APR to APY Calculator
The same yield, quoted with and without compounding.
The same rate on every schedule
APY produced by an APR of 40.00 % as the compounding interval shortens.
| Compounding | APY | vs APR |
|---|---|---|
| Hourly | 49.18 % | +9.18 % |
| Every 8 hours | 49.17 % | +9.17 % |
| Daily | 49.15 % | +9.15 % |
| Weekly | 48.95 % | +8.95 % |
| Monthly | 48.21 % | +8.21 % |
| Quarterly | 46.41 % | +6.41 % |
| Annually | 40.00 % | -0.00 % |
| Continuous | 49.18 % | +9.18 % |
How it works
APR and APY describe the same yield: APR is what one year pays with nothing reinvested, APY is what it pays once every payout starts earning too. The gap between them is not a bonus — it is entirely a statement about how often the interest is credited.
The gap widens with the rate, not with the schedule: at 5% APR the difference between daily and annual compounding is a tenth of a percentage point, at 100% it is 71 points. That is why low-yield products advertise APY and high-yield ones quote whichever number is larger, and why two pools are only comparable once both are converted to the same quote.
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How the APR to APY Calculator works
This APR APY calculator converts APR to APY and APY to APR using your chosen compounding frequency. Here APR means the nominal annual yield before compounding, and APY means the effective annual yield after reinvesting earnings. Enter 10 for 10%; use decimal rates such as 0.10 when calculating the formulas by hand.
The same rate can produce different annual earnings when payouts are reinvested annually, monthly or daily. Compare the compounding schedule as well as the headline rate. This is a yield converter; it does not calculate the fees included in a loan's disclosed APR.
How to convert APR to APY
APY = (1 + APR ÷ n)ⁿ − 1, where n is the number of compounding periods per year. With 10% APR compounded daily, n = 365: (1 + 0.10 ÷ 365)³⁶⁵ − 1 = 0.105156, or approximately 10.5156% APY.
The table uses the same 10% APR and a $1,000 deposit held for 365 days. It assumes a constant rate, full reinvestment at each interval and no additional deposits, withdrawals or costs.
| Compounding | Periods per year | APY at 10% APR | Balance after one year |
|---|---|---|---|
| Annual | 1 | 10.0000% | $1,100.00 |
| Monthly | 12 | 10.4713% | $1,104.71 |
| Daily | 365 | 10.5156% | $1,105.16 |
How to convert APY to APR
APR = n × ((1 + APY)^(1/n) − 1). For 10% APY with daily compounding, 365 × (1.10^(1/365) − 1) gives approximately 9.5323% APR. A $1,000 balance still earns $100 over a full year: APY already includes the reinvestment.
Select APY → APR above and enter the compounding frequency used by the product. Monthly and daily compounding give different nominal APRs for the same APY. For continuous compounding, use APY = e^APR − 1 and APR = ln(1 + APY).
What the compounding frequency actually changes
Only one thing: how often the interest you have already earned starts earning. The APR is split into n equal slices, each slice is credited, and the next slice is charged against the larger balance. That is the whole mechanism, and it is why APY = (1 + APR ÷ n)ⁿ − 1.
The effect is small at low rates and violent at high ones, because it is compounding on itself. At 5% APR, moving from annual to daily compounding buys you 13 basis points. At 100% APR the same move buys you 71 percentage points. Anyone quoting a triple-digit APY is quoting a number whose size comes mostly from the exponent, not from the underlying yield.
The continuous limit, and why the numbers stop growing
Shortening the interval does not increase the yield without bound. As n rises the expression converges on e^APR − 1, so 100% APR cannot exceed 171.8% APY however finely it is sliced. Hourly compounding is already within a couple of basis points of that ceiling.
This is worth knowing precisely because per-block and per-second yields are marketed as if the frequency itself were the product. It is not. Between daily and continuous compounding there is almost nothing left to win; the rate is what you are actually buying.
Applying it to crypto rates
For staking rewards or lending, choose the schedule on which earnings are actually reinvested. A liquidity pool's fee APR does not imply automatic compounding. Reinvestment costs and changing rates can make realised earnings differ from the projection.
Perpetual funding is a separate cash flow. Use the funding rate calculator for payment amounts at a fixed notional and holding period. Converting an annualised funding rate to APY only models a hypothetical reinvestment schedule; it does not reproduce an exchange's funding charges on an unchanged position. This converter also accepts negative nominal rates for compounded-loss scenarios.
Reading the result honestly
Every APY is a projection, not a promise: it assumes the current rate holds for a full year and that every payout is reinvested at that rate. Crypto yields rarely hold for a month. Use the figure to compare two offers on the same day, not to forecast a year of income.
The projection panel makes the assumption visible by compounding your deposit at the effective rate over the period you enter. If a rate only survives a fortnight, enter a fortnight — the annualised headline and the money actually earned are very different quantities.
FAQ
What is 10% APR in APY?
At daily compounding, 10% APR is approximately 10.5156% APY. At monthly compounding it is 10.4713%, and at annual compounding it is 10%. The answer depends on how often earnings are reinvested.
What is 10% APY in APR?
With daily compounding, 10% APY corresponds to approximately 9.5323% nominal APR. Enter 10 in APY → APR mode and select Daily. Changing the compounding frequency changes the APR.
Is APY always higher than APR?
For a positive nominal rate compounded more than once a year, APY is higher. Annual compounding makes the two equal. For a negative rate in this model, compounding generally gives a less negative effective rate: a smaller loss in magnitude, not a larger negative number.
How do I convert APY back to APR?
Switch the direction on the calculator, or apply APR = n × ((1 + APY)^(1/n) − 1). The frequency must be the one the APY was quoted at — converting a daily-compounded APY as if it were monthly gives an APR that belongs to no product.
Which number should I use when comparing two pools?
Either, as long as both are expressed the same way and both are net of costs. APY is the fairer comparison when the platforms compound on different schedules; APR is the more honest input when you plan to withdraw the earnings rather than reinvest them.
How do I turn a funding rate into an annual figure?
Multiply the rate per interval by the number of intervals in a year — 1,095 at the 8-hour schedule most venues use — to get the APR, then compound it at that same interval for the APY. The funding calculator does the first step from a position size and a holding period.
Does this account for fees or taxes?
No. The conversion uses the rate you enter. Platform fees, transaction costs and taxes require a separate calculation from their amounts and timing. If a product quotes a rate already net of a fee, avoid subtracting that fee twice.