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.
| Load | Watts | Hours/day | Wh/day |
|---|
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.
Everything above is quoted at 25 °C, and almost nothing lives at 25 °C. A bank in a van, a shed, a boat locker or a loft spends much of the year colder than that, and capacity goes with it. Size for the coldest night you expect to need it, not for the label.
The discharge numbers are not close: lead-acid gives up roughly 0.8% of its capacity per degree below 25 °C, and lithium about 0.3%, because the loss is ionic mobility in the electrolyte rather than a slowing reaction. At −10 °C that is the difference between about 72% and about 90% of the label.
But you cannot charge lithium below freezing. Doing it plates metallic lithium onto the anode, which is permanent, cumulative, and eventually a short circuit — so the battery management system simply refuses, and a bank that will not take charge on a cold morning is worse than one that is merely smaller. Lead-acid will accept a charge at −10 °C quite happily. That single asymmetry decides more van and boat installations than any capacity figure, and the answer to it is a heated battery compartment rather than a different chemistry.
Cycle life is not a fixed number — it is a steep function of how deeply you discharge. Halving the depth of discharge does not double the life, it roughly triples it for lead-acid, and the capacity you gave up to do it was only half. So the energy delivered over the bank's whole life goes up as you work it less hard, and the cost of each kilowatt-hour goes down.
That is why the right question at the point of purchase is not "what is the cheapest bank that runs my loads overnight" but "what does a kilowatt-hour cost me over ten years". The two have different answers, and the second one usually says buy more capacity than you need and treat it gently.
A 100 Ah lead-acid battery at 12 V is 1.2 kWh on the label. Worked to the conventional 50% depth of discharge it gives 0.6 kWh a cycle for about 600 cycles — roughly 360 kWh over its life. At £130 that is 36p a kilowatt-hour.
Two of them, worked to 25% instead, give the same 0.6 kWh a cycle — but at a quarter depth the life stretches to roughly 1,760 cycles, so the pair delivers about 1,050 kWh for £260: 25p a kilowatt-hour. Twice the money, a third less per unit of energy, and the bank also rides out a cold night without complaint.
Run the same arithmetic for LiFePO₄ and the gap closes from the other direction: a far higher cycle count at a far higher price, plus the cold-charging constraint. Which one wins depends on how often you actually cycle it — daily in a liveaboard, and lithium is cheaper per kilowatt-hour within a couple of years; a dozen weekends a year, and the lead-acid bank will reach its calendar life long before its cycle life and the cheaper purchase wins.
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.
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.
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.
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.
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.
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 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.
A great deal, and it is modelled above. Lead-acid gives up roughly 0.8% of its capacity per degree below 25 °C — about a fifth of it by 0 °C — while lithium loses nearer 0.3% a degree, because the loss is ionic mobility rather than a slowing reaction. But lithium must not be charged below freezing without a heater, which is a safety limit rather than a performance one, and a bank that will not accept charge on a cold morning is a worse problem than one that is merely smaller.
A healthy battery at the start of its life, correctly charged before the discharge. Temperature and cycle life are modelled — capacity derated linearly below 25 °C at a rate set by chemistry, and life against depth of discharge on the standard power-law curve, which is a fit to published cycle charts rather than a physical law. Prices used for the cost per kilowatt-hour are typical UK retail and will not be yours. Not modelled: 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.
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