Battery Runtime Calculator

Runtime estimation converts a charge rating into an energy budget and then divides by demand. Cell capacity is normally quoted in milliamp-hours, which measures charge rather than energy; multiplying by nominal voltage gives watt-hours, so 5,000 mAh at 3.7 V is 18.5 Wh. Nominal voltage is a representative average over the discharge, not a constant. A lithium cobalt oxide or NMC cell rated at 3.7 V actually runs from about 4.2 V fully charged down to a 3.0 V cutoff, while lithium iron phosphate is quoted at 3.2 V and a lead-acid cell at 2.0 V. Dividing usable energy by load power in watts yields runtime in hours. The efficiency term absorbs everything between the cell terminals and the load. Switching regulators typically run 85 to 95 percent efficient, linear regulators often only 50 to 70 percent, and internal resistance dissipates further energy as heat. C-rate, meaning discharge current divided by rated capacity, is the other major correction: a cell characterised at a 0.2C discharge will deliver noticeably less than its nameplate capacity at 1C or 2C, an effect described empirically by Peukert's law. Temperature and age compound the shortfall. Below 0 degrees C available capacity commonly falls 20 to 40 percent, and most lithium-ion cells retain only about 80 percent of original capacity after 300 to 500 full cycles. A calculated runtime should therefore be read as an optimistic upper bound for a new cell at room temperature.

The ampere-hour became the standard way to rate a cell during the second half of the nineteenth century, once electrochemical storage moved from laboratory curiosity to industrial equipment. Alessandro Volta's pile of 1800 demonstrated sustained current from a chemical stack, and Gaston Plante's lead-acid cell of 1859 provided the first practical rechargeable battery, refined by Camille Faure in 1881 into a form that could be manufactured in quantity for telegraph and lighting service. Rating by charge rather than energy suited an industry in which cell chemistry, and therefore voltage, was effectively fixed across products. The rate dependence of capacity was quantified by the German scientist Wilhelm Peukert, who in 1897 published the empirical relation showing that available capacity of a lead-acid battery declines as discharge current rises. Lithium-ion changed the numbers rather than the method. John Goodenough's identification of lithium cobalt oxide as a cathode material in 1980, together with Akira Yoshino's carbon anode work later that decade, allowed Sony to commercialise the first lithium-ion cell in 1991; Goodenough, Yoshino and M. Stanley Whittingham shared the 2019 Nobel Prize in Chemistry for that lineage. Regulatory practice has since partly returned to energy units, with air transport rules issued through ICAO and IATA written in watt-hours rather than milliamp-hours.