Sword damage with armor in Minecraft Bedrock

The fun way to know it would be to go into creative mode, spawn a few volunteers, give them some armor, and science it out :)

The quick way to know it is to check the Wiki page on armor, and the part specific to Bedrock Edition.

According to those pages, each armor point reduces 4% of the damage taken. For a full, unenchanted set, that would be 80% less with diamond or netherite, 60% less with iron, 48% with chainmail, 44% with gold _{(huh, I thought it was better than iron but less durable!)}, and 28% less damage with leather.

If your diamond sword deals 8 damage points per hit, somebody wearing iron armor would take only 3.2 damage points, without any enchantments or critical hits.