APR and APY are not the same thing, and the gap widens with compounding frequency. Enter either one and this calculator gives you the other, alongside a comparison across frequencies.
Equivalent APY
10.5156%
APR 10% compounded daily
| Compounding | Periods/year | APY |
|---|---|---|
| Daily | 365 | 10.5156% |
| Weekly | 52 | 10.5065% |
| Every 2 weeks | 26 | 10.4959% |
| Monthly | 12 | 10.4713% |
| Quarterly | 4 | 10.3813% |
| Annually | 1 | 10% |
| Continuous | ∞ | 10.5171% |
Notice where the diminishing returns sit: going from annual to monthly gains almost half a point, while going from daily to continuous gains hundredths. The base rate matters far more than the frequency.
APR is a nominal rate: it describes what something yields over a year without accounting for interest earning further interest. APY is the effective rate: it includes that compounding. So for the same underlying yield, APY is always equal to or greater than APR, and the gap depends on how often compounding happens.
The formula is direct. Starting from an APR expressed as a decimal and n compounding periods per year, APY is (1 + APR/n)^n - 1. A 10% APR compounded annually is still a 10% APY. Compounded monthly it becomes 10.47%. Compounded daily, 10.52%. In the limit, with continuous compounding, the expression converges to e^APR - 1, which is 10.52%.
What is interesting is where the diminishing returns sit. Going from annual to monthly gains almost half a percentage point; going from daily to continuous gains less than a hundredth. Protocols advertising per-block compounding are not offering much more than one compounding daily: the real advantage is in the base rate, not the frequency.
In DeFi this distinction matters more than usual because platforms are not always consistent. Some lending protocols publish APR and leave compounding to you; others publish APY assuming you reinvest every block, which is only true if the protocol auto-compounds. If you have to claim and reinvest manually, the gas on each claim eats part of the advantage, and for small positions it can make more frequent compounding actively worse. These numbers are mechanics, not a forecast: an advertised DeFi rate can change from one block to the next.
