APY vs APR: The Compounding Math Every DeFi Yield Quoter Hopes You Ignore

You're shopping for a place to park the same stablecoin, and two platforms are competing for your deposit. Platform A advertises 20% APR. Platform B advertises 22.13% APY. B looks better by more than two full points — and if you move your money for that reason, you'll be choosing between two numbers that describe, mathematically, the identical offer.

That's not rounding. A 20% APR compounded daily produces exactly a 22.13% APY. The two platforms are stating the same economics in different units — the way 100 kilometres and 62.1 miles are the same distance. The trouble is that DeFi rarely labels its units, and the industry has learned that the bigger-looking number wins the deposit.

APR and APY aren't competing measures of profitability. They're the same yield, expressed before and after compounding. Once you can convert between them, most of the noise in yield dashboards collapses into something you can compare — and a few famous "too good to be true" numbers reveal themselves for what they are. Here's the formula, two tables worth bookmarking, a worked example, and the five quoting traps that decide your real return.

Same letters, different promises

Start with one-sentence definitions, because everything else follows from them:

• APR (Annual Percentage Rate) describes a rate: simple annualized interest with no reinvestment assumed. Earn 1% a month and the APR is 12%.
• APY (Annual Percentage Yield) describes an outcome: what you end the year with after each period's earnings are added to the balance and start earning on themselves. Earn 1% a month, reinvest it, and the APY is 12.68%.

Because APY counts the compound effect and APR doesn't, one rule is absolute: for the same underlying rate, APY ≥ APR — always. The two only meet when compounding happens once a year or never. A protocol whose APY is higher than its APR isn't being generous, and one quoting APR while rivals quote APY isn't being modest. In both cases, someone picked the unit that flatters the product.

DeFi inherited that TradFi playbook and added a twist: the same protocol will quote whichever unit makes its dashboard look better, sometimes across near-identical products. The unit was chosen for marketing, not comparability — which is exactly why you need to be able to move between them yourself.

The conversion formula (and a table to bookmark)

The bridge between the two units is a single formula:

where n is the number of compounding periods per year. APR/n is the rate per period, the exponent compounds it, and subtracting 1 leaves the annual growth. In the mathematical limit of continuous compounding, the formula becomes APY = e^APR − 1 — the ceiling that no amount of extra frequency can beat.

Here is one rate — 10% APR — expressed as APY at every common frequency:

Two lessons hide in that table. First, at ordinary rates frequency matters less than intuition suggests: daily compounding on 10% adds about half a point, and nothing beyond daily adds anything visible — daily and continuous both round to 10.52%. Second, most of the compounding benefit is already captured by monthly. That detail becomes money later, when gas enters the picture.

A worked example: suppose a product pays 5% APR and compounds it daily (we'll see shortly who actually does this in practice). Deposit $10,000 and after one year you hold $10,000 × (1 + 0.05/365)^365 ≈ $10,513. What you'd actually measure — the outcome — is 5.13% a year. That's the APY. The 5% was the promise; 5.13% is the truth the formula produces, and only because compounding really happened 365 times.

The gap explodes as rates climb

At 10%, compounding is a rounding error. At DeFi rates, it's a headline. Because compounding is exponential, the APR→APY gap doesn't grow linearly — it accelerates. Daily compounding (n = 365):

Read the last row in reverse, too: a farm showing "200% APY" is, in its best case, describing an APR of about 110% — a promise to more than double your money before a single compounding event, held constant for a year. Numbers in this range should trigger more questions than excitement.

The practical rule: at low single-digit rates, casually comparing APR to APY costs you little. At double-digit rates, comparing without converting is the miles-versus-kilometres mistake — same trip, different numbers, wrong conclusion. The 20% APR vs 22.13% APY scenario from the opening was the smallest version of it.

Who actually compounds for you?

The formula quietly assumes every reward is reinvested the instant it's earned. In practice, someone has to do that — and the unit a product quotes often tells you who:

So when a staking product quotes APR, read it as a quiet disclosure: the compounding you're imagining is your job — one gas-paid transaction at a time. When an LST quotes APY, the mechanism does it for you; our LST yield staking guide covers the rebasing-versus-price-accrual mechanics. Neither number is wrong, but only one of them matches the formula's assumption out of the box.

Five quoting traps (the part most explainers skip)

Converting units is necessary but not sufficient. These five traps are why even a correctly converted APY can fail to describe your year. Each comes with a check you can run before depositing.

Trap 1: The quote assumes a constant rate for a year

APR and APY both annualize a snapshot: "this rate, held for 365 days." DeFi rates reprice every block as utilization, emissions and TVL shift — a lending pool at 20% APY today can be at 6% next month, and a farm can fall to near zero when its incentive program ends. Check the 30-day average rate, not the spot number — DeFiLlama's yields dashboard shows both side by side. For a sense of what realistic, durable rates look like, see our rundown of the best stablecoin yields in 2026.

Trap 2: High APY is usually an emission schedule

When a protocol pays 80% APY in its own token, it is mostly printing its reward and handing it to you. That's a token distribution with extra steps, not durable yield: sell pressure grows as emissions flow, and your realized return is the quoted APY multiplied by however far the token falls. Emissions yield and real yield — paid in assets others actually want, like ETH, USDC or protocol fee revenue — are different animals, and we separate them in Real Yield vs Emissions. Check: what token is the reward paid in, and who is structurally buying it?

Trap 3: Compounding is never automatic — and gas can flip it negative

Every claim-and-restake is a transaction: roughly $5–15 on Ethereum mainnet, cents on a healthy L2. Weekly harvesting on mainnet means 52 transactions a year — $260–780 — to capture perhaps two or three extra points of APY. On a $500 deposit that's spectacularly negative carry: the chain out-earns you. On an L2 the same discipline costs a few dollars, which is why small portfolios should compound on L2s or not at all. We ran the full break-even math in Gas Fees vs Yield. Check: (extra APY × position size) versus (number of claim transactions × gas).

Trap 4: APY excludes every other cost you'll pay

The quoted number is gross. It ignores gas on entry and exit, swap slippage, management and performance fees, lockups and unbonding windows — and, if you're a liquidity provider, impermanent loss, which is frequently the biggest omitted line of all. Check: build the net stack before depositing; our impermanent loss guide covers the LP case.

Trap 5: Comparing platforms without normalizing units

The opening scenario, generalized: any "comparison" of 20% APR against 22.13% APY — or of 12% against 12.5% at different compounding frequencies — is unit-shopping, however unintentional. Check: convert every offer to APY at daily compounding (or everything to APR) before ranking them.

Here's the sentence worth keeping: APR tells you a rate; APY tells you where a rate goes if someone keeps reinvesting it. Neither tells you what you'll earn — only a net calculation does.

So run it. Convert every quote to the same unit, ask what token the yield is paid in and who's buying it, count the gas your compounding schedule will burn, and subtract everything the headline left out. If you'd rather not hand-evaluate (1 + r/n)^n, the DifiCalc yield calculator converts APR↔APY, models any compounding frequency, and nets out gas and fees before you commit a dollar.

And one question to carry into your next dashboard session: when a protocol shows you a triple-digit APY — who is on the other side of that trade, and what do they get out of it? If you can't answer in ten seconds, that number isn't a return. It's an invitation.

Sources and further reading

• Investopedia — Annual Percentage Rate (APR) — the standard definition and how lenders use it to look cheaper.
• Investopedia — Compound Interest — the math that turns an APR into an APY.
• ethereum.org — Staking — how native staking rewards accrue, and why compounding them is on you.
• DeFiLlama Yields — pool-level rates with 30-day averages, for reality-checking any quote.

Frequently asked questions

Is APY better than APR?

Neither is better — they're different units for the same yield. APY includes compounding and APR doesn't, so for the same offer APY ≥ APR, always. APY is the more useful number for savings-style products where reinvestment actually happens; APR is the more honest number for products whose rewards sit idle until you redeploy them. What matters is converting both to one unit before comparing.

How do I convert APR to APY?

Use APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year — 365 for daily. For example, 20% APR compounded daily is (1 + 0.20/365)^365 − 1 = 22.13% APY. For continuous compounding the limit is APY = e^APR − 1. To convert back, APR = n × ((1 + APY)^(1/n) − 1).

Does DeFi yield compound automatically?

Usually not. Most lending markets and LP farms credit rewards as separate tokens that sit idle until you manually claim and restake them — and every step costs gas. The exceptions: liquid staking tokens such as stETH and jitoSOL compound automatically through rebasing or price accrual, and auto-compounder vaults harvest and reinvest for you in exchange for a performance fee. A product quoting APR rather than APY is often quietly telling you the compounding is your job.

Why is quoted APY never what I actually earn?

Four things stack up: quotes annualize a snapshot of a rate that moves every block; headline APYs are frequently paid in inflationary emission tokens whose price falls as supply grows; compounding requires transactions whose gas can exceed the benefit on small positions; and the quote excludes gas, slippage, fees, lockups and impermanent loss. A 20% headline on a small LP position can net out to single digits — or negative.

Related reading: Real Yield vs Emissions (what's actually funding that APY), Gas Fees vs Yield (the compounding break-even math), Impermanent Loss (the LP's hidden cost) and LST Yield Staking (compounding done for you). More in the DifiCalc blog.