Battery Runtime & Capacity
How long a battery runs a load, or the Ah/Wh needed for a runtime, from voltage, capacity, depth of discharge, inverter efficiency and a Peukert exponent.
Runtime in hours (or the capacity to buy), the watt-hours actually usable, the current the battery sees, the C-rate, and the Peukert-corrected figure when you give the exponent.
Example: A 12 V 100 Ah battery cycled to 50 % holds 600 usable Wh: a 60 W load runs 10 h. For 8 h at 120 W you need 160 Ah — 166 Ah with a Peukert exponent of 1.2.
Watt-hours in,
watt-hours out.
The energy arithmetic, what depth of discharge and inverter loss do to it, when the Peukert correction applies, and what a nominal capacity does not promise.
Runtime and capacity
A battery's energy is voltage × amp-hours (Wh = V × Ah); the part you may use is that × depth of discharge. A load of P watts through an inverter of efficiency η draws P ÷ η from the battery, and P ÷ η ÷ V amperes. Runtime = usable Wh ÷ battery watts. The reverse question — capacity for a wanted runtime — is the same equation solved for Ah: (P ÷ η × hours) ÷ DoD ÷ V. A load given in amps is taken at the battery, after the inverter.
Peukert's correction
Lead-acid capacity depends on how fast it is drawn: a 100 Ah (20 h) battery gives less than 100 Ah at 10 A. Peukert's relation captures it: t = H × (C ÷ (I × H))^k, with C the rated capacity at the H-hour rate and k the battery's exponent (from the datasheet or a two-rate test; 1 means no correction). At exactly C/H the result equals the ideal; above it the runtime shrinks, below it grows. The depth-of-discharge fraction is applied to the corrected full-discharge time — an approximation the page states. Lithium packs have exponents near 1 and are better handled by the datasheet's discharge curves.
Depth of discharge and efficiency
Both default to 100 % — meaning no allowance, not a recommendation. Cycle life falls steeply with depth of discharge for most chemistries, and inverters lose a few to fifteen percent depending on load; the right figures are on the battery and inverter datasheets and depend on how many cycles you want. The C-rate (current ÷ capacity) is shown so you can check it against the battery's continuous discharge limit.
What the number does not settle
Nominal capacity is measured new, at the rated current and temperature. Age, cold, high currents and the inverter's low-voltage cutoff all reduce what you get; a loaded battery's voltage also sags, so a constant-power inverter draws more current near the end. Charging, fusing and wiring are the datasheet's and the code's. Inputs stay in your browser; the same four anonymous usage counts as the rest of the site apply.