A matched betting calculator is solving one specific, well-defined arithmetic problem: given the odds on both sides of a bet, what size does the second bet need to be so the overall result comes out close to the same regardless of which side wins. Here is what it is actually doing underneath.
The basic idea
Start with a bonus bet or qualifying bet of a known size, at known odds. The calculator needs to find a cover stake, at the odds available on the opposing side, such that the payout if the first bet wins, minus what is lost on the cover, comes out close to equal to the payout if the cover wins instead, minus what is lost on the first bet. Set those two outcomes equal to each other and solve for the cover stake, and that is the core of the calculation.