Battery Runtime & Discharge Estimator
Calculates runtime (hours and minutes) for an existing battery bank under a continuous or intermittent load using Peukert's equation. To size the total battery capacity needed for an off-grid system, use the Battery Bank Sizing Calculator.
Enter the values above and click Calculate to view recommendations and engineering specifications.
Peukert's Law: Why High Loads Drain Batteries Faster
Calculation Assumptions
- Lead-acid discharge derated using Peukert exponent (k = 1.15 to 1.30).
- LiFePO4 treated as Peukert-neutral (k ~ 1.02 to 1.05) with linear flat-curve discharge.
Engineering Limitations
- BMS high-rate cutoff limits can terminate discharge before 100% capacity is drained.
A 100Ah AGM lead-acid battery under a 100A load (1C) suffers severe Peukert collapse, lasting only ~28 minutes; a 100Ah LiFePO4 battery under the same load runs for ~55 minutes.
In 1897, German scientist Wilhelm Peukert proved that the available capacity of a lead-acid battery decreases non-linearly as the rate of discharge increases:
For lead-acid batteries with a Peukert exponent $k \approx 1.18$ to $1.25$, pulling a heavy 1500W microwave load through an inverter drains the battery up to 40% faster than pulling the same energy at a slow 50W trickle.
Conversely, LiFePO4 lithium batteries have an almost perfectly flat Peukert exponent ($k \approx 1.02$ to $1.04$). You can draw heavy inverter currents without suffering the steep internal chemical resistance losses seen in lead-acid cells.
Frequently Asked Questions
How long will a 100Ah battery run a 500W load?
On a 12V system, a 500W load powered through an inverter (88% efficiency) draws approximately 47.3 Amperes DC. From a 100Ah LiFePO4 battery with 80Ah usable capacity, runtime is approximately 1.7 hours (102 minutes). On a lead-acid battery, Peukert's law reduces usable capacity under high C-rates, delivering under 1.1 hours.
What is Peukert's Law and how does it affect battery runtime?
Peukert's Law dictates that the available capacity of a lead-acid battery decreases rapidly as the rate of discharge increases. While a 100Ah battery can deliver 5A for 20 hours (the standard 20-hour rating), drawing 50A will deplete the battery in under 1 hour rather than 2 hours. Lithium batteries have a near-ideal Peukert exponent (1.02 to 1.05), delivering virtually full nameplate capacity even under heavy loads.
How does inverter idle consumption affect battery runtime?
Pure sine wave inverters consume between 15W and 45W of continuous standby power (idle tare loss) simply by being switched on, even with no AC appliances plugged in. Over a 24-hour period, an idle 3000W inverter consumes 40Ah to 60Ah of 12V battery power, which can deplete smaller battery banks.
How do you calculate runtime for a 12V compressor refrigerator?
Compressor 12V fridges cycle on and off based on ambient temperature. A typical 50L fridge draws ~45W when running, but operates at a 30% to 50% duty cycle in moderate weather, consuming an average of 1.2A to 1.8A per hour (30-45 Ah per day). A 100Ah lithium battery can power such a fridge for 2 to 3 full days without recharging.