Peukert Battery Runtime Calculator

The Peukert Battery Runtime Calculator answers the question every off-grid, marine and RV owner eventually asks: my battery says 100 Ah, so why did it die in three hours? Dividing amp-hours by amps is the estimate almost everyone uses, and on lead-acid it is optimistic by a wide margin. This calculator applies Peukert's law to give the runtime you will actually see, shows the effective capacity the pack really delivers at your load, and tells you how many amp-hours the Peukert effect is quietly taking away.

What Is the Peukert Effect?

A battery's capacity is not a fixed pot of amp-hours. It is a figure measured under one specific test condition — normally a slow, steady discharge over 20 hours for lead-acid, or one hour for lithium. Draw current faster than that test and you get less total charge out before the voltage collapses. Two things cause it: internal resistance turns part of the energy into heat instead of useful current, and the chemical reaction cannot diffuse through the plates fast enough, so some active material is never used at all. German scientist Wilhelm Peukert described the relationship in 1897, and it still models real lead-acid behaviour remarkably well.

Peukert's Law Formula

The classic statement of the law is that capacity times current raised to the exponent is a constant. In the practical form used for runtime, with a capacity rated at a known hour rate:

• t — runtime in hours to a fully flat battery
• C — rated capacity in amp-hours, as printed on the label
• H — the hour rate that capacity was measured at (20 h for most lead-acid, 1 h for lithium)
• I — the actual discharge current in amps
• k — the Peukert exponent for that chemistry, always at least 1

Multiplying the runtime by the current gives the effective capacity — the amp-hours that genuinely reach your load at that rate:

Notice what happens when k = 1: the bracket disappears and the formula collapses to the familiar \( t = C / I \). That is the naive estimate, and it is only correct for a battery that does not care how fast you drain it.

Typical Peukert Exponents by Chemistry

These are typical published ranges rather than datasheet truth for any individual pack. If your manufacturer publishes capacity at two different hour rates, work out your own exponent from those two points — the method is below — and enter it in the exponent box.

How to Find Your Own Peukert Exponent

Any two capacity ratings at different rates are enough. Convert each rating into its test current \( I = C / H \), then:

For example, a battery rated 100 Ah at the 20-hour rate (5 A for 20 h) and 85 Ah at the 5-hour rate (17 A for 5 h) gives \( k = (\log 20 - \log 5) / (\log 17 - \log 5) \approx 1.13 \) — a decent AGM.

A Worked Example

Take a 100 Ah flooded deep-cycle battery rated at the 20-hour rate, with a Peukert exponent of 1.25, powering a 25 A load:

• The rating current is 100 ÷ 20 = 5 A, so 25 A is five times harder than the test.
• Peukert runtime: \( t = 20 \times (100 / (25 \times 20))^{1.25} \approx 2.68 \) hours to flat.
• Effective capacity: 25 A × 2.68 h ≈ 67 Ah — a third of the label has vanished.
• The naive estimate would have promised 100 ÷ 25 = 4 hours. Reality is 1 h 20 min shorter.
• Stopping at a healthy 50% depth of discharge, you actually get about 1 h 20 min.

That gap between "4 hours" and "an hour and twenty minutes" is why so many first battery banks disappoint. Sizing on the label rather than on the effective capacity is the single most common mistake in off-grid design.

What Else Changes Real Runtime

How to Use This Calculator

1. Pick the chemistry: choosing a battery type fills in a typical Peukert exponent, the hour rate its capacity is normally quoted at, a sensible depth of discharge and a nominal voltage.
2. Enter the rated capacity: type the amp-hours on the label and confirm the hour rate beside it. Getting the hour rate right matters as much as the exponent.
3. Fine-tune the exponent: drag the slider or type a value from your datasheet. The hint under it explains what that exponent implies.
4. Describe the load: enter amps directly, or switch to watts and supply the system voltage and inverter efficiency.
5. Set the cut-off and temperature, then press Calculate Runtime and compare the real answer with the naive one.

Frequently Asked Questions

What is the Peukert effect?

The Peukert effect is the drop in usable battery capacity as the discharge current rises. A 100 Ah lead-acid battery rated at the 20-hour rate delivers its full 100 Ah only at about 5 A. Draw 50 A from it and you may get 60–70 Ah before it is flat, because internal resistance and slow chemical diffusion waste part of the stored charge as heat and leave part of the active material unreacted.

What is Peukert's law?

Peukert's law relates discharge time to discharge current. In the practical form used by this calculator, runtime t = H × (C ÷ (I × H))^k, where C is the rated capacity in amp-hours, H is the hour rate that capacity was measured at, I is the actual discharge current, and k is the Peukert exponent. When k equals 1 the law collapses to the familiar t = C ÷ I.

What is a typical Peukert exponent?

Flooded deep-cycle lead-acid is usually 1.2 to 1.3, gel about 1.2, AGM about 1.1 to 1.15, and lead-carbon about 1.1. LiFePO4 and Li-ion sit around 1.02 to 1.05, which is why lithium banks hold their rated capacity almost regardless of load. NiMH and NiCd are around 1.1. An exponent of exactly 1.0 would be a perfect battery, and nothing real reaches it.

How do I find the Peukert exponent for my battery?

Take two capacity ratings from the datasheet at different hour rates, for example 100 Ah at 20 hours and 85 Ah at 5 hours. The exponent is k = (log t₁ − log t₂) ÷ (log I₂ − log I₁), using the currents C ÷ H for each rating. If your datasheet gives only one rating, start from the typical value for the chemistry.

Does the Peukert effect apply to lithium batteries?

Only slightly. LiFePO4 and Li-ion have very low internal resistance, so their Peukert exponent is close to 1.0 and their usable capacity barely changes between a gentle draw and their rated continuous current. That is one of the main practical advantages of lithium over lead-acid in off-grid, marine and RV banks. Push a lithium cell far past its continuous rating and heat, not Peukert, becomes the limit.

Why should I not discharge a battery to zero?

Cycle life falls sharply with depth of discharge. Lead-acid banks are conventionally sized for a 50% depth of discharge, which can give several times the cycle count of deep 80–100% cycles. LiFePO4 tolerates 80–90% comfortably. This calculator applies your chosen depth of discharge to the Peukert runtime, so the headline figure is the time to your cut-off rather than to a dead battery.

Why does cold weather reduce battery runtime?

Low temperature slows the chemical reactions inside the cell and raises internal resistance, so less of the stored charge is available before the voltage collapses. A lead-acid battery typically delivers about 80% of its rated capacity at 0 °C and around 60% at −20 °C. The calculator applies that derating to the rated capacity before the Peukert maths runs.

Is Peukert's law accurate for real loads?

It is a very good approximation for steady discharge, which is what it was derived from. It is less exact for loads that switch on and off, because a resting battery partially recovers between pulses — real results for a fridge or a winch usually land somewhere between the Peukert figure and the naive one. Treat the Peukert answer as the conservative planning number.

Additional Resources

• Peukert's Law - Wikipedia
• Deep-Cycle Battery - Wikipedia
• Depth of Discharge - Wikipedia