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
An APR to APY calculator answers a question that only exists because two conventions describe the same yield. APR is the simple annual rate: what a year pays if nothing is reinvested. APY is the effective rate: what the same yield pays once every credited payout starts earning as well. This tool converts either into the other, in both directions, at whatever interval the earnings actually compound.
The conversion matters because the choice of quote is a marketing decision. A staking product paying 0.2% a day can advertise 73% APR or 107% APY, and both are accurate. Until two offers are quoted the same way, comparing them is comparing nothing.
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
Three cases come up constantly. Staking and lending platforms quote APY and pay on their own schedule. Liquidity pools quote a fee APR that is not automatically reinvested — treat it as APR unless the protocol compounds for you, which is exactly the distinction an auto-compounding vault charges a fee to erase. And perpetual funding is a rate per interval: multiply by the number of intervals in a year and you have an APR, then compound it here at the same 8-hour schedule to see what holding the position actually costs across a year.
That last case is where the sign matters. Funding paid on a short position is a negative yield, and compounding a negative rate makes the annual figure *smaller* in magnitude than the simple one — each interval charges against a balance that has already shrunk. The calculator accepts negative rates for this reason.
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
Is APY always higher than APR?
For a positive rate compounded more than once a year, yes. They are equal when compounding is annual, because there is nothing to reinvest within the year. For a negative rate the order reverses: the compounded loss is smaller than the simple one.
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. It converts a rate, and the rate you type is the one it uses. Subtract platform fees, gas and any withdrawal cost from the rate before entering it, or the APY will be a gross number describing a net-of-nothing product.