Convert between APR and APY rates for DeFi investments. Quickly calculate APR to APY or APY to APR conversions to help you find the best deals in DeFi.
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How often interest compounds
APR (Annual Percentage Rate) is the simple interest rate you earn over a year without compounding. If you invest $1,000 at 10% APR, you earn exactly $100 in a year - straightforward and predictable. APR doesn't account for earning "interest on interest."
APY (Annual Percentage Yield) includes compound interest effects. With 10% APY and monthly compounding, you earn interest each month that itself earns interest. $1,000 at 10% APY becomes $1,104.70 - that extra $4.70 is pure compound interest gain. APY is always ≥ APR.
DeFi protocols advertise both APR and APY, sometimes interchangeably. A protocol offering "20% APR" with daily compounding actually delivers ~22.13% APY! Always convert to APY for accurate comparisons. This calculator helps you compare apples-to-apples.
The same APR yields different APYs based on compound frequency: 10% APR becomes 10.00% APY (annual), 10.38% APY (quarterly), 10.47% APY (monthly), or 10.52% APY (daily). More frequent = higher APY = more money for you.
Aave might show "5% APR" for USDC lending. With continuous compounding (every block), that's actually ~5.13% APY. Over a year on $10,000, you earn $513 instead of $500 - an extra $13 from compound effects. Multiply this across larger deposits and longer periods, and it adds up significantly.
Some protocols advertise APY because it looks higher (good marketing). Others show APR to appear conservative. New protocols might show "500% APY!" without mentioning it's only for the first week. Always verify: Which rate? What frequency? How long does it last?
Select APR to APY if you know the simple interest rate and want to see the compound yield. Select APY to APR if you know the advertised yield and want to find the underlying simple rate. Most DeFi users convert APR to APY to see real returns.
Input the percentage rate from the DeFi protocol's documentation. For example, if Curve Finance shows "15% APR" for a stablecoin pool, enter 15. Be precise - even 0.5% differences matter on large deposits.
Choose how often rewards compound: Daily (365x) for most DeFi protocols,Weekly (52x) for some farms, Monthly (12x) for traditional staking,Quarterly (4x) or Annually (1x) for simpler protocols.
The calculator shows: Converted Rate (your answer), Original Rate (what you entered),Rate Difference (compound interest bonus), and Per Period Rate (interest per compound cycle). Use these to compare protocols accurately.
Protocol A: "15% APR" (monthly). Protocol B: "15.5% APY" (daily). Which is better? Convert both to APY with daily compounding: A becomes ~16.08% APY, B stays ~15.5% APY. Protocol A wins despite lower advertised rate! This calculator prevents costly mistakes.
Yield farming: Convert farm APR to APY. Staking: See real compound returns.Lending: Compare lending platform rates. Liquidity pools: Calculate LP rewards.Research: Verify protocol claims before investing.
You find a DeFi protocol advertising "20% APR" with daily compounding. What's your actual yield?
Result: ~22.13% APY. You earn 2.13% more than advertised due to daily compounding! On $10,000, that's an extra $213 annually.
APY = ((1 + APR/100 / n)^n - 1) × 100
Where n = compound frequency (times per year)
APR = 10%, Monthly compounding (n = 12):
APY = ((1 + 10/100 / 12)^12 - 1) × 100
APY = ((1 + 0.008333)^12 - 1) × 100
APY = (1.10471 - 1) × 100 = 10.47%
Each period, you earn APR/n on your current balance. After n periods, the (1 + rate)^n compound growth formula reveals your total return including all compound effects. Subtracting 1 and multiplying by 100 converts to percentage.
APR = ((1 + APY/100)^(1/n) - 1) × n × 100
Where n = compound frequency (times per year)
APY = 10%, Monthly compounding (n = 12):
APR = ((1 + 10/100)^(1/12) - 1) × 12 × 100
APR = ((1.10)^0.08333 - 1) × 12 × 100
APR = (1.007974 - 1) × 12 × 100 = 9.57%
This reverses the APR-to-APY formula. Taking the nth root ((1/n exponent)) finds the per-period multiplier, subtracting 1 gives the per-period rate, and multiplying by n × 100 annualizes it. It "unwraps" the compound interest to reveal the simple rate.
The formulas are inverses of each other. Converting APR→APY→APR (or APY→APR→APY) with the same compound frequency returns you to the original rate. This mathematical relationship ensures accuracy.
Pro tip: For very high compound frequencies (daily/continuous), APY approaches e^(APR/100) - 1, where e ≈ 2.71828. This is why 100% APR with continuous compounding ≈ 171.83% APY.
When comparing protocols, convert everything to APY with the same compound frequency (daily is standard). Protocol A: "15% APR daily" → 16.18% APY. Protocol B: "15.5% APY monthly" → ~15.5% APY daily. A wins despite lower advertised rate. This prevents apples-to-oranges comparisons.
A protocol advertising "20% APY with daily compounding" only delivers that IF it auto-compounds. Manual claiming requires you to restake rewards daily - unrealistic with gas fees. Always verify: Is it truly auto-compounding? Some protocols claim daily compounding but only compound when users claim.
Higher compound frequency is better only if gas-free. On Ethereum mainnet, claiming + restaking can cost $20-100. If you're earning $50/month at 20% APY on $3,000, daily compounding with manual claims loses money to gas. Choose protocols with gas-free auto-compounding or accept less frequent compounding.
New DeFi protocols often launch with "500% APY!" that drops to 50% in weeks as TVL grows. The advertised 500% APY assumes the rate stays constant - it won't. Calculate realistic long-term APY by checking 30-day rate trends. A stable 30% APY beats a decaying 500% APY.
Protocol A: "15% APY, withdraw anytime." Protocol B: "18% APY, 6-month lock." B's extra 3% APY = ~1.5% semi-annual premium for illiquidity. Is giving up 6 months flexibility worth $150 on $10,000? Calculate the dollar value of the APY difference before committing to locks.
Some DeFi yields come from token emissions: "30% APY" = 5% in stablecoins + 25% in protocol tokens. If the token price drops 50%, that "30% APY" becomes 5% + 12.5% = 17.5% real APY. Always separate base yield (stables/ETH) from token emissions when using this calculator.
Most DeFi rates are variable - they fluctuate based on supply/demand. Today's "10% APY" might be 7% next week. When using this calculator for long-term planning, use conservative estimates. Check 90-day average APY, not current spikes. Fixed-rate protocols (Notional, Yield) let you lock today's APY for months.
Liquidity pool "50% APY" doesn't include impermanent loss (IL). If the token pair diverges 2x in price, you lose ~5.7% to IL. A 50% APY LP with 10% annual IL = 40% effective APY. For LP yields, subtract estimated IL before celebrating high APY numbers.
Create a spreadsheet of all protocols you're considering. Convert each to "APY with daily compounding" using this calculator. Then factor in: (1) Token emission risk (reduce APY by 20-50%), (2) Lock-up penalty (reduce APY by 1-3%), (3) Gas costs (subtract estimated annual gas), (4) IL for LPs (subtract 5-15%).
The protocol with the highest adjusted APY after all deductions is your best choice. A "30% APY" protocol might have 18% adjusted APY, while a "20% APY" protocol has 19% adjusted APY - making the second one better!
How much does compound frequency really matter? Let's see the same 10% APR converted to APY at different frequencies:
10% APR → 10.00% APY (no change)
One compound event means APR = APY. $10,000 → $11,000 exactly.
10% APR → 10.38% APY (+0.38% gain)
$10,000 → $11,038. Quarterly compounding adds $38 over annual.
10% APR → 10.47% APY (+0.47% gain)
$10,000 → $11,047. Common in traditional finance and some DeFi.
10% APR → 10.51% APY (+0.51% gain)
$10,000 → $11,051. Good balance for some DeFi protocols.
10% APR → 10.52% APY (+0.52% gain)
$10,000 → $11,052. Standard in modern DeFi. Near-optimal compounding.
10% APR → 10.52% APY (theoretical max)
Mathematical limit. Daily is 99.99% as good as continuous.
1. Diminishing returns: Going from annual (1x) to monthly (12x) adds 0.47%. Going from monthly to daily adds only 0.05% more. The first frequency improvements matter most.
2. Dollar impact scales: On $10,000, daily vs annual is $52/year. On $100,000, it's $520/year. On $1M, it's $5,200/year. Large deposits demand optimal compounding.
3. Higher APR = bigger frequency impact: At 50% APR, daily vs annual adds ~5.5% to APY (not 0.52%). At 100% APR, it adds ~72% to APY! The compound frequency bonus scales exponentially with higher base rates.
4. Practical limit: For most DeFi users, daily compounding is optimal. Beyond daily, the gains are negligible unless you're dealing with millions of dollars or very high APRs.
Mistake: Comparing "Protocol A: 15% APR" with "Protocol B: 15% APY" and thinking they're equal. Reality: B is better - APY includes compounding, APR doesn't. Always convert to the same metric before comparing. This calculator prevents this costly error.
Mistake: Seeing "20% APY" and assuming all 20% APYs are equal. Reality: 20% APY with annual compounding means the base APR is 20%. 20% APY with daily compounding means the base APR is ~18.23%. The first is better! Always check compound frequency when comparing APYs.
Mistake: Choosing a protocol with "25% APY daily compounding" but it requires manual daily claiming. Reality: You won't claim daily (gas fees + time), so you get closer to weekly/monthly compounding = lower actual APY. Only trust daily compound claims if the protocol auto-compounds.
Mistake: Calculating returns with "30% APY" for 5 years. Reality: DeFi APYs are variable and often decline. Today's 30% might be 15% next month and 8% next year. Always use conservative estimates (50-70% of current APY) for long-term calculations.
Mistake: Celebrating "100% APY" on a protocol's native token. Reality: If the token price drops 70%, your 100% APY in tokens = 30% gain in dollars = loss after considering initial drop. APY only matters if the underlying asset maintains value. Stablecoins eliminate this risk.
Red Flag: A protocol claiming "15% APR and 14% APY." Reality: This is mathematically impossible. APY must always be ≥ APR for any positive interest rate. If you see APR > APY, it's either a typo, scam, or the protocol doesn't understand their own math. Avoid.
Red Flag: "500% APY sustainable long-term!" Reality: Unless the protocol has massive revenue or is printing tokens aggressively (inflation dilution), 500% APY is unsustainable. Verify: Where does the yield come from? Trading fees? Token emissions? If it's emissions, expect rapid APY decay.
Red Flag: "Up to 100% returns!" without specifying APR or APY, compound frequency, or duration. Reality: Vague language hides unfavorable terms. Legitimate protocols clearly state: "X% APY with daily compounding" or "X% APR." If they won't specify, assume the worst and move on.