Battery Capacity Calculator

An electrical battery comprises two electrodes, a cathode (-ve) and an anode (+ve), a separator and an electrolyte.
Whilst the cathode is generally regarded as negative and the anode is generally regarded as positive, this arrangement specifically refers to flow direction, so, in some applications, this positivity relationship may be reversed.

In a typical lithium-ion battery, these components are usually made from the following materials^#:
The anode is made from graphite.
Carbon in this form allows the intercalation of lithium atoms within its lattice structure without significantly changing its volume, although this works best with small atoms such as lithium, beryllium, boron, etc.
The cathode is made from a lithium-metal oxide such as; Li.Mn₂.O₄, Li.Co.O₂, Li.Fe.O₄.P, etc.
The separator allows the flow of positively charged ions, but not negatively charged electrons. It is usually made from Mn.O₂.
The electrolyte is the substance that carries the lithium ion between the electrodes. It is usually a lithium salt; Li.As.F₆, Li.Cl.O₄, Li.P.F₆, Li.B.F₄, Li.C.F₃.S.O₃, etc. dissolved in an organic solvent such as; C₃.H₄.O₃ or C₅.H₁₀.O₃
However, as long as the anode accommodates the donor ions, the cathode possesses donor atoms, and the electrolyte facilitates the flow of donor ions, the donor can be any atom. The reason we have defaulted to lithium for the donor atom is because it has the highest specific energy capacity and is the easiest to intercalate.

# Li.Mn₂.O₄ = Lithium manganese oxide, Li.Co.O₂ = Lithium cobalt oxide, Li.Fe.O₄.P = Lithium iron phosphate, Mn.O₂ = Manganese oxide, Li.As.F₆ = Lithium Hexafluoroarsenate, Li.Cl.O₄ = Lithium perchlorate, Li.P.F₆ = Lithium hexafluorophosphate, Li.B.F₄ = Lithium tetrafluoroborate, Li.C.F₃S.O₃ = Lithium triflate, C₃.H₄.O₃ = Ascorbic acid, C₅.H₁₀.O₃ = Diethyl Carbonate

Fig 1. A Typical Battery

The arrangement looks something like Fig 1, albeit the electrodes may be any shape, and preferably thin-flat sheets (usually coiled) in rechargeable batteries in order to minimise the ion-flow distances and therefore charge times. That said, as discussed in our battery page, you should be aware of the problems associated with 'fast-charging', which will significantly damage and shorten the life of the battery.

The way a battery works is explained on our related web-page.

The purpose of a battery is to provide electrical energy to drive a mechanism, and this is done by ionising metal atoms; pulling the electron(s) from its outer shell, and storing the ionised atoms in the anode (during charging). When connected to your circuit, the ionised atoms will be pulled across to the cathode by the electrons flowing in the circuit. When all of the ionised atoms are in the cathode, the battery's energy will be fully drained. The amount (quantity) of energy in a battery is determined by the mass of ionised metal in its electrodes.
You can use any element you like in a battery, the only thing you need to make it work is the ionisation of its outermost electron shells. That said, however, the smaller the atomic mass, the greater the ionisation energy capacity (J/kg).
Even though beryllium, for example, has two electrons in its outer shell and the same number of shells as lithium, its RAM means that you need a third greater metal-mass to that of lithium for the same energy capacity (J/kg). And in the case of gold, you need more than 567 times the metal-mass. Moreover, the larger the atom the greater the energy required (drain) in swapping the ions between electrodes in both operation and charging.
And it is far harder to pull very large atoms through the separator, electrode shields and the electrode matter than it is for elements such as lithium.

Battery Design

The shape and size of a battery is configured to suit design specific holders and connectors, but what provides the battery with the operational power and period is the mass of ionised metal contained in its electrodes.

This mass depends upon the element used and/or its operational temperature. It can be estimated today by numerous available methods, but they are simply estimates. They concentrate on only one element (e.g. lithium) and few of which include temperature as a variable. But now we understand how atoms work, we can calculate accurately how much metal is required.

To determine this metal-mass in the battery calculator, you simply enter; operational ambient temperature, operational period and the circuit power (Watts); and Battery will tell you how much of the selected elemental-mass you need. But now, your results will be exact (not estimated) for any metal; not just lithium.

Today, the quantity of lithium (massₑ) for a battery is estimated using a factor; 3-grammes per Watt.hour; and this estimate only applies to lithium at room temperature.
But now, it is possible to calculate accurately the elemental mass (m) using the known properties of lithium at any operational temperature.
A comparison calculation for four typical battery specifications @ 300K is provided in the Table below.

battery:	CR 2016	A76 LR44	NB 4L	AA	units
battery mass	0.0019	0.0017	0.0175	0.0167	kg
energy	3	1.5	3.7	3.6	J/C (V)
flow	0.017	0.0316	0.152	0.05	C/s (A)
mass	0.001082469	0.001006059	0.011936869	0.003820477	kg
massₑ	0.000765	0.000711	0.008436	0.0027	kg
Comparison of elemental masses both estimated and calculated

This calculation not only provides yet further vindication of the Newton-Coulomb atom; it now allows us to calculate the mass for any element at any temperature. As you can see in the above Table, estimated values are not always as accurate as we would like.

Like our friction-coefficient calculator, we don't simply provide calculations for the industry norm, we provide it for any situation. It is CalQlata's understanding of the way the atom works that allows us to do this for the battery.

Battery Calculator - Technical Help

Units

You must use the metric units specified in the calculator. Imperial conversion factors are provided in the calculator's Technical Help menu item.

Input Data

Select the desired elemental matter; hydrogen to uranium. The ionic matter in most of today's batteries tend to be lithium (Z=3).
output power; P (W or J/s): energy intensity (or power rating) of the circuit or equipment to be activated by the battery.
operational temperature; Ṯ (K): the operational temperature of the battery; outer-shell proton-electron pair temperature is calculated automatically.
operational period; t (hr): this value only applies to the operational time of the circuit or driven equipment, it does not include down-time.
percentage mass; mₜ (%): the percentage ion-mass to battery mass. This currently varies between 10% and 15%.

Output Data

calculated mass; m (kg): the calculated (based upon atomic energy) ionic [matter] mass needed to operate your circuit or driven equipment.
estimated mass; mₑ (kg): the estimated (lithium only) ionic [matter] mass needed to operate your circuit or driven equipment. see Accuracy below.
energy capacity; EC (J/kg): the output energy available for your circuit or driven equipment per unit battery mass. It is important to understand that charging your battery will require four times this energy.

Applicability

Battery is applicable to any battery, factual or fictional, at any specified temperature and using any ionised element.

Accuracy

The calculated value (m) is totally accurate according to the data entered. However, the battery's performance may be limited if its other materials; electrolyte, shields, electrodes, separator, etc. are less than perfect; i.e. damaged as a result of fast-charging.
Also, battery performance is very much dependent upon connector purity, even if everything else is as it should be.
It is expected that a contingency of approximately 5% should be added to the calculated value (m).
Whilst a commonly quoted estimate of 3 grammes per Watt-hour is used in Battery, it is variously quoted between 3 & 5g/Whr. We find that 4.3 grammes per Watt-hour is most accurate. This estimated value only applies to lithium ionised metal.