.1–1.3 (significant loss at high rates). Modern LiFePO4 is nearly flat at 1.02–1.05 because internal resistance is so much lower.
Where do I find k for my battery?
Quality lead-acid datasheets list capacities at multiple discharge rates (C/20, C/10, C/5); fitting a power-law curve to those points yields k. If only one rating is given, assume 1.15–1.25 for flooded lead-acid, 1.10–1.15 for AGM/gel, 1.05 for high-quality deep-cycle AGM.
Why does this matter most for lead-acid?
Lead-acid cells have relatively high internal resistance and slow electrochemical kinetics, so high currents waste more energy as heat and leave chemistry unreacted. Lithium chemistries have far lower internal resistance, so they suffer much less rate-dependent capacity loss.
Does Peukert apply below the rated rate?
The formula predicts higher-than-nominal capacity at lower-than-rated currents, but real batteries don\'t actually gain capacity indefinitely — self-discharge and chemical side-reactions put a ceiling on effective capacity at very low rates. Don\'t extrapolate k below the rated discharge time with confidence.
How do temperature and age affect this?
Cold reduces usable capacity by 10–40% regardless of Peukert. Age reduces capacity permanently. Both effects stack on top of Peukert derating. A 10-year-old lead-acid bank in cold weather at high current may deliver only 30% of its nameplate rating.
Common Use Cases
UPS Sizing
A 100 Ah SLA battery rated at C/20 (5 A) will deliver full capacity at 5 A. At 30 A (a typical small server load), Peukert with k=1.2 predicts ~70 Ah effective — 30% less runtime than nameplate math suggests.
Trolling Motor Planning
A 100 Ah deep-cycle battery at 50 A trolling motor draw, k=1.15 → ~65 Ah effective, 78 min runtime instead of the naive 120 min. Plan the fishing trip accordingly.
Solar Off-Grid Design
When sizing a lead-acid bank for intermittent heavy loads (water pumps, power tools), apply Peukert at the peak current to avoid under-sizing. A 400 Ah bank at 100 A draw delivers only ~280 Ah in real use with k=1.2.
EV Conversion Range
Cheap lead-acid EV conversions famously disappoint on range — Peukert at the 100–200 A draws of a typical motor strips 30–50% from nameplate capacity. Lithium conversions avoid this entirely.
Datasheet Cross-Check
Compare multiple capacity ratings from a single datasheet (C/20, C/10, C/5). If they match within 10%, k ≈ 1.05; if they vary 20–40%, k is 1.15+ and the battery is best used only at moderate rates.
Last updated: