Battery Capacity Calculator (Ah, Wh and Runtime)

The difference between Ah and Wh

Amp hours (Ah) describe how much charge a battery can deliver, watt hours (Wh) how much energy it stores. Voltage links the two:

Wh = Ah × V

A 12 V 100 Ah battery holds 1200 Wh and a 24 V 100 Ah battery holds 2400 Wh. Compare batteries of different voltage by Wh, not Ah.

How long will a battery run a load?

t = Ah × V × k × η / P

k is the share of rated capacity that is really used, η the efficiency of the inverter between battery and load, and P the load power.

Example

A 12 V 100 Ah battery feeds a 120 W load through a 90 percent efficient inverter, using half of its capacity. Usable energy is 1200 × 0.5 × 0.9 = 540 Wh and the runtime is 540 / 120 = 4.5 hours. The battery supplies 120 / (0.9 × 12) = 11.1 A.

Why is usable capacity below 100 percent?

The capacity on the label applies to a stated discharge time. Discharge the battery faster and it delivers less. Draining a battery completely also shortens its life, so manufacturers give a depth of discharge limit. The share varies a lot between battery types: take it from the manufacturer's data.

Limits

The calculation holds voltage constant and ignores temperature and ageing. The runtime is a first estimate. For loads that must not stop, size the runtime from the manufacturer's constant power discharge tables and add an ageing margin.