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APY to APR Calculator
Convert between APY and APR at any compounding frequency, and see exactly what compounding adds.
APY vs APR, and how to convert them
APR (annual percentage rate) is the simple yearly rate with no compounding. APY (annual percentage yield) includes compounding, so it is always equal to or higher than the APR. The formula is APY = (1 + APR / n)^n − 1, where n is the number of compounding periods per year; reverse it with APR = n × ((1 + APY)^(1/n) − 1).
The more frequently interest compounds, the wider the gap. At low rates the difference is small, but at the high APRs common in DeFi it becomes significant, which is why comparing an APY against an APR without converting is misleading.
Protocols are inconsistent: lending markets usually quote APY while borrow costs are often APR. Always convert to the same basis before comparing. Otomato alerts you when the live rate on a position you hold changes, so you are comparing today's numbers, not last week's.
The complete guide
APY vs APR: the difference is compounding
APR, the annual percentage rate, is the plain yearly rate with no compounding. APY, the annual percentage yield, folds compounding in, so it is always equal to or higher than the APR. The only thing separating the two numbers is how often interest is added back to the balance.
Convert APR to APY with (1 + APR / n) raised to the power n, minus 1, where n is the number of compounding periods per year. Reverse it with n times ((1 + APY) to the power 1/n, minus 1).
Why the gap matters in DeFi
At a 5% rate the difference between APY and APR is a rounding error. At the double-digit rates common in DeFi it is large, and comparing an APY on one protocol against an APR on another without converting will point you at the wrong choice.
- Lending markets usually quote APY, with compounding baked in.
- Borrow costs are often shown as APR.
- Auto-compounders quote APY because they harvest and restake for you.
- Always convert to the same basis before you compare two yields.
Remember that DeFi rates move
Whichever basis a protocol quotes, the number is a snapshot. Supply and borrow rates float with utilization and incentives and can change within a day. Otomato alerts you when the live rate on a position you hold moves, so you are always comparing today's numbers.
Frequently asked questions
- What is the difference between APY and APR?
- APR (annual percentage rate) is the simple yearly rate with no compounding. APY (annual percentage yield) includes the effect of compounding, so it is always equal to or higher than the APR. The more often interest compounds, the wider the gap between the two.
- How do you convert APR to APY?
- APY = (1 + APR / n)^n − 1, where n is the number of compounding periods per year. To go the other way, APR = n × ((1 + APY)^(1/n) − 1). This calculator does both directions at the compounding frequency you choose.
- Which rate do DeFi protocols quote?
- It varies. Lending markets usually quote APY (compounding baked in), while borrow costs are often shown as APR. Always check which one a protocol means before comparing, because at high rates the difference is large. Otomato alerts you when the live rate on a position you hold moves.
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