APY vs APR Converter

When you compare yields across DeFi protocols, staking platforms, and crypto savings accounts, you are often comparing incompatible numbers. One platform advertises 12% APY. Another quotes 11.5% APR. A third offers 10.8% "daily compound interest." These are not the same yield expressed differently — they represent meaningfully different actual returns depending on how frequently earnings are compounded. Converting between APR and APY, and understanding what compounding frequency does to effective yield, is foundational to making accurate comparisons in crypto finance.

Realistic APY Ranges in 2026

Understanding what a given number means in context helps calibrate expectations. ETH staking through liquid protocols (Lido, Rocket Pool) offers approximately 3–5% APY — this is real yield from network fees and issuance, structurally sound and relatively low risk for crypto. USDC/USDT lending on Aave during normal market conditions yields 4–8% APY, rising toward 10–15% when borrowing demand is high near bull market peaks. BTC-correlated LP pools on major DEXes yield 5–20% APY in fees alone depending on volume and concentration. High-yield farming pools advertising 50–200% APY almost always include governance token emissions as the primary yield component — the real yield from fees or interest is far lower, and the token value supporting the high APY can decline rapidly if protocol growth slows.

The Difference Between Stated APY and Realized APY

Even when a protocol states an APY accurately based on current conditions, your realized APY will differ from the stated rate for several reasons. Stablecoin lending rates on Aave are variable and change every block as utilization rates shift; a protocol displaying 8% APY today might average 5% over your actual holding period. Fee income on Uniswap pools depends on trading volume, which fluctuates with market conditions. Governance token rewards are denominated in a token whose price changes independently of the stated yield. For any position where the APY is variable or token-denominated, the stated figure is a snapshot, not a guaranteed return. Monitoring actual yield against stated yield over the first weeks of a position provides valuable signal about whether the advertised rate is achievable.

The Core Definitions: APR vs APY

APR, or Annual Percentage Rate, is the simple annualized rate without any compounding. If a protocol offers 12% APR and pays out once a year, you earn exactly 12% on your principal. APY, or Annual Percentage Yield, is the effective annual return after accounting for compounding. If that same 12% APR compounds monthly, the APY is (1 + 0.12/12)^12 − 1 = (1.01)^12 − 1 = 1.12683 − 1 = 12.683%. The more frequently compounding occurs, the higher the APY relative to the stated APR. The relationship is strictly one-directional: APY is always equal to or greater than APR, with equality only when there is no compounding at all — i.e., annual compounding with a single payment at year end.

The Conversion Formulas

Converting APR to APY given n compounding periods per year:

APY = (1 + APR/n)^n − 1

Converting APY back to APR for the same compounding frequency:

APR = n × ((1 + APY)^(1/n) − 1)

For daily compounding (n = 365) at 12% APR: APY = (1 + 0.12/365)^365 − 1 = 12.747%. For weekly compounding (n = 52): APY = (1 + 0.12/52)^52 − 1 = 12.734%. For monthly compounding (n = 12): APY = 12.683%. For quarterly compounding (n = 4): APY = 12.551%. The differences are small at 12% but become meaningful at higher rates. At 100% APR compounded daily, APY = (1 + 1.00/365)^365 − 1 = 171.46%. At 100% APR compounded monthly, APY = 160.54%. The compounding frequency premium expands dramatically at high rates, which is why high-yield DeFi protocols that advertise APR rather than APY can create misleading comparisons.

Periodic Rate and What It Tells You

The periodic rate is the APR divided by the number of compounding periods: APR / n. At 12% APR with daily compounding, the daily rate is 12% / 365 = 0.03288%. This is the rate applied to your balance each day before being added back into principal. It seems small, but the effect over 365 applications is meaningful. The periodic rate is useful when evaluating protocols that quote fees or rates per block — particularly on Ethereum and similar chains. Block times on Ethereum average 12 seconds, producing roughly 2.6 million blocks per year. Some protocols specify yield in per-block terms because that is what the smart contract computes; multiplying the per-block rate by blocks per year gives you APR, from which you can derive APY for standardized comparison.

Practical Steps for Comparing Yields Accurately

Before allocating capital to any yield-bearing crypto product, convert all quoted rates to APY using the same compounding frequency. Identify whether the platform's compounding is automatic or manual — manual compounding reduces your effective APY to the degree that you do not reinvest promptly. Distinguish base yield (from real interest or fees) from token emission yield (governance tokens, incentive programs) and assess each component separately for risk and sustainability. Use the APY to calculate your expected 12-month ending balance on a fixed principal, then subtract any gas costs for entering, exiting, or claiming rewards — particularly relevant on Ethereum mainnet where even at moderate gas prices, small positions can see meaningful fee drag on the final realized yield.

How DeFi Protocols Use These Terms

DeFi lending and yield farming protocols compound rewards in different ways depending on their design. Aave and Compound express supply APY which already assumes continuous reinvestment — they display APY, not APR. Uniswap v3 fee income is typically quoted as APY based on fee revenue over recent periods. Many yield aggregators like Yearn Finance auto-compound rewards multiple times per day, and their displayed APY reflects that actual compounding behavior. In contrast, some protocols quote APR because they distribute tokens periodically and do not automatically reinvest them. You must claim rewards manually and decide whether to reinvest. When a protocol says "earn 20% APR in governance tokens," the APY depends entirely on how often you claim and reinvest — daily reinvestment would produce approximately 22.13% APY, but if you compound annually it remains 20%.

Why Compounding Frequency Changes the Comparison

The intuition behind compounding frequency matters for practical platform evaluation. A platform that compounds daily at 10% APR delivers 10.52% APY. A platform that compounds monthly at 10.4% APR delivers 10.904% APY — despite the lower stated APR, the less-frequent compounding produces a higher APY because the base rate is higher. Platforms that distribute rewards daily but require manual reinvestment effectively function as APR platforms from the user's perspective unless the user actively compounds. Platforms that auto-compound transform APR into a higher APY on the user's behalf. When comparing platforms, the question is always: what will my ending balance actually be in twelve months? That requires converting all rates to APY on the same compounding basis before comparison.

Continuously Compounding Interest and Its Crypto Applications

At the mathematical extreme, as compounding frequency approaches infinity, the formula converges to continuous compounding: APY = e^(APR) − 1, where e is Euler's number (approximately 2.71828). At 12% APR with continuous compounding, APY = e^0.12 − 1 = 12.75% — nearly identical to daily compounding because the practical difference between compounding 365 times per year and infinite times is very small. Some DeFi protocols that compound per-block on high-throughput chains like Solana (with sub-second block times) approach continuous compounding in practice. For most yield calculation purposes, daily compounding is a sufficient approximation. The conceptual importance of continuous compounding is that it sets the mathematical ceiling — no finite compounding frequency can produce a higher APY than continuous compounding for the same APR.