Estimates for 'inflation expectations': the 'breakeven' rates. What are they?

«Popular market measures of US inflation expectations are climbing sharply higher in the wake of this week’s Federal Reserve meeting, which analysts say hinted at officials being willing to tolerate higher inflation before tightening monetary policy more aggressively.

So-called “breakeven rates”, which are a rough estimate of expected inflation derived from comparing the yields of conventional and inflation-proof Treasuries, have jumped markedly this month, and have gone even higher since Wednesday’s Fed meeting»

Could you please explain how are these breakeven rates estimated? And why they can be a 'rough estimate' of expected inflation?

Any help would be appreciated.

• @Wecon Thanks, I thought that it was more complicated than that... – An old man in the sea. Mar 21 '16 at 21:45
• @Wecon, why not write up your comment as an answer? – BKay Mar 22 '16 at 14:42
• @BKay, thanks for the suggestion. My first idea was that, possibly, more thorough or formal analyses or explanations would follow. But, indeed, on second thoughts I'll remove my comment and repost it as an answer. – Wecon Mar 22 '16 at 19:38

Intuitively, this is the story: The interest rate on inflation-linked bonds (which means that the coupon payments are adjusted for inflation) can be seen as a real interest rate, because one is always exactly compensated for the realized inflation. Subtracting this real interest rate ($r$) from a nominal interest rate ($i$) gives the average inflation expectaction ($\pi^e$) over the period remaining before maturity. Just use the fisher-equation to see this: $r=i−π^e$.