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Battery Runtime Calculator (Peukert's Law)

Estimate how long a battery will last at a given discharge current using Peukert's law, and see how much shorter that is than a naive capacity-divided-by-current estimate.

Estimated runtime
4.06 hours
Naive estimate (capacity ÷ current)
5 hours
Peukert-adjusted vs. naive estimate
81.2%

How it works

Peukert's law models a battery's usable capacity shrinking as the discharge current rises above its rated rate, since higher currents lose more energy to internal resistance and chemical kinetics rather than delivered load. Runtime T = H × (C ÷ (I × H))ⁿ, where C is the capacity in Ah the manufacturer rated at a discharge time H in hours (e.g. a '100Ah at the 20-hour rate' battery has C=100, H=20), I is the actual discharge current, and n is the battery's own Peukert exponent. Verified via web search against Wikipedia's own Peukert's law reference and Battle Born's 'What Is Peukert's Law' explainer.

An ideal, non-derating battery has n=1, and the formula reduces exactly to the naive T = C ÷ I estimate most people reach for first. Real batteries have n > 1 — lead-acid commonly 1.1-1.3, lithium chemistries closer to 1.0 — so this calculator also reports the Peukert-adjusted runtime as a percentage of that naive estimate, since the whole point of the law is that the naive figure overstates runtime once the discharge current climbs well above the rated rate. The Peukert exponent is left as a value you enter yourself rather than picked from a chemistry dropdown, since the exact figure is specific to a battery model's own datasheet.

FAQ

Where do I find my battery's Peukert exponent and rated hour rate?

Both are usually on the battery's datasheet. The rated hour rate is the discharge time the printed Ah capacity was measured at (commonly the 20-hour or 100-hour rate for lead-acid batteries); the Peukert exponent, if published, sits typically between 1.05 and 1.3 for lead-acid and closer to 1.0 for lithium chemistries. If it isn't published, 1.1-1.15 is a commonly used estimate for a healthy lead-acid battery — but it's still an estimate, not a fixed fact, so a real datasheet value is always better.

Why does the naive C ÷ I estimate overstate runtime?

Because it assumes the battery delivers its full rated capacity no matter how fast you draw it down. In reality, drawing current faster than the rate it was rated at wastes more energy internally, so less of the rated capacity is actually usable — the higher the discharge current relative to the rated rate, and the higher the Peukert exponent, the bigger that gap gets.

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