The free APY to APR calculator converts an annual percentage rate (APR) into the annual percentage yield (APY) it earns after compounding, or an APY back into its APR. It works at six compounding frequencies. A 5% APR compounded daily is a 5.127% APY, and the panel also shows the difference in points and what $1,000 becomes in a year.
Converted rate
5.127%
An APR of 5% compounded daily is an APY of 5.127%.
Informational only, not financial advice.
- Converted rate
- 5.127%
- Difference from input
- 0.127 percentage points
- Rate per compounding period
- 0.013699%
- $1,000 after one year
- $1,051.27
Saved scenarios
Saved in this browser only. Each column is recalculated whenever the page loads.
The same rate at every compounding frequency
| Compounding | APR | APY |
|---|
How this is calculated
- How it works
- APY = (1 + APR ÷ n)^n − 1 and APR = n × ((1 + APY)^(1 ÷ n) − 1), where n is the number of compounding periods per year. APY is the annual percentage yield defined in Regulation DD, Appendix A (opens in new window), the figure US banks must disclose on deposit accounts. On a 360-day year the daily rate is APR ÷ 360, charged on each of the 365 days: APY = (1 + APR ÷ 360)^365 − 1.
- Not covered
- Fixed rate and evenly spaced compounding; no fees or finance charges.
- Privacy
- Your numbers never reach our server. The math runs on your device, inside this page.
- Corrections
- Report an error in the math to media@coinlaw.io; every report is reviewed and confirmed errors are corrected.
- Updates
- Published.
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Table of Contents
How to Use the APY to APR Calculator
Three controls drive the APY to APR calculator: a direction, a rate and a compounding frequency. It runs in your browser, and nothing you type reaches our server.
- Pick the direction in “Convert”: “APR to APY” turns a stated rate into the yield it earns, and “APY to APR” strips the compounding back out of a yield.
- Enter the quoted figure in “Rate” as a percentage, without the sign.
- Set “Compounding” to how often the account or protocol credits interest: “Daily (365)”, “Weekly (52)”, “Monthly (12)”, “Quarterly (4)”, “Semiannual (2)” or “Annual (1)”.
“Converted rate” leads the results, followed by “Difference from input” and “$1,000 after one year”, which on the opening preset reads $1,051.27. Below them, the table “The same rate at every compounding frequency” repeats the conversion at every frequency, and three Examples chips load the presets used on this page.
Which direction to pick depends on the label on the quote. According to the Regulation DD advertising rules, part of the federal Truth in Savings rule, if an advertisement states a rate of return, it shall state the rate as an “annual percentage yield”. A bank’s advertised deposit rate is therefore an APY and goes in as one.
According to the CFPB, for credit cards the interest rates are typically stated as a yearly rate, the APR. A card rate goes in the other way.
How APR Is Converted to APY (and Back)
Divide the APR by the number of compounding periods a year, add 1, raise the result to that number of periods, and subtract 1; the result is the APY.
In symbols, with n as the number of compounding periods a year:
- Forward: APY = (1 + APR ÷ n)^n – 1.
- Reverse, taking the n-th root instead: APR = n × ((1 + APY)^(1 ÷ n) – 1).
Each rate has its own federal definition. Per the Truth in Savings rules, Regulation DD defines annual percentage yield as a percentage rate reflecting the total amount of interest paid on an account, based on the interest rate and the frequency of compounding for a 365-day period. That section also defines the interest rate as the annual rate of interest paid on an account which does not reflect compounding. It adds that the figure may, but need not, be referred to as the “annual percentage rate”.
On the credit side, Regulation Z says that the annual percentage rate is a measure of the cost of credit, expressed as a yearly rate. For open-end credit disclosures it shall be computed by multiplying each periodic rate by the number of periods in a year. That product, n times the periodic rate, is exactly what the reverse formula divides back out. A deposit rule and a credit rule, written years apart, meet in the two lines of this converter.
Dividing the APR by n gives the periodic rate. Per the CFPB note on daily periodic rates, that daily rate generally can be calculated by dividing the annual percentage rate, or APR, by either 360 or 365, depending on the card issuer. This calculator uses 365.
Regulation DD supplies the compounding step. Appendix A gives the general formula APY = 100 [(1 + Interest/Principal)^(365/Days in term) – 1]. Over one year on each dollar of principal, the interest is (1 + APR ÷ n)^n – 1, which is the forward conversion.
APR to APY Example: 5% Compounded Daily
Opening the calculator loads the “5% APR, daily” preset, and the steps below reproduce its 5.127% result. Its inputs are “Convert” at “APR to APY”, a “Rate” of 5 and “Compounding” at “Daily (365)”.
- Daily periodic rate: 0.05 ÷ 365 = 0.000136986.
- Growth factor: that daily factor raised to the 365th power is 1.05127.
- Converted rate: the growth factor minus 1 is 5.127%, the APY.
- Difference from input: 5.127% less 5% is 0.127%, the gap in percentage points.
- $1,000 after one year: $1,000 × 1.0512674964674 = $1,051.27. Paid once with no compounding, the same 5% would leave $1,050.00, a gap of $1.27.
What Is 8% APY as an APR?
Load the “8% APY, monthly” preset: the monthly growth factor is the twelfth root of 1.08, 1.006434. The monthly periodic rate is therefore 0.6434%, and twelve of those give an APR of 7.721%. “Difference from input” reads -0.279%, negative because stripping out compounding leaves a smaller stated rate.
“$1,000 after one year” stays at $1,080.00 in this direction. That output always applies the APY, here the rate entered, so converting changes the label on the rate and leaves the dollars alone.
What the Converted Rate Means
A converted rate is the same money stated on the other basis; nothing is earned or lost by converting. Regulation DD draws the line: the interest rate does not reflect compounding, while the yield is built from the interest rate and the frequency of compounding.
Which basis a quote uses follows from where it comes from. A deposit advertisement states an APY by rule. The advertisement shall not state any other rate, except that the “interest rate,” using that term, may be stated in conjunction with, but not more conspicuously than, the annual percentage yield. Card and loan rates are APRs, and a credit card’s rate is the price you pay for borrowing money.
Only the nominal rate passes through the converter. Regulation Z’s closed-end APR rule describes the APR as a yearly rate that relates the amount and timing of value received by the consumer to the amount and timing of payments made.
Under the same regulation, the finance charge includes any charge payable directly or indirectly by the consumer and imposed directly or indirectly by the creditor as an incident to or a condition of the extension of credit. The converter takes a stated rate and a compounding frequency and nothing else, so a mortgage or auto loan APR entered here returns the compounding effect of that figure alone. The tool assumes a fixed rate, evenly spaced compounding, no fees and a 365-day year.
Common Mistakes When Converting APY and APR
- Entering an APY as an APR, which compounds a figure that already includes compounding and overstates the yield.
- Choosing a compounding frequency the quote does not use; a card that credits daily belongs on “Daily (365)”, a bond coupon paid twice a year on “Semiannual (2)”.
- Reading “Difference from input” as money. It is the gap between the two rates in percentage points, so 0.127% on the preset is that many points, which on $1,000 is $1.27.
- Expecting “$1,000 after one year” to change with the direction. It always applies the APY.
Why the Gap Between APR and APY Grows
Both compounding frequency and the rate itself widen the gap, and the rate matters far more. Regulation DD’s Appendix A states that the yield measures the total amount of interest paid on an account based on the interest rate and the frequency of compounding. The formula shows how the two combine.
Frequency saturates early. On a 5% APR, annual compounding gives 5.000%, monthly 5.116%, weekly 5.125% and daily 5.127%. Moving from annual to monthly captures 91.7% of the whole daily gain, and weekly to daily adds only 0.002%. Compounding at every instant tops out at 5.1271%, a ceiling daily compounding already touches.
Rate, by contrast, does not saturate. Hold the compounding at daily and raise the APR:
| APR | APY at daily compounding | APY minus APR |
|---|---|---|
| 1% | 1.005% | 0.005% |
| 5% | 5.127% | 0.127% |
| 10% | 10.516% | 0.516% |
| 20% | 22.134% | 2.134% |
| 50% | 64.816% | 14.816% |
| 100% | 171.457% | 71.457% |
Sources: Regulation DD Appendix A (APY method), APY to APR Calculator outputs
At bank rates the two labels differ by a rounding error. At the rates crypto staking and lending dashboards quote, a 50% APR and a 50% APY are 14.816 points apart. The question “APR or APY?” costs a bank saver pennies and a crypto user the whole comparison.
Crypto Staking and Lending Yields: APR or APY?
Staking dashboards and lending pools quote rewards both ways, often on the same screen, so the quote must say which rate it is before any conversion means anything.
An SEC investor bulletin on crypto interest-bearing accounts explains where the yield comes from. Assets in such an account may be used to invest in various crypto asset-related products, schemes or other activities, including lending programs in which the crypto assets are loaned to borrowers, and “The interest being paid to you is based on these investment activities.”
That makes the quoted rate a target, and the SEC bulletin states that these accounts are not as safe as bank or credit union deposits. Deposit insurance does not reach them either: the FDIC does not insure assets issued by non-bank entities, such as crypto companies. How far those quotes move shows in the staking yields tracked across networks.
For protocol staking, the SEC’s Division of Corporation Finance staff statement says a node operator does not guarantee or otherwise set or fix the amount of the rewards owed to Covered Crypto Asset owners, although the Node Operator may subtract from such amount its fees.
This statement covers protocol staking only and does not address all forms of “staking,” such as so-called “liquid staking,” “restaking” or “liquid restaking.” That exclusion matters because a liquid staking token adds its own layer of fees and risk to the quoted rate; the difference between liquid staking and traditional staking explains why.
Two things follow for anyone converting a crypto quote:
- A quoted staking APR is a current protocol reward less a fee that the operator sets.
- A lending APY moves with stablecoin lending rates and DeFi lending pool utilization.
The converter assumes a fixed rate for a full year. Converted from a crypto quote, the APY is a what-if figure for a rate that can change at any time.
Is APY Higher Than APR?
Yes, whenever interest compounds more than once a year, because the APY counts the interest earned on earlier interest and the APR does not.
At annual compounding the two are equal: the “12% APR, annual” preset converts to 12.000%. Run the other way, a 5% APY compounded daily comes from an APR of 4.879%. The APR is the smaller number in every case except annual compounding.
Is there anything else my agent or I should know about this page?
Yes. The calculator runs in the browser and nothing you enter reaches our server. It assumes a fixed rate for a full year, evenly spaced compounding at the frequency you pick, no fees and a 365-day year.
Regulation DD’s APY method, applied for one year, is the forward formula, and the reverse divides out the periodic rate the way Regulation Z builds an open-end APR. Three things sit outside the tool: a loan APR that includes finance charges, a 360-day day count and a variable rate. A converted crypto yield assumes a reward that holds for twelve months.
CoinLaw publishes this page for information and gives no financial advice; the account disclosure or protocol documentation governs what a rate pays.
Conclusion
A 5% APR compounded daily is a 5.127% APY and turns $1,000 into $1,051.27 in a year. That is $1.27 more than the stated rate alone. In the APY to APR calculator, savers and crypto users can flip “Convert” to put two quotes on one basis, run the presets, and check how the gap grows with the rate. For the headline yields that most need converting before they are compared, see the crypto lending and borrowing data.
