Is expiation (kaffarah) obligatory for one who swore to do a specific act while angry, then did not carry it out after calming down? And what is its measure if it is obligatory?

Whoever swears an oath and then sees that something else is better than it, must do that which is better and expiate their oath, according to the Hadith of the Prophet (peace be upon him).

Since you have refrained from the action that involved error, you have been guided to what is correct, and you are required to offer an expiation for the oath.

The expiation for an oath is: feeding ten needy persons from the average of the food you provide your own families, or clothing them, or freeing a slave. And whoever cannot find any of these, then they must fast for three days; as Allah says: "Allah will not impose blame upon you for what is unintentional in your oaths, but He will impose blame upon you for what you intended of oaths. So its expiation is the feeding of ten needy people from the average of that which you feed your [own] families or clothing them or the freeing of a slave. But whoever cannot find [or afford] – then a fast of three days. That is the expiation for your oaths when you have sworn. And guard your oaths. Thus does Allah make clear to you His verses that you may be grateful." (Al-Ma'idah: 89).

For feeding, it is sufficient to give one and a half kilograms of wheat, rice, or similar food to each needy person, or to feed them a lunch or dinner. For clothing, a garment that is sufficient for prayer and protects from heat or cold is enough.