What Is Peukert’s Law?

Lead-acid batteries are commonly rated with a capacity in amp-hours based on a standardized discharge period, often 20 hours. Unfortunately real batteries do not deliver that many amp-hours at every load. If you draw current quickly, less total charge is available before the voltage drops to an unusable level. In 1897 the German scientist Wilhelm Peukert described this behavior with the empirical equation now known as Peukert’s law. It relates the discharge time to the current by way of an exponent :

Here is the reference current used for the rated capacity and is the rated discharge time. Solving for gives:

The exponent is typically between 1 and 1.3 for lead-acid cells. Values above 1 indicate that higher currents shorten runtime more than proportionally, while describes an ideal battery with no such effect.

How to Use This Calculator

The battery label often lists a capacity such as 100 Ah at the 20-hour rate. That means if you discharge the battery over 20 hours, drawing 5 A, it should provide the full 100 Ah. If you need more current, the total amp-hours will decrease. Enter the rated capacity, the corresponding hour rating, the Peukert exponent, and your planned discharge current. The calculator then solves the equation above to estimate how many hours the battery can sustain that load.

Where Peukert’s Law Matters

This effect is most noticeable in deep-cycle batteries used for solar power storage, off-grid cabins, and trolling motors. Car batteries primarily deliver short bursts for starting engines and are less often measured this way, although the concept still applies. Understanding the relationship between current and runtime helps you size a battery bank appropriately. A common mistake is assuming that doubling the load simply halves the runtime. With Peukert’s law, the drop can be steeper.

Suppose a 200 Ah battery has a Peukert exponent of 1.2 at the 20-hour rate. Discharging at 40 A rather than 10 A would not give 5 hours, as a naive calculation might suggest. Plugging the numbers into the equation yields a runtime closer to 3 hours. That difference could be critical if you rely on the battery for backup power or to run essential equipment overnight.

Choosing the Right Exponent

The Peukert exponent is normally provided by the manufacturer, though you can approximate it by conducting discharge tests at two different currents and solving for . Values around 1.1 indicate a high-quality battery with good charge retention under heavy loads, while values approaching 1.3 reflect more pronounced losses. Temperature, age, and state of charge also affect the effective exponent, so the number is not perfectly constant. Still, it offers a useful ballpark for planning.

A Sample Calculation

Imagine you own a 100 Ah deep-cycle lead-acid battery rated at the 20-hour rate, and the datasheet lists a Peukert exponent of 1.15. You plan to power an inverter that draws 15 A. Inserting the values into the formula yields:

This works out to roughly 7.6 hours of useful runtime. If you reduce the load to 10 A, the predicted time jumps to about 13 hours, demonstrating how slower discharge dramatically extends capacity.

Limitations and Reality

Peukert’s law is an approximation. It assumes the battery is fully charged, in good condition, and operating at a moderate temperature. At very low currents or near the end of discharge, other chemical effects come into play, so the model can overestimate runtime. Nonetheless, it captures the general trend and is widely used in the renewable energy community, on boating forums, and by hobbyists building battery-powered systems.

Modern lithium-ion batteries behave differently and typically do not follow Peukert’s law as strongly. Many datasheets for lithium cells provide curves of capacity versus discharge current instead. Still, understanding Peukert’s idea can help you appreciate the improvements offered by newer chemistries compared to the older flooded or sealed lead-acid designs.

How This Tool Works

The form on this page accepts the rated capacity in amp-hours, the hour rating used for that capacity, the Peukert exponent, and your desired discharge current. It converts these to a reference current by dividing capacity by the rated time. Then it solves the law for at the chosen current. The result is displayed below the button. A copy button lets you place the value on your clipboard for quick sharing or logging.

Experiment for Yourself

If you want to measure the exponent of your own battery, discharge it at two different known currents and record the hours it lasts each time. You can rearrange Peukert’s equation to solve for . Try entering each test result into the calculator to see how they compare. By repeating the test at various stages of battery life, you may notice the exponent increasing as the plates age.

Conclusion

A simple amp-hour rating only tells part of the story about how long a battery will run. Peukert’s law reveals the impact of high or low current draw on usable capacity. Whether you maintain an off-grid cabin, power an electric trolling motor, or keep a backup sump pump ready, this tool can help estimate runtime and plan your energy needs. With care and periodic testing, you’ll better understand your batteries and avoid unexpected outages.