Peukert Battery Discharge Calculator
Introduction: estimating lead-acid discharge runtime with Peukert's law
This Peukert battery discharge calculator estimates runtime when a battery's actual discharge current differs from the current used for its published capacity rating. The model is most useful for lead-acid batteries, whose effective capacity falls as current rises because internal resistance, chemical diffusion limits, voltage sag, and heat losses become more significant.
A battery labeled 100 Ah at the 20-hour rate is not guaranteed to supply 100 Ah at every load. That rating corresponds to 100 Ah / 20 h = 5 A, so the battery should run for about 20 hours at 5 A under rating conditions. At 20 A, its runtime is usually shorter than the simple 100 Ah / 20 A = 5 hour estimate.
Peukert battery discharge inputs
- Rated capacity: the amp-hour capacity printed on the battery or datasheet.
- Hour rating: the duration of the capacity test, often 20 hours for deep-cycle lead-acid batteries.
- Peukert exponent: the battery-specific factor that describes the high-current capacity penalty. Ideal behavior is close to 1.0; flooded lead-acid batteries are often around 1.2 to 1.35; aged or stressed batteries may have a higher value.
- Discharge current: the steady load current in amps for the runtime estimate.
The Peukert battery-runtime formula, step by step
For the entered battery rating, the calculator first finds the rated discharge current:
It then applies Peukert's law in the form used by this runtime estimate, which preserves the battery's published hour-rating point:
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, this reduces to the ideal amp-hour relationship t = C / I.
Worked example: Peukert runtime for a 100 Ah battery at 20 A
Consider a 100 Ah lead-acid battery rated for 20 hours with a Peukert exponent of 1.20. Its rated current is 100 Ah / 20 h = 5 A. At a steady 20 A load:
- 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 calculation gives 5 hours. The Peukert result instead shows the runtime and amp-hours lost to a sustained high-current lead-acid discharge.
Plain-text formula: ratedCurrent = capacityAh ÷ hourRating; runtimeH = hourRating × (ratedCurrent ÷ loadCurrent)^k; deliveredAh = loadCurrent × runtimeH; k is the Peukert exponent.
Source/version metadata: Peukert’s law was published by Wilhelm Peukert in 1897 for lead-acid cells; typical exponents: flooded lead-acid 1.2–1.35, AGM 1.05–1.15, gel 1.1–1.25, lithium iron phosphate 1.01–1.05 (nearly ideal). The law loses accuracy at very low currents, at heavy currents outside the datasheet range, and in cold conditions. Last reviewed July 2026.
Peukert runtime sensitivity to discharge current
| 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. |
Why lead-acid capacity shrinks at high current: the physics
Peukert behavior in a lead-acid battery begins with its chemical reaction at the plates. Discharge consumes acid at plate surfaces, and fresh acid must diffuse from the bulk electrolyte to sustain the reaction. At a gentle 20-hour discharge, diffusion can keep up and much of the active material participates. At high current, surface layers deplete more quickly, voltage can sag to the cutoff earlier, and some active material remains unavailable during that discharge. Internal resistance adds to the loss because resistive heating rises with the square of current.
Peukert’s 1897 observation compresses these interacting effects into an empirical power law. The exponent is not a universal battery constant: it reflects a particular battery's construction, condition, test endpoint, and operating range. That is why a manufacturer's discharge tables or published exponent are preferable to assuming one value for every lead-acid battery.
How to use this Peukert battery runtime calculator well
Start with the battery datasheet: enter the published amp-hour capacity, the hour rate for that rating, and the stated Peukert exponent if one is supplied. If no exponent is available, treat a chemistry-based estimate as a planning assumption and compare the result with the manufacturer's constant-current discharge data. Enter the average DC current drawn from the battery. For cycling loads such as a refrigerator, a time-weighted average may be more useful than the compressor's running current, while inverter-fed loads should be evaluated from the inverter's battery-side draw.
The displayed runtime is a modeled time to the discharge endpoint implicit in the chosen rating and formula, not a recommended depth-of-discharge target. A practical battery plan should also account for the allowed depth of discharge, the voltage cutoff of connected equipment, temperature, battery age, and reserve capacity. Use the calculator to compare steady-current scenarios, then confirm an important installation against the relevant manufacturer curves.
Limitations and assumptions for Peukert battery discharge estimates
This Peukert calculator assumes a steady discharge current and uses an empirical lead-acid runtime relationship rather than a full electrochemical simulation. It is most appropriate when the entered capacity, hour rating, and exponent describe the same battery and test conditions. Lithium-ion packs commonly show a smaller Peukert effect, and their usable runtime can instead be governed by watt-hours, voltage limits, BMS cutoff behavior, temperature, and converter efficiency. For safety-critical systems, use manufacturer discharge curves and field testing.
Peukert battery questions off-gridders ask
What Peukert exponent should I use for my battery?
Use the exponent in the battery datasheet whenever it is available. Typical values are about 1.2 to 1.35 for flooded lead-acid, 1.05 to 1.15 for AGM, and 1.1 to 1.25 for gel batteries. A value close to 1 produces a result close to the simple amp-hour calculation; a larger value applies a stronger penalty at high current.
Does Peukert's law apply to lithium batteries?
It can be used with an exponent close to 1 when a manufacturer provides one, but it is chiefly a lead-acid runtime model. For lithium packs, voltage limits, the battery-management-system cutoff, temperature, and the manufacturer's discharge curves can be more important than a Peukert adjustment.
Why does my battery last less time than the calculator predicts?
The estimate assumes the rated capacity, exponent, and load current represent the actual installation. Cold temperature, battery age, voltage sag, an inverter's input current, wiring losses, and a cutoff reached before full chemical discharge can all shorten observed runtime. Compare the result with the manufacturer's discharge data for the relevant temperature and endpoint voltage.
Can capacity lost at high discharge current return after resting?
A rest period can allow chemical concentrations within a lead-acid battery to rebalance, so an intermittent load may behave differently from one continuous high-current discharge. This calculator models a steady current and should not be treated as a detailed recovery model for cycling loads.