Theoretical Capacity Calculator
Turn an active material formula and its electron count into theoretical mAh/g, with element mass fractions and specific energy.
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What it does
A theoretical capacity calculator answers one question: how many electrons one gram of this material can store. The answer is pure stoichiometry, the number of electrons transferred per formula unit divided by the mass of that formula unit. There is no fitting, no measurement and no assumption beyond a complete reaction, which is exactly why it is worth computing before any cell is built.
How it works
The arithmetic comes from the Faraday constant. One mole of electrons carries 96485.33212 coulombs, and one milliamp-hour is 3.6 coulombs, so one mole of electrons is 26801.48 mAh. Divide by the molar mass of the formula unit and the result is in mAh/g. For LiFePO4 the molar mass is 157.755 g/mol, so n = 1 gives 169.9 mAh/g. Multiplying by the average voltage gives specific energy: 169.9 mAh/g times 3.4 V is 578 Wh/kg, the material-level figure usually quoted as roughly 580 Wh/kg.
Worked example
Take silicon with n = 3.75: 3.75 times 26801.48 divided by 28.09 gives 3578.6 mAh/g. The same silicon with n = 1 would report 954 mAh/g, which is a perfectly ordinary looking number and completely wrong. Take graphite, conventionally written C6 with n = 1: 26801.48 divided by 72.07 gives 371.9 mAh/g. Both use the same formula; only the choice of end point changed.
When to use it
Use this when screening a new active material, when checking a capacity claim in a paper before trying to reproduce it, or when converting between gravimetric capacity and the areal loading your coating line can actually reach. It also settles the practical versus theoretical argument: if a LiFePO4 cell delivers 140 mAh/g, that is 82 percent of 169.9, and the missing 18 percent is not chemistry but inactive material, first-cycle loss and polarisation.
FAQ
- Why does the same material give different theoretical capacities?
- Because the electron count per formula unit is a choice rather than a constant. Silicon written as one atom with n = 1 gives 954 mAh/g; the value quoted everywhere, 3579 mAh/g, corresponds to n = 3.75, the fully lithiated composition Li15Si4. The same trap applies to graphite, which is conventionally written C6 with n = 1 to give 372 mAh/g; writing it as C with n = 1 would give 2232 mAh/g, one lithium per carbon, which never happens.
- What is the difference between theoretical capacity and what a cell actually delivers?
- Theoretical capacity assumes every atom reacts and nothing else is in the electrode. A real cell contains binder, conductive additive, current collector and separator, and it operates between voltage limits rather than to full conversion. LiFePO4 is the clearest example: 169.9 mAh/g theoretically, about 160 mAh/g for the material in practice, and roughly 140 mAh/g at cell level once inactive components are counted. For intercalation materials practical values land at 70 to 90 percent of theoretical; for conversion and alloying materials the gap is far larger because the first cycle consumes lithium irreversibly.
- Why is specific energy in Wh/kg equal to capacity in mAh/g times voltage?
- Because the units are constructed that way. One milliamp-hour at one volt is 3.6 coulombs times one volt, which is 3.6 joules, and 3.6 joules per gram is exactly 1 watt-hour per kilogram. So the multiplication needs no conversion factor. LiFePO4 at 169.9 mAh/g and 3.4 V gives 578 Wh/kg at the material level. Cell-level energy density is far lower, typically 120 to 160 Wh/kg, because of all the inactive mass that carries no charge.
- Can I use this for a blended or doped material?
- Not directly, because the formula unit has to be well defined for the division to mean anything. For a blend you can combine two components analytically. Capacity of a mixture is the mass-weighted harmonic mean rather than the arithmetic mean, so with capacities C1 and C2 at mass fractions w1 and w2 the mixture capacity is 1 / (w1/C1 + w2/C2). For a dopant present at a few percent it is usually easier and accurate enough to ignore it and compute the host material alone.