Two personas, different arcana
Look up the two arcana on the fusion chart to find the result's arcana. Then add the two base levels, divide by two, round down and add one. The result is the lowest persona of that arcana whose base level is at least that number.
Example: Izanagi (Fool, level 1) + Pixie (Magician, level 2) gives a level target of 2 in the Temperance arcana, so the result is Apsaras (level 4).
If the target is higher than every persona in that arcana, you get the strongest one available. If the result would be one of your two ingredients, the game moves up to the next persona instead.
Two personas, same arcana
Fusing two personas of the same arcana always produces that arcana. The game takes the averaged level plus one and gives you the strongest persona at or below it, skipping both ingredients. This is useful for stepping down to a persona you skipped.
Three personas
Triple fusion uses a second chart. The highest-level ingredient is set aside; the other two are combined into an intermediate arcana; then that arcana and the set-aside persona's arcana give the final arcana. The level target is the average of all three base levels plus 4.25, and the result is the lowest persona at or above it. See the triple fusion guide.
Personas you can't fuse normally
17 personas only come from special fusions with a fixed ingredient list. The strongest persona of each arcana also requires its Social Link at rank 10. Our calculator marks both, and its recipe filter can hide them.
Your level matters
You can't create a persona whose base level is above your own level. If a recipe gives a persona you can't make yet, level up first or pick a lower recipe from the list.