Four deductions, in the order they apply
The arithmetic everyone starts with is capacity divided by load. A 200 Ah 12 volt bank is 2,400 watt-hours, and a 300 watt load ought to run for eight hours. It will not, and the reasons stack multiplicatively rather than adding up.
| Deduction | Typical size | What it is |
|---|---|---|
| Depth of discharge | ×0.5 to ×0.8 | The share of nameplate capacity you are willing to use before the cycle-life cost becomes unacceptable |
| Inverter efficiency | ×0.85 to ×0.94 | Only on AC loads. Worse at light load than at half load. |
| Discharge rate | ×0.6 to ×1.0 | Lead-acid delivers less total capacity when drained quickly. Lithium is far flatter. |
| Temperature | ×0.6 to ×1.0 | Cold cells hold less. Both chemistries lose capacity, lead-acid faster. |
Multiply a 50 percent depth, a 90 percent inverter, a 0.8 rate factor and a 0.85 cold factor together and you keep 31 percent of the label. That is the difference between eight hours and two and a half, and it is why runtime estimates made by dividing are almost always optimistic by a factor of two or three.
Depth of discharge is a purchase decision, not a setting
Every cycle-life curve slopes the same way: shallow cycles last longer. Where the chemistries differ is how steep that slope is and where the conventional working limit sits. Lead-acid is traditionally held to 50 percent, and going deeper repeatedly shortens life sharply enough that most people who do it replace the bank sooner than they expected. Lithium iron phosphate tolerates 80 to 100 percent routinely, and the cycle-life penalty for deep discharge is much gentler.
That single difference is why the two chemistries cannot be compared on nameplate amp-hours. A 100 Ah lead-acid battery offers about 50 usable amp-hours; a 100 Ah LiFePO4 offers 80 to 100, weighs a third as much, and does not care nearly as much how quickly you take it. Compare them on usable energy per dollar over their expected cycle count, and the answer looks very different from the sticker.
Peukert, and what it actually models
Lead-acid capacity falls as discharge current rises, because the sulphuric acid inside the plates cannot diffuse fast enough to keep the reaction fed at the surface. Take current out slowly and the whole plate participates; take it fast and only the outer material does. The classic description is Peukert law, and in the form used here the effective capacity is the rated capacity multiplied by (C / (I × H)) raised to the power of n minus 1, where C is the rated amp-hours, H is the number of hours that rating was measured over, I is the actual current and n is the Peukert exponent.
An exponent of 1 means no effect at all. Lead-acid typically runs 1.1 to 1.3, so a 100 Ah battery rated over 20 hours and drained at 50 amps might deliver around 56 amp-hours rather than 100. LiFePO4 sits near 1.02 to 1.05, which is why lithium banks behave much closer to the naive arithmetic and why lithium can be sized on energy rather than on discharge rate for most household loads.
One thing the model does not capture: voltage sag. A heavily loaded lead-acid bank drops terminal voltage well before it runs out of energy, and an inverter with a low-voltage cutoff will shut down at that voltage regardless of how much charge remains. In practice that often ends the runtime before the calculation says it should.
Cold is the deduction people never plan for
A bank in an unheated garage, a van in the mountains, or an outbuilding in February is not at room temperature, and battery ratings are given at 25 °C. Near freezing, lead-acid commonly gives up 20 to 25 percent of its capacity and lithium 10 to 15. Below that both fall further.
For lithium there is a second and more serious issue that has nothing to do with capacity: charging below freezing plates metallic lithium on the anode, which is permanent damage and can eventually cause an internal short. Well-made packs either block charging below a threshold in their management system or include a self-heating circuit that warms the cells before accepting current. Some cheap packs do neither, and the owner does not discover this until spring. Discharging cold is generally acceptable; charging cold is not.
Lead-acid has its own cold failure mode. A fully charged lead-acid battery resists freezing because the electrolyte is dense with acid, but a deeply discharged one is closer to water and will freeze, split the case and end the battery. A lead-acid bank left flat over a cold winter is often dead by spring for exactly this reason.
Where runtime fits in a system
Runtime answers a question about one event: the power is out, or the sun has gone, and this is what you have. It does not answer how big the bank should be, which depends on how many consecutive bad days you want to survive and on what recharges it. For sizing, the battery bank sizing calculator works the problem from days of autonomy; for the load list that feeds both, the off-grid load audit calculator gives the daily watt-hours; and for the other half of the cycle, the battery charge time calculator shows how long the bank takes to come back.
A PV array is energized whenever light falls on it. There is no switch on the panel that turns it off, and a module lying face up on the grass is a live source. DC arc faults do not self-extinguish the way an AC arc does, because DC current never passes through zero. A battery bank can deliver thousands of amps into a short circuit without any warning noise, and a dropped wrench across two terminals is a serious burn and fire hazard rather than a spark. Lithium cells that have been damaged, punctured, or charged below freezing can fail violently, and the failure is not always immediate. Nothing on this page is a wiring, commissioning or battery-assembly procedure, and none of it should be used as one.
Questions people ask
How long will a 100Ah battery run a 1000W load?
On paper a 100 Ah 12 volt battery holds 1,200 watt-hours, so a 1,000 watt load looks like about 72 minutes. In reality, on lead-acid held to 50 percent depth, through a 90 percent inverter, at a discharge rate around 90 amps that triggers a substantial Peukert deduction, you would be fortunate to see 25 minutes. The same 100 Ah in LiFePO4 at 80 percent depth with a much smaller rate penalty gives roughly 50 to 55 minutes. A 1,000 watt load on a single 100 Ah 12 volt battery is a hard draw for either chemistry, and on lead-acid it is closer to abuse than to use.
Why does my battery monitor disagree with this calculator?
Usually because it is measuring something the calculator is estimating. A shunt-based monitor counts coulombs in and out and applies its own Peukert and efficiency settings, which may not match the ones entered here. It also knows the actual state of charge the bank started at, which this page assumes is full. And a monitor that has not been synchronised at a full charge for a while drifts, sometimes badly. Where they disagree, the monitor is usually closer to the truth about the present, and the calculator is more useful for asking what-if questions before you buy anything.
Does discharging slower give me more total energy?
For lead-acid, genuinely yes: the Peukert relationship works both ways, and a battery rated over 20 hours will deliver more than its rated amp-hours if drained over 100. That extra capacity is real but it is not something to design around, because the loads that would use it are trivially small. This calculator caps the rate factor at 1 for exactly that reason — it will deduct capacity for a fast discharge but will not credit you for a slow one. For lithium the effect is small enough at household currents to ignore.
What depth of discharge should I actually use?
It is an economic choice, not a technical limit, and the datasheet cycle-life curve is where the answer lives. Every chemistry gives more total lifetime energy at shallow depth and more usable energy per cycle at deep depth, and the optimum depends on how much the bank costs and how many years you want out of it. As orientation only: lead-acid is conventionally worked to 50 percent for daily cycling and 30 percent if longevity matters more than size; lithium iron phosphate is routinely worked to 80 percent and often deeper, with the last 10 percent costing disproportionately in cycle life on some cells. Ask the manufacturer for the cycle count at each depth and do the multiplication.
Does the inverter efficiency figure apply to DC loads?
No, and untick the inverter box when the load is DC. Energy going from a 12 volt bank to a 12 volt fan passes through wire and a fuse and nothing else. The inverter only enters the calculation when the load needs AC. This is more than a rounding detail on a small system: a 90 percent inverter costs you 11 percent more battery for the same work, and the inverter idle draw, which this page does not model at all, can cost more again over a full night. If you want that included, the off-grid load audit page treats idle draw as its own line.