APY to APR Converter

DeFi protocols quote APY, lending platforms quote APR, and the difference between the two becomes meaningful at higher rates and longer time horizons.

This converter takes either rate plus a compounding frequency and returns the other. APR is the simple annual rate ignoring compounding. APY (also called EAR or APY) is what you actually earn after compounding the simple rate at the stated frequency. At 5% APR compounded daily, the APY is about 5.13%. At 50% APR compounded daily, it's 64.8%.

The practical use is comparing offers across platforms that quote rates differently. A protocol advertising 12% APY isn't equivalent to a competitor offering 12% APR — the APR equivalent of 12% APY (daily compounding) is about 11.33%, which can be enough to flip your decision.

The formula is simpler than it looks. APY = (1 + APR/n)^n − 1, where n is the compounding frequency per year. APR = n × ((1 + APY)^(1/n) − 1) for the reverse direction. As n approaches infinity, both formulas converge to the continuous case: APY = e^APR − 1, which is the cleanest mathematical form. For most rates you'll encounter, the difference between daily compounding (n=365) and continuous compounding is well under a hundredth of a percent — but it matters when you're comparing yields across protocols that quote differently.

Worked example: a DeFi lending pool advertises 12% APY. Compounding daily, that converts to about 11.33% APR. A competing pool advertises 11.5% APR. At first glance the second one looks worse, but converted to APY it's 12.18%. The competitor is actually better. This kind of comparison is why the converter exists — different protocols quote differently, and the headline number isn't always the right comparison.

The pain you avoid: getting fooled by big APYs. Liquidity mining programs in the 2020-2021 DeFi wave routinely advertised four- and five-digit APYs ('30,000% APY!') that mathematically required the underlying token price to stay constant for a year while the protocol kept paying out at the current rate. Neither assumption held. Converting to APR doesn't fix that, but it strips the compounding amplification and makes the underlying simple rate visible. A protocol paying 10,000% APY is paying about 461% APR. Still huge, but the gap from APY to APR tells you it's compounded heavily, which means it depends on continuous reinvestment.

What APY can't tell you: token-denominated yield versus stablecoin yield. A protocol paying 50% APY in its native token can be worth less in dollars than a stablecoin pool paying 5% APY, if the token price drops 50% during the year. Always think about yield in the asset you actually want to end up holding. APY-to-APR conversion is just arithmetic — the substantive decision is which currency the yield denominates in, and that's a separate question.