Battery Discharge Curve Calculator
Find a battery's actual runtime and delivered capacity at any discharge current using Peukert's Law, from its rated capacity and hour rate.
🔋 What is a Battery Discharge Curve?
Peukert's Law models how a battery's usable capacity shrinks as you discharge it faster, a real effect that a simple "capacity divided by current" runtime estimate completely misses. Published by Wilhelm Peukert in 1897, it expresses runtime as t = H x (C / (I x H))^k, where C and H are the battery's rated capacity and rated hour rate, I is the actual discharge current, and k is a chemistry-specific exponent.
Engineers and off-grid system designers use this calculation to size battery banks realistically for inverters and high-current loads, predict how much less capacity a battery delivers under a heavy load than its nameplate suggests, compare lead-acid against lithium chemistries on a like-for-like basis, and avoid the common mistake of assuming amp-hour capacity is a fixed, rate-independent number.
A common point of confusion is treating the printed amp-hour rating as valid at any discharge rate. It is only accurate at the specific hour rate it was measured at (commonly printed as C10, C20, or C100), discharging faster delivers meaningfully fewer amp-hours, and this calculator's "percent of rated capacity" result shows exactly how much less.
This calculator computes actual runtime and delivered capacity at any discharge current from your battery's rated capacity, rated hour rate, and Peukert exponent, and plots how runtime falls as discharge current rises, visually showing the Peukert effect.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Discharging at the Rated Rate
C = 100 Ah, H = 20 h, k = 1.2, I = 5 A
Example 2 — Fast Discharge, Same Battery
C = 100 Ah, H = 20 h, k = 1.2, I = 20 A
Example 3 — Small Lead-Acid Battery, Fast Rate
C = 50 Ah, H = 10 h, k = 1.1, I = 10 A
❓ Frequently Asked Questions
🔗 Related Calculators
What is Peukert's Law?
Peukert's Law is an empirical formula, published by Wilhelm Peukert in 1897, that models how a battery's usable capacity decreases as discharge current increases. It captures the real-world observation that a battery delivers noticeably fewer amp-hours when discharged quickly than when discharged slowly.
What is the formula for battery runtime using Peukert's Law?
t = H x (C / (I x H))^k, where H is the rated discharge time in hours, C is the rated capacity in amp-hours at that rated time, I is the actual discharge current, and k is the Peukert exponent (a battery-chemistry-specific constant greater than or equal to 1).
What is a typical Peukert exponent value?
Flooded lead-acid batteries typically have k between 1.1 and 1.3, AGM and gel lead-acid batteries are similar, and lithium-ion or LiFePO4 batteries are much closer to ideal, often 1.0 to 1.05, meaning they lose far less capacity under heavy discharge than lead-acid chemistries.
Why does a battery deliver less capacity at higher discharge currents?
At higher currents, internal resistance losses and slower ion/chemical diffusion inside the battery waste more energy as heat and leave active material less fully utilized before the terminal voltage drops below a usable cutoff, so less of the theoretical stored energy is actually delivered to the load.
What does 'C20' or 'C10' mean on a battery datasheet?
It specifies the hour rate the rated capacity was measured at, C20 means the capacity figure is what the battery delivers when discharged steadily over 20 hours. This calculator's H input should always match the rate used for whichever capacity figure C you enter.
How do I find my battery's Peukert exponent if it isn't published?
Manufacturers sometimes publish it directly, or you can estimate it from two capacity ratings at different hour rates on the same datasheet (e.g. C5 and C20) using the two-point form of Peukert's equation. Without either, use the typical range for the chemistry: 1.1 to 1.3 for lead-acid, 1.0 to 1.05 for lithium.
Does Peukert's Law apply to lithium-ion batteries?
It can be applied, but lithium chemistries deviate from Peukert behavior less than lead-acid, since their internal resistance and diffusion characteristics are more favorable at higher currents. Many lithium datasheets report only a modest capacity drop even at high C-rates, reflected in a Peukert exponent close to 1.0.
What happens if I discharge at a current higher than the rated rate?
Runtime drops faster than a simple linear (capacity/current) estimate would suggest, and delivered capacity (in amp-hours) falls below the rated nameplate value. This calculator's 'percent of rated capacity' result quantifies exactly how much less you actually get at your chosen current.
Is delivered capacity ever greater than the rated capacity?
Yes, discharging more slowly than the rated hour rate (a lower current than C/H) can deliver slightly more than the nameplate amp-hour rating, since Peukert's Law is symmetric around the rated point, though most datasheets don't emphasize this because very slow discharges are less commonly tested.
What units does this calculator use?
Rated capacity is entered in amp-hours (Ah), rated discharge time in hours, discharge current in amps, and the Peukert exponent is a dimensionless number (typically 1.0 to 1.3). Runtime is returned in hours and delivered capacity in amp-hours.