Peukert's Law and Its Effect on Batteries

Peukert's law, was presented by the German scientist Wilhelm Peukert in 1897, It expresses the change in capacity of rechargeable batteries at different rates of discharge. As we pull more current out of the battery, the available capacity of the battery decreases.

We considered the peukert's constant while designing our battery life calculator consequently we wrote this article to breakdown the Peukert Constant in simple terms, explains why it matters, and show how our calculator uses it to give more accurate discharge predictions.

Peukert's effect is rarely understood by beginners because they expect a linear discharge current / battery capacity but intuitively we should understand that even if a 100AH battery means that it should be able to supply 100A for 1 hour, If you pull out 100Amps from a battery it would overheat and most certainly last up to 1 hr.

A Peukert constant of 1.00 means the battery delivers its full rated capacity at any discharge rate. A higher constant (1.1, 1.2, 1.3…) means capacity drops significantly at high loads.

The harder you pull from the battery, the less energy you can actually get out.

Peukert's effect is especially strong in lead acid batteries, moderate in NiMH/NiCd, and minimal in lithium batteries. The main reason is that inside every rechargeable battery, electrical energy comes from electrochemical reactions occurring at the anode and cathode. These reactions depend on the movement of ions through the electrolyte and electrons through the external circuit.

When you discharge the battery slowly, the chemical processes have time to keep up. But when you discharge the battery quickly (higher current), several limiting factors emerge.

1) The battery tries to pull ions from the electrolyte toward the electrode faster. But diffusion can only transport ions at a certain maximum speed. Eventually, the ion concentration near the electrode drops too low and the reaction slows dramatically, even though there is still plenty of active material elsewhere in the cell. The electrochemical reactions inside the battery cannot keep up with fast current draw. You “starve” the reaction locally, causing the voltage to drop prematurely.

2) Batteries have internal resistance (electrolyte, electrodes, separators, contacts).

Voltage under load is:

V_load = V_oc - I · R_internal

When current increases battery heats up and internal resistance increases, and this causes voltage to collapse faster

For lead acid and NiCd/NiMH, internal resistance is moderately high, so this effect is significant. For lithium batteries, internal resistance is very low that’s why their Peukert constant is close to 1.0.

High current = deeper voltage sag = earlier cut off.

The Peukert Equation

Most engineering tools use the classic Peukert formula:

$ t = \frac{C}{I^k} $

Where:

t = runtime (hours)

C = rated battery capacity (Ah at the reference rate)

I = discharge current (amps)

k = Peukert constant

A Simple Example

Suppose you have:

100Ah lead acid battery

Peukert constant k = 1.25

Discharge current = 50A

Expected runtime without Peukert would be:

$ t = \frac{100}{50} = 2 $ hours

But applying Peukert:

$ t = \frac{100}{50^{1.25}} \approx 1.7 $ hours

Actual usable capacity: ≈ 85Ah, not 100Ah.