Peukert Battery Discharge Calculator
What Peukert's Law Estimates
Peukert's law estimates how long a battery will run when the discharge current is different from the current used for its published capacity rating. It is most useful for lead-acid batteries, where pulling current faster than the rating current reduces effective capacity because internal resistance, chemical diffusion limits, voltage sag, and heat losses become more important.
A battery labeled 100 Ah at the 20-hour rate is not guaranteed to deliver 100 Ah at every load. The 20-hour rating means the test current is 100 Ah / 20 h = 5 A. At 5 A, the battery should last about 20 hours under rating conditions. At 20 A, it will usually last much less than the simple 100 Ah / 20 A = 5 hour estimate.
Inputs
- Rated capacity: the amp-hour capacity printed on the battery or datasheet.
- Hour rating: the test duration for that capacity, often 20 hours for deep-cycle lead-acid batteries.
- Peukert exponent: a chemistry and condition factor. Ideal batteries are close to 1.0; flooded lead-acid batteries are often around 1.2 to 1.35; aged or stressed batteries may be higher.
- Discharge current: the actual load current in amps for the scenario you want to estimate.
Formula
The calculator first finds the rated discharge current:
It then applies Peukert's law in a form that preserves the battery's published hour rating:
Here, t is runtime in hours, H is the capacity hour rating, Ir is the rated current, I is the actual discharge current, and n is the Peukert exponent. When n = 1, the formula collapses to the simple ideal estimate t = C / I.
Worked Example
Suppose a 100 Ah lead-acid battery is rated at 20 hours and has a Peukert exponent of 1.20. The rated current is 100 Ah / 20 h = 5 A. If the actual load is 20 A:
- Rated current: 5 A.
- Current ratio: 5 A / 20 A = 0.25.
- Runtime: 20 h × 0.251.20 ≈ 3.79 h.
- Effective delivered capacity: 20 A × 3.79 h ≈ 75.8 Ah.
The ideal linear estimate would be 5 hours, so Peukert's law shows why high current can remove a large share of usable capacity.
Current Sensitivity
| Load current | Runtime at n = 1.20 | Effective capacity | Interpretation |
|---|---|---|---|
| 5 A | 20.00 h | 100 Ah | Matches the 20-hour rating point. |
| 10 A | 8.71 h | 87 Ah | Higher current starts reducing usable capacity. |
| 20 A | 3.79 h | 76 Ah | Runtime is well below the linear 5-hour estimate. |
| 40 A | 1.65 h | 66 Ah | Heavy discharge makes the Peukert penalty large. |
Limitations
Peukert's law is an empirical model, not a full electrochemical simulation. It is best for lead-acid batteries over moderate conditions. Lithium-ion packs usually have lower Peukert effects and are often better modeled from watt-hours, voltage limits, BMS cutoff behavior, temperature, and converter efficiency. For safety-critical systems, use manufacturer curves and field testing.