Amp Hour Calculator

The Ah calculator converts the basic relationship of batteries - charge equals current times time - into various values needed for planning energy systems. Enter two of three values (capacity, current and time), and the calculator will calculate the third value. If you add in voltage as well it will convert Ah to Wh. After opening the additional area it takes into account depth of discharge, determines specifications of battery combinations (in series or parallel) and shows C-rating.

What are ampere hours?

Ampere-hours (Ah) measure charge. They tell you how much charge one amp of current will carry in an hour. So a battery with 100 Ah can theoretically supply 100 amps for one hour, 10 amps for ten hours or 1 amp for one hundred hours.

Milliampere hours (mAh) are one thousandth of an amp hour so a 1000 mAh smartphone battery has the same capacity as a 1 Ah battery. Amp hours describe charge not energy. To get energy you also need voltage, and that's where watt hours come in.

How to use this calculator:

Begin with the triangular relationship for charge. Fill in two of three values (battery capacity, load current and time), leaving the third value blank. The calculator will compute the value you left out. So using this same tool, you can determine how long a battery will last at a given load, calculate the capacity required for a task or figure out what continuous current a battery can supply.

To display the stored energy shown in watt hours, first set the system voltage, typically to 12, 24 or 48 volts. Then select the desired panel. The discharge depth and efficiency convert the theoretical run time into a realistic plan value. The battery module panel indicates whether the cells are connected in series or parallel. The C-Rate panel shows the current strength and time behind the values of 1C or 0.5C.

Ampere hour formula:

The charge is equal to the product of current and time:

Q (charge in ampere-hours), I (current in amperes) and t (time in hours). Rearranged, this gives: the run time is equal to capacity divided by current.

For example, a 50 Ah battery powering an appliance that draws 10 amps has a theoretical run time of 50 divided by 10, or 5 hours. If the discharge is limited to 80 percent depth of discharge, then the actual run time reduces to 4 hours, which is the figure to use for planning purposes.

Conversion of Ampere hours to Watt hours.

It is not enough to just state the ampere-hours (Ah) to determine how much energy a battery stores as the energy also depends on the voltage. To obtain watt-hours (Wh), multiply the ampere-hours by the volts:

A battery with a voltage of 12V and capacity of 100Ah stores an amount of energy that is equal to 100 multiplied by 12, or 1200Wh. The same amount of energy of 1200Wh can also be stored in a system with a higher voltage of 24V but lower capacity of only 50Ah. For this reason it's fairest to compare batteries based on their watt-hours. Conversely you divide the watt-hours by the voltage:

Discharge depth, series and parallel connection as well as C-rate

In actual use batteries should not be fully discharged. Lead acid battery banks typically have a depth of discharge of about 50 percent while Lithium can tolerate up to 80 to 100 percent. The usable capacity is the rated capacity multiplied by this percentage, and losses from the inverter reduce it further.

The wiring affects the battery bank. When batteries are wired in series, voltages add up while amp hours remain the same. When batteries are wired in parallel, amp hours add up while voltage remains the same. The C rate describes how fast a battery is charged or discharged: at 1C rate, a 100 Ah battery will charge or discharge with 100 amps and be empty within an hour; at .5C rate it will charge or discharge with 50 amps and take two hours.

The following table lists the symbols used by this calculator.

Purpose of the ampere hour calculator:

It can be used to determine the battery specifications for solar installations, motorhomes, boats and off-grid systems, estimate the run time of devices or emergency power supplies, compare battery banks in watt-hours. Engineers use it to check if a battery can handle the load of an engine or actuator while hobbyists use it to plan the running time of drones and cellphones on batteries.

Tips for realistic estimates:

Consider the results in ampere-hours as a best case scenario. Temperature, ageing and high discharge rates reduce available capacity, and the Peukert effect means lead acid batteries deliver less power at higher loads. Plan with some safety margin, use the panel to indicate depth of discharge and compare different voltage batteries in watt hours.

This calculator is for educational and planning purposes only. The actual battery performance will vary with temperature, ageing, discharge rate and chemical composition. Therefore please treat the results as estimates, and consult manufacturer's data sheets for critical systems.