How this battery runtime calculator works
“How long will my battery last?” sounds like simple division (capacity over load), but the naive answer is often 30–50% too optimistic. This calculator accounts for every factor that shortens real runtime:
- Depth of discharge (DoD). Lithium iron phosphate (LFP) batteries can use 80–100% of their capacity; lead-acid batteries should stop at about 50% to avoid rapid ageing.
- Inverter losses. Running AC appliances from a battery costs 7–15% in conversion, plus the inverter’s own idle consumption every hour it is switched on.
- Peukert’s law. Lead-acid batteries deliver less charge at high currents. The calculator applies Peukert’s equation relative to the battery’s rated discharge time (20 hours for most lead-acid ratings).
- Temperature and age. Capacity falls in the cold (roughly 1% per °C below 25 °C for lead-acid) and as batteries age; end-of-life is usually defined at 70–80% of original capacity.
Pick the devices you want to keep running in an outage, or enter your own total, and the calculator returns the runtime, the current and C-rate, a runtime curve for other loads, and the battery size you would need for your target backup time.
The formulas
Here H is the rated discharge time (20 h), C the effective capacity in Ah and k the Peukert exponent (1.1–1.3 for lead-acid, about 1.03 for LFP).
Worked example: two 200 Ah LFP batteries in a power outage
The defaults describe two 12.8 V 200 Ah LiFePO₄ batteries in parallel (5.12 kWh nominal, 4.61 kWh usable at 90% DoD) powering a fridge (60 W average), router (15 W), LED lighting (45 W) and a 50-inch TV (90 W): 210 W in total. Through a 90%-efficient inverter with 20 W idle draw, the battery supplies 253 W, a gentle 0.05C. Runtime is about 18 hours 11 minutes, comfortably above the 12-hour target.
Swap in two 12 V 200 Ah AGM batteries and the picture changes: usable energy halves to 2.4 kWh at 50% DoD and runtime falls to about 9 hours 24 minutes. At a 1,000 W load the AGM bank lasts only 1 hour 41 minutes — 21% less than simple division suggests, because Peukert’s law penalises the 94 A discharge current.
How to read the results
- Backup time is the time to reach your DoD limit, not to a completely flat battery.
- Battery drain shows how much the inverter adds. If its idle draw is a large share of a small load, DC appliances or a smaller inverter extend runtime noticeably.
- C-rate above the chemistry’s comfortable limit (about 0.2–0.3C for lead-acid, 1C for LFP) triggers a warning.
- Capacity for target sizes the battery bank you would need, Peukert and temperature included. Refine the configuration with the battery bank size calculator.
Typical runtimes (12 V 100 Ah = 1.2 kWh nominal, via inverter)
| Load | LFP (90% DoD) | AGM (50% DoD) |
|---|---|---|
| Router + modem (15 W) | ≈ 30 h | ≈ 17 h |
| CPAP without humidifier (40 W, DC) | ≈ 29 h | ≈ 16 h |
| Fridge average (60 W) | ≈ 13 h | ≈ 6.5 h |
| Essentials 200 W | ≈ 4.7 h | ≈ 2 h |
| Microwave 1,000 W | ≈ 1 h | ≈ 20 min |
Values include a 90% inverter and 20 W idle (except the DC CPAP); real figures vary with battery age and temperature.
Tips to extend backup time
- Know your average loads. A fridge or freezer label shows its maximum; its average over a day is typically a third to a half. Measure with a plug-in energy meter or use the appliance energy cost calculator.
- Switch off the inverter when nothing AC is needed, or run routers, lights and CPAPs directly from 12 V.
- Keep batteries warm. A battery in an unheated garage at 0 °C can lose 10–25% of capacity.
- Don’t oversize the inverter. A 3 kW inverter idling at 40 W can consume more than the router you want to keep online.
- Recharge with solar. Even a few hundred watts of panels can extend an outage indefinitely in summer; see the off-grid solar calculator.
Limitations
Real batteries show voltage sag near empty, which may trip an inverter’s low-voltage cut-off before the nominal DoD is reached. Peukert’s law is an empirical approximation valid over moderate current ranges; at very low currents it overpredicts capacity, so the calculator caps the gain at 15% for lead-acid. Battery-management-system limits, cell imbalance and ambient temperature changes during discharge are not modelled. Battery packs whose capacity is given in mAh at 3.6–3.7 V (power banks) should be converted to Wh first.
Method & assumptions
Usable energy = nominal capacity (Ah × V × number, or kWh) × depth of discharge × state of health × temperature factor (lead-acid ≈ −1%/°C below 25 °C, lithium ≈ −0.4%/°C). Battery drain = load ÷ inverter efficiency + inverter idle power (for AC loads).
Runtime (Peukert's law): t = H × [C ÷ (I × H)]^k × DoD, where C is the effective Ah capacity, I = drain ÷ battery voltage, H the rated discharge hours (20 h for lead-acid) and k the Peukert exponent. For lithium, k is near 1 and runtime ≈ usable Wh ÷ drain W.
Frequently asked questions
How long will a 100Ah battery last?
How do I calculate battery runtime?
How long can a 10 kWh battery power a house?
What is the Peukert effect?
Why does my battery last less than the calculation?
What size battery do I need for 24 hours of backup?
Sources & references
- Peukert, W. (1897). Über die Abhängigkeit der Kapazität von der Entladestromstärke bei Bleiakkumulatoren. Elektrotechnische Zeitschrift 20
- Battery University: BU-503: How to calculate battery runtime; BU-502: Discharging at high and low temperatures
- IEEE Std 1188 / IEEE 485: Sizing and maintenance of lead-acid batteries for stationary applications
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