Use 'on the button' to show confidence in the precision of something, like a guess or estimate. He declared that his estimate was right on the button, and it turned out he was correct.
Pro Tip 2/3
Positive Connotation
'On the button' often carries a positive feeling, praising someone's accuracy or correctness. Your answer to the complex question was on the button!
Pro Tip 3/3
Casual Speech
The phrase is informal and is typically found in casual conversation, not in formal writing or speech. When talking about exact measurements, she said it was right on the button.