I keep a small mental note every time a farm dashboard flashes a number at me, because half the time I cannot tell whether the protocol is quoting me APR or APY, and the two are not close once the rate gets big. A pool advertising 12 percent and a pool advertising 12 percent can be earning very different things depending on which one you are actually looking at, and nobody labels it clearly. So before I compare any two yield opportunities, the first thing I do is figure out which unit each one is quoted in and convert them both to the same one. It sounds pedantic. It is the single cheapest edge available in DeFi.
What the two numbers actually mean
APR is the simple rate. If a pool pays 10 percent APR and you deposit and never touch it, you get 10 percent over a year, full stop. It assumes no compounding. It is a straight line.
APY is the compounded rate. It assumes you take whatever you earn and put it back to work at some frequency, so you start earning yield on your yield. The more often that reinvestment happens, the higher the effective return, even though the underlying rate never changed. Same engine, different accounting.
The conversion between them is where people get lost, so here is the actual formula. If you have a nominal APR of r and you compound n times per year, then APY equals (1 + r divided by n) raised to the power of n, minus 1. That is it. If n goes to infinity, meaning you compound continuously, APY approaches e to the power of r, minus 1. You will basically never hit the continuous case in practice, but it tells you the ceiling.
Two things fall out of that formula immediately. First, at low rates the gap between APR and APY is tiny. A 5 percent APR compounded daily is roughly 5.13 percent APY, which is noise. Second, the gap explodes as the rate climbs, because you are raising a bigger number to a power. This is the part that matters in DeFi, where the headline rates are absurd.
Why a 100 percent APR farm is not a 100 percent return
Here is where the intuition breaks for most people. Say a farm quotes 100 percent APR. Feels like your money doubles in a year. It does not, and the direction of the error depends on whether they mean APR or APY.
If 100 percent is a true simple APR and you never compound, you earn exactly 100 percent. You do double. But almost no yield farm works that way, because rewards drip out continuously and you can harvest and re-stake them. If you take that same 100 percent APR and compound it daily, the APY is closer to 172 percent. Compound it hourly and you are near 171 to 172 percent as well, since you are already close to the continuous ceiling of roughly 172 percent. So the honest reinvested return on a 100 percent APR farm, if gas is free and the rate holds, is much higher than 100 percent.
Now flip it. If the dashboard is showing you 100 percent APY, that is the compounded number already, and the underlying simple rate is lower. Back it out and the APR sitting behind a 100 percent APY compounded daily is roughly 69 percent. So the same headline of 100 percent describes two very different pools depending on the label. Quoting APY makes a farm look bigger. Quoting APR makes it look smaller. Protocols pick whichever flatters them, which is exactly why you cannot compare two farms until you have forced them into the same unit.
The part the formula does not tell you: reward-token decay
All of the math above assumes the thing you earn holds its value. In DeFi that assumption is usually wrong. Most high-APR farms pay you in the protocol's own emission token, and those tokens are frequently being minted faster than anyone is buying them. So while you are compounding your position number, the price of each unit you earn is sliding underneath you.
A quoted APY is denominated in the reward token. Your actual return is denominated in whatever you care about, usually a stablecoin or ETH or BTC. If a farm pays 200 percent APY in a token that loses 60 percent of its price over the same period, your real return is a fraction of the sticker, and it can easily go negative. I have watched pools quote triple-digit yields the whole way down while every farmer in them was quietly losing money in dollar terms. The dashboard was not lying about the token count. It just was not measuring the thing that pays your rent.
So the reward token price path is the hidden variable, and it is the one that actually decides whether the farm was worth it.
A workflow for normalizing any quoted rate
When I look at a new opportunity, I run the same short checklist before I compare it to anything else.
- Figure out the unit. Is this APR or APY? If the page does not say, assume nothing and look for the compounding frequency. If they mention compounding or auto-compounding, it is probably APY.
- Convert everything to APR, the simple base rate, so all your candidates are on one ruler. Use the formula backward: APR roughly equals n times the quantity (1 plus APY) to the power of 1 over n, minus 1.
- Ask what token pays the yield. If it is the protocol's emission token, treat the headline as optimistic and mentally haircut it for expected price decay.
- Subtract your real compounding cost. Auto-compounders and gas eat into the reinvestment loop. On an expensive chain, compounding daily can cost more than it earns on a small position, which collapses your APY back toward the raw APR.
- Re-quote everything in the asset you actually hold. A yield in a depreciating token is not comparable to the same yield in a stablecoin, no matter what the two APYs say side by side.
The rule of thumb I keep is simple. At single-digit rates, APR and APY are basically interchangeable and you can ignore the distinction. Above roughly 20 or 30 percent, the gap is large enough that mislabeling it changes your decision, and above 100 percent the label matters more than a lot of people's actual due diligence. That is exactly where protocols love to quote the flattering number.
None of this requires fancy tooling. It is one formula and the discipline to apply it before you deploy capital instead of after. When I am lining up several opportunities across chains, I normalize them all to the same base rate and the same settlement asset first, which is the kind of boring pre-trade check we bake into how we surface yields inside Blockcircle, and only then do I compare. The farm that wins on the raw dashboard is often not the one that wins once everything is quoted in the same terms, and the whole point of the exercise is to find out which is which before your money is already in.