Peukert Battery Discharge Calculator

Introduction: 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.

The Peukert formula, step by step

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, I_r 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: a 100 Ah battery at 20 A

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:

1. Rated current: 5 A.
2. Current ratio: 5 A / 20 A = 0.25.
3. Runtime: 20 h × 0.25^1.20 ≈ 3.79 h.
4. 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.

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.

Current Sensitivity

Why capacity shrinks at high current: the physics

A lead-acid battery stores energy in the chemical conversion of lead and lead dioxide plates with sulfuric acid electrolyte. Discharge consumes acid at the plate surfaces, and fresh acid must diffuse in from the bulk electrolyte to keep the reaction fed. At the gentle 20-hour rate, diffusion keeps pace and nearly all the active material participates. At high current the surface layers deplete faster than diffusion can replenish them, the reaction becomes starved, voltage sags to the cutoff early, and a large fraction of the plate interior never reacts at all. Internal resistance compounds the effect: the power lost as heat scales with the square of current, so a doubled load quadruples resistive losses.

Wilhelm Peukert’s 1897 insight was that this whole cascade compresses into a single power law: capacity delivered varies with current raised to a constant exponent. The exponent is an empirical fingerprint of a battery’s construction — thin automotive starting plates suffer less than thick deep-cycle plates at high rates, and modern lithium cells, whose kinetics are far faster, barely exhibit the effect at all. The law is over a century old and still ships in marine battery monitors, which is a rare compliment for a one-parameter empirical model.

How to use this Peukert calculator well

Pull three numbers from the battery datasheet: the amp-hour rating, the hour rate it was measured at (C/20 is standard for deep-cycle lead-acid, C/10 for some AGM), and, if published, the Peukert exponent. When the exponent is missing, estimate it from chemistry — 1.25 is a fair default for flooded lead-acid, 1.1 for AGM, 1.03 for LiFePO4 — or compute it from two published rate/runtime pairs. Then enter the real average load. For loads that cycle, like a fridge, use the duty-cycle average rather than the compressor’s running draw, and remember that inverter loads add 10–15 percent on top of the DC arithmetic.

Read the runtime against a depth-of-discharge budget: the calculator predicts time to full discharge, but lead-acid batteries live far longer when you stop at 50 percent, so a practical trip plan uses half the reported hours. Lithium chemistries flip both assumptions — their exponent is nearly 1.0 and 80–90 percent discharge is routine — which is why the same load math produces such different system sizes.

Limitations and assumptions

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.

Peukert questions off-gridders ask