Rate converter
APR to APY Calculator
Last updated: October 2026
A savings account advertised at 5.00% APR and one advertised at 5.116% APY can pay exactly the same interest. The first number leaves out compounding and the second includes it. This converter turns one into the other for any compounding schedule, in either direction.
Enter a balance to see the interest a year adds in dollars, then compare every compounding schedule in one table. Use it to compare savings offers, or to see what a credit card APR costs once interest compounds daily.
Inputs
The rate, how often it compounds, and a balance.
Calculating the default example.
Two names for one account
APR, the annual percentage rate, is the yearly rate before compounding. APY, the annual percentage yield, is what a full year of compounding produces. When interest is added once a year, the two match. When it is added monthly or daily, each payment of interest starts earning interest too, so the APY comes out higher.
Compare savings accounts by APY, because it already includes compounding. Compare loans by APR, but remember a card balance you carry grows faster than the APR alone suggests.
What each number means
- The first result is the converted rate, rounded to three decimals.
- The gap shows how many percentage points compounding adds over the APR.
- The yearly interest assumes no deposits, withdrawals, payments, or fees for one year.
The same rate on every schedule
Each row holds your rate and balance fixed and changes only the compounding. In APR to APY mode the APR stays the same and the APY moves. In APY to APR mode the APY stays the same and the APR moves. Your selected schedule is highlighted.
| Schedule | APR | APY | 1-Year Interest |
|---|
Example 1: $10,000 in savings at 5.00% APR
Put $10,000 in an account paying a 5.00% APR. If the bank added interest once a year, you would earn $500 and the APY would also be 5.00%.
With monthly compounding, the bank adds 5% ÷ 12, about 0.417%, each month. By December the balance has earned $511.62, so the APY is 5.116%. Daily compounding at 5% ÷ 365 reaches 5.127%, or $512.67. Continuous compounding, the mathematical limit, reaches $512.71. Moving from monthly to daily compounding adds $1.05 a year on $10,000.
The 360-day convention is the exception. Some institutions divide the rate by 360 but apply it on all 365 days. That pushes the APY to 5.200%, or $519.98, almost $20 more than the stated rate suggests.
Example 2: a $5,000 card balance at 24.99%
Credit card interest is usually stated as an APR, but most cards charge it daily. Suppose $5,000 sits on a card at 24.99% and nothing is paid, charged, or added in fees for a year.
If the issuer divides the APR by 365 and compounds daily, the balance grows by $1,418.94, an effective yearly rate of 28.379%. If the issuer divides by 360, it grows by $1,441.24, or 28.825%. Either way you pay over three points more than the stated APR on a balance you carry for the full year.
Real balances change every month as you pay and spend, so treat these as the upper bound for a balance left alone. The credit card payoff calculator handles a balance you are paying down.
Example 3: reading a 4.50% APY ad backward
A savings ad says 4.50% APY. Switch the converter to APY to APR to find the interest rate behind it. With daily compounding, the interest rate is 4.402%. With monthly compounding, it is 4.410%.
Both produce $450 a year on $10,000, which is the point of an APY. Two accounts with the same APY pay the same yearly interest no matter how often each compounds, so you do not need to convert APYs when comparing savings offers. Convert when one offer quotes an APR and the other quotes an APY.
What the disclosures are required to say
Under Regulation DD, the federal Truth in Savings rule, the annual percentage yield reflects the total interest paid on an account based on the interest rate and the compounding frequency over a 365-day period. Account disclosures must state both the annual percentage yield and the interest rate, using those terms.
For credit cards, the Consumer Financial Protection Bureau explains that the interest rate is typically stated as a yearly rate, the APR. The daily periodic rate generally comes from dividing the APR by 360 or 365, depending on the issuer, and interest compounds daily. For a mortgage, the APR includes points, broker fees, and other charges, so it is a cost measure rather than the interest rate alone.
The formulas behind the converter
For a schedule with n compounding periods a year, APY = (1 + APR ÷ n)n − 1. Annual uses n = 1, monthly n = 12, weekly n = 52, and daily n = 365. The 360-day option divides the APR by 360 and compounds on 365 days. Continuous compounding uses APY = eAPR − 1.
APY to APR reverses each formula: APR = n × ((1 + APY)1/n − 1), or the natural logarithm of (1 + APY) for continuous compounding. Rates display rounded to three decimals, and the yearly interest is the balance times the APY, rounded to the cent. Review the methodology limitations for how the site handles rounding and assumptions.
Mistakes when comparing rates
- Comparing one bank's APR with another bank's APY as if they were the same measure.
- Assuming a card at 24.99% APR costs 24.99% a year on a balance you carry. Daily compounding pushes it higher.
- Treating a mortgage APR as the interest rate. It includes fees, so converting it to an APY mixes two different things.
- Expecting daily compounding to change a savings decision. At typical savings rates, the rate itself matters far more than the schedule.
- Forgetting that a variable rate can change during the year, which makes any one-year figure an estimate.
Good fits
- Comparing a savings offer quoted in APR with one quoted in APY.
- Seeing what a card APR costs once it compounds daily.
- Finding the interest rate behind an advertised APY.
- Checking how much the compounding schedule matters.
Limits
- Loans with fees built into the APR, such as mortgages.
- Balances with deposits, payments, or new charges during the year.
- Promotional or tiered rates that change mid-year.
- After-tax returns. The after-tax cash comparison handles taxes.
APR and APY questions
These answers cover how the two rates relate and what the converter assumes.
What is the difference between APR and APY?
APR is the yearly rate before compounding. APY is the yearly rate after compounding, so it shows the interest a full year actually adds. With monthly compounding, a 5.00% APR equals a 5.116% APY.
How do you convert APR to APY?
Divide the APR by the number of compounding periods in a year, add 1, raise the result to the number of periods, and subtract 1. For 5% compounded monthly: (1 + 0.05 / 12) to the 12th power, minus 1, gives 5.116%.
How do you convert APY to APR?
Reverse the formula. Add 1 to the APY, take the root equal to the number of periods, subtract 1, and multiply by the number of periods. A 4.50% APY compounded daily comes from a 4.402% rate.
Is APY always higher than APR?
APY is higher whenever interest compounds more than once a year and the rate is above zero. With annual compounding the two are equal.
Does daily compounding make a big difference?
Less than most people expect at savings rates. At 5%, daily compounding adds about one cent per $100 a year over monthly compounding. At credit card rates the gap is larger.
Why do banks show APY and lenders show APR?
Federal rules require deposit accounts to disclose the annual percentage yield, and loans and cards to disclose the annual percentage rate. The higher-looking number for savings is the APY, and the lower-looking number for borrowing is the APR.
Can I use this for a mortgage APR?
Only with care. A mortgage APR includes points and fees, so it is not a pure interest rate. The converter treats any APR you enter as a plain yearly interest rate with no fees.
Is this financial advice?
No. It is an educational estimate, not financial, credit, or legal advice. Use the rates and terms in the written account or loan disclosure.
Put the rate to work
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Educational estimate only. This converter does not provide financial, credit, or legal advice. Use the interest rate and APY in the written account or loan disclosure before deciding.