Electrical · storage

Battery Sizing & Runtime

What a bank actually delivers, which is never what the label says.
runtime

The bank

Lead-acid

1.00 would mean capacity is independent of draw. Nothing is 1.00.

Runtime

At your load
The bank
The load

What you are running

DC loads come straight off the battery. AC loads go through an inverter, which takes its cut before anything reaches the appliance — and draws a standing current whenever it is switched on, whether or not anything is plugged in.

LoadWattsHours/dayWh/day
The Peukert effect

Capacity falls as you pull harder

A battery rated 100 Ah is rated at one specific discharge current — usually the 20-hour rate, which is 5 A. Pull 50 A and a lead-acid battery delivers nothing like 100 Ah, because the reaction cannot keep up with the demand. Lithium barely notices, which is most of why it displaced lead in deep-cycle service.

Field notes

Why banks come up short

How it works

Three deductions from the nameplate

The number on the case is the best case: a full charge, discharged slowly, all the way flat, at room temperature, when new. Every step away from that costs you, and the losses multiply rather than add.

Depth of discharge

Taking a lead-acid battery below about 50% shortens its life sharply, so half the nameplate is the working figure. LiFePO₄ tolerates 80–90%. Usable Wh = V × Ah × DoD, and the difference is stark: 12 V × 100 Ah is 600 Wh of lead-acid but 960 Wh of lithium from the same label.

The Peukert effect

t = H · (C / (I·H))k, where H is the rating period (20 h), C the rated capacity and k the Peukert exponent. At exactly the rated current this returns exactly the rated time, for any k — which is the check that the formula is being used correctly. Above it, capacity falls away.

Worked example

A 100 Ah lead-acid battery at its 5 A rating delivers the full 100 Ah over 20 hours. Pull 50 A and with k = 1.25 it lasts 1.12 hours — just 56 Ah, a little over half the label. The same draw on LiFePO₄ with k = 1.05 yields 89 Ah. Add a 50% depth-of-discharge limit to the lead-acid and you are working with about a quarter of the number on the case.

Why does my battery never last as long as the label suggests?

Three deductions, and they multiply. Depth of discharge takes half of a lead-acid battery before you start; the Peukert effect takes more the harder you pull; and an inverter takes another 10–20% of whatever is left. A 1,200 Wh nameplate can be 400 Wh of real work.

What Peukert exponent should I use?

Roughly 1.1–1.3 for lead-acid — flooded at the lower end, AGM in the middle, cheap batteries higher. LiFePO₄ is about 1.02–1.05, which is why it is barely worth modelling for lithium. If the manufacturer publishes capacity at two discharge rates you can solve for the real exponent rather than guessing.

Series or parallel?

Series multiplies voltage and leaves capacity alone; parallel does the opposite. Same total energy either way, but higher voltage means lower current for the same power, which means thinner cable and smaller losses. That is why large systems are 48 V rather than 12 V.

Does cold weather matter?

A great deal, and this page does not model it. Lead-acid loses roughly 20% of its capacity at 0 °C and about half at −18 °C. Lithium holds capacity better but must not be charged below freezing without a heater, which is a safety limit rather than a performance one.

What this page assumes

A healthy battery at around 20 °C, at the start of its life, correctly charged before the discharge. Not modelled: temperature, ageing and state of health, charge acceptance and recharge time, cable and connection losses, self-discharge, cell imbalance in a series string, BMS cut-offs, and the voltage sag that may trip a load long before the calculated capacity is used up.

An estimate for sizing, not a specification. Peukert exponents and depth-of-discharge limits vary by manufacturer and by battery age — use the datasheet for the cells you actually have. Lithium batteries must not be charged below freezing without a heater, and every bank needs correctly rated protection.
Version history · unchanged

No changes to this tool’s own behaviour since the earliest archived release (v1.20). The full history for the site is in the changelog.