APR vs APY Calculator

Convert any interest rate between APR and APY for any compounding frequency, or reverse the calculation to find the APR behind any advertised APY.

Convert APR → APY

Annual Percentage Rate (APR)

The stated or nominal interest rate before compounding.

Compounding Frequency

How often interest is compounded per year (n = 12).

Formula used: APY = (1 + APR ÷ n)ⁿ − 1

Results

Enter a rate and compounding frequency, then click Calculate to see the conversion.

APY will always be ≥ APR when n > 1

Last updated: July 28, 2026

APR vs APY: What Each Number Actually Means

The two most common interest rate figures in personal finance, APR and APY, describe the same loan or deposit from two different angles. APR vs APY is not a matter of one being correct and the other misleading; both serve a specific purpose, and understanding which one to use in a given comparison is the key to evaluating any financial product accurately. An APR vs APY calculator makes the conversion instantaneous, but knowing why the two numbers differ helps you spot when a lender or bank is presenting a figure that flatters their product.

APR stands for annual percentage rate. It is the nominal or stated rate before the mathematical effect of compounding is applied. When a mortgage lender quotes you a 7.00% APR, they mean that the base interest cost is 7.00% of the outstanding balance per year. APY stands for annual percentage yield, the effective rate after compounding within the year is included. If that 7.00% mortgage compounds monthly, the APY rises to approximately 7.229%, because each month's interest accrues on a slightly larger balance than the month before. Banks are required by Regulation DD to disclose APY on deposit accounts using a standardized formula, and lenders are required by the Truth in Lending Act to disclose APR on consumer loans. Which is why you see APR on loan offers and APY on savings accounts.

The APR to APY conversion formula is: APY = (1 + APR ÷ n)^n − 1, where n is the number of compounding periods per year. The reverse formula is: APR = n × ((1 + APY)^(1/n) − 1). Both formulas are built into the calculator above. For a deeper explanation of how compound interest accumulates over time, the compound interest calculator lets you model multi-year growth on any deposit with any compounding schedule.

How Compounding Frequency Drives the APR vs APY Gap

The compounding frequency, how many times per year interest is calculated and added to the balance, is the single variable that determines how far APY diverges from APR. At annual compounding, APR and APY are identical because there is no intra-year reinvestment of interest. Add monthly compounding and a small gap opens. Switch to daily compounding and the gap widens further, though it approaches a ceiling defined by the continuous compounding limit of e^APR − 1.

To make this concrete: at a 5.00% APR, the APY produced by each standard frequency is approximately 5.0000% (annually), 5.1162% (semi-annually), 5.0945% (quarterly), 5.1162% (monthly), and 5.1267% (daily). The difference between monthly and daily compounding is only 0.0105 percentage points, negligible in dollar terms for most deposit balances, but meaningful when comparing how banks describe their rates. A bank advertising a 5.1162% APY using monthly compounding is offering the same effective return as one advertising a 5.00% APR compounded monthly. The annual percentage rate vs annual percentage yield comparison only resolves cleanly once you know the compounding schedule for both products. The all-frequency table in the calculator above shows the APY for every frequency at once, eliminating the guesswork.

According to the FDIC's national rate tables, savings account APYs are published on a standardized basis precisely to make this comparison easier; every bank must use the same formula, so any two APYs can be compared directly without knowing the underlying compounding schedule.

When APR Matters Most: Loans, Mortgages, and Credit Cards

For borrowers, APR is the primary comparison metric because federal law requires lenders to disclose it on a standardized basis. Mortgages, auto loans, personal loans, and credit cards all carry a disclosed APR, and comparing those APRs across offers gives you a fair baseline. The effective interest rate calculator use case arises when you want to translate that APR into its true annual cost, the APY, so you can understand what you are paying once compounding is applied to your outstanding balance.

Credit cards are the most dramatic example. A credit card advertised at 24% APR with daily compounding carries an effective APY of approximately 27.11%. If you carry a $5,000 balance for a full year, you pay not $1,200 (24% × $5,000) but closer to $1,356, a $156 difference driven entirely by the compounding effect. The credit card interest calculator models this payoff math in full detail, including minimum payment scenarios and the months-to-payoff timeline. Using the APR vs APY calculator before that tool lets you confirm the effective annual cost before you model the payment plan.

Mortgages typically compound monthly, producing a modest but real gap between the quoted APR and the true effective rate. A 7.00% mortgage APR with monthly compounding carries an APY of about 7.229%. Over a $400,000 30-year mortgage, that 0.229% difference adds thousands of dollars to the total interest paid. The gap matters most when comparing a mortgage against other debt or when deciding whether to pay down the mortgage early versus investing the extra cash at an expected market return.

When APY Matters Most: Savings Accounts, CDs, and Deposits

For savers and investors, APY is the correct number to compare. Because APY already incorporates the compounding schedule, two products with the same APY will produce the same dollar return on an equal deposit over one year, regardless of whether one compounds daily and the other compounds monthly. Regulation DD mandates this standardization precisely so consumers can compare savings account offers without needing to understand each bank's compounding convention.

Certificates of deposit advertise APY, and the locked-in nature of a CD means that APY is guaranteed for the full term. High-yield savings accounts also advertise APY, but that rate is variable and can change without notice. When you use the compound interest rate calculatorin the reverse direction, entering an APY to find the underlying APR. You are essentially reverse-engineering the bank's math to understand the base rate before compounding. This can be useful when comparing a savings account APY to a loan APR on a common basis, such as evaluating whether the interest you earn on savings outpaces the interest you pay on a low-rate debt. Our CD vs savings calculator extends this comparison into a full side-by-side dollar analysis including early withdrawal penalties and liquidity tradeoffs.

One area where APR appears on the deposit side is in I-bonds and some Treasury products, where the Treasury discloses a semi-annual rate that must be doubled to get an annual figure. Entering the semi-annual rate doubled (the composite annual rate) into this APR vs APY calculator with semi-annual compounding converts it to the equivalent APY, making it directly comparable to a bank savings rate.

Practical Tips for Using the APR vs APY Calculator

The most common use case for an APR vs APY calculator is comparing a loan offer to a savings rate. For example, suppose you have cash sitting in a 4.80% APY savings account and you are considering whether to use it to pay off a personal loan quoted at 6.50% APR. Enter 6.50% APR with monthly compounding, the typical schedule for personal loans, and the calculator shows an effective APY of about 6.696%. Since 6.696% (what the loan costs) exceeds 4.80% (what your savings earns), using the savings to pay off the loan improves your net financial position by approximately 1.90% annually on every dollar applied. This type of effective interest rate calculatorreasoning is the fastest way to evaluate debt-payoff decisions without building a full spreadsheet. For questions about the banking products referenced in these comparisons, the banking tools category on this site covers everything from savings account projections to loan amortization.

A second practical use is validating bank disclosures. If a bank advertises a 5.12% APY on a savings account that compounds monthly, you can enter 5.00% APR with monthly compounding into the calculator and confirm you get 5.116% APY, close but not exactly 5.12%, which might indicate the bank is rounding or using a slightly different APR. The Consumer Financial Protection Bureau's bank account resources explain your rights under Regulation DD and what disclosures banks must provide. Any significant mismatch between the disclosed APY and what the calculator produces from the stated APR is worth investigating with the bank directly before opening an account.

Frequently Asked Questions

What is the difference between APR and APY in an APR vs APY calculator?

APR, or annual percentage rate, is the stated nominal interest rate before the effect of compounding is applied. APY, or annual percentage yield, is the effective rate that reflects how often interest is compounded within a year. When a bank compounds interest more than once per year, your money grows slightly faster than the APR suggests, and the APY captures that extra growth. An APR vs APY calculator automates the conversion so you can compare products on equal terms without doing the exponent math by hand.

How does an APR vs APY calculator compute the conversion?

The forward conversion from APR to APY uses the formula APY = (1 + APR / n)^n − 1, where n is the number of compounding periods per year. For the reverse direction, the formula rearranges to APR = n × ((1 + APY)^(1/n) − 1). Both formulas assume that the stated rate and the compounding frequency are consistent. That is, the APR is expressed as an annual figure and the periods per year match the actual compounding schedule. The APR vs APY calculator on this page applies whichever formula matches the direction you choose.

Why is APY always higher than APR when compounding occurs more than once a year?

Each compounding period adds interest to the running balance, which means subsequent periods earn interest on previously credited interest. That snowball effect produces an effective annual return that exceeds the nominal APR. The more frequently compounding occurs, the larger the gap: daily compounding at 5.00% APR produces an APY of 5.1267%, while annual compounding at the same APR produces an APY of exactly 5.00% because there is no intra-year compounding. APR and APY are only identical when interest is compounded once per year.

When should I use APR instead of APY when comparing financial products?

APR is most useful when comparing loan costs, because lenders are required by the Truth in Lending Act to disclose the APR on consumer loans, and it provides a standardized baseline for comparison. When shopping for mortgages, auto loans, or personal loans, comparing APRs gives you an apples-to-apples view of the stated cost before fees. APY, on the other hand, is the correct metric for savings accounts, CDs, and any product where you earn interest, because it tells you what you will actually receive after compounding is applied to your deposit.

Does the APR vs APY calculator work for credit cards?

Yes, and it is particularly revealing for credit cards. Credit cards typically advertise a periodic rate, often a daily rate, multiplied by 365 to get a stated APR, but interest actually compounds daily on any unpaid balance. Entering a credit card APR into the APR vs APY calculator with daily compounding shows the true effective annual cost of carrying a balance, which is always higher than the headline APR. On a 24% APR card with daily compounding, the effective APY is roughly 27.11%, a meaningful difference that illustrates why carrying a credit card balance is so expensive.

What compounding frequency do most savings accounts and CDs use?

Most high-yield online savings accounts and certificates of deposit compound interest daily or monthly. Daily compounding produces the highest APY for a given APR, which is why online banks often advertise it as a selling point. Brick-and-mortar banks and some credit unions may compound monthly or quarterly. The difference between daily and monthly compounding at typical savings rates is small, less than 0.02% APY at a 5% APR, but the APR vs APY calculator lets you see the exact gap for any combination you are evaluating.

How does the APR vs APY difference affect a mortgage?

Mortgage interest is typically compounded monthly, meaning the annual percentage rate understates the effective annual cost by a small margin. At a 7.00% mortgage APR with monthly compounding, the effective APY is approximately 7.229%. Over a 30-year loan, that compounding effect accumulates into thousands of dollars of additional interest. The APR vs APY calculator can convert any mortgage rate to its effective equivalent, helping you compare fixed-rate mortgages against each other or weigh a mortgage against other debt on an annual-cost basis.

Can the APR vs APY calculator show me the difference for every compounding frequency at once?

Yes. After you enter a rate and click Calculate, the tool displays an all-frequency comparison table showing the converted rate at daily, monthly, quarterly, semi-annual, and annual compounding simultaneously. The row matching your selected frequency is highlighted so you can confirm your primary result while seeing how the output would change at other schedules. This table is especially useful when a bank does not clearly disclose its compounding schedule, because you can bracket the likely range with monthly and daily rows.

What is the continuous compounding limit of the APR vs APY calculator?

Continuous compounding is the mathematical limit where n approaches infinity, producing an APY equal to e^APR − 1, where e is Euler's number (approximately 2.71828). At a 5% APR, continuous compounding yields an APY of about 5.1271%, only 0.0004 percentage points above daily compounding. Most real-world financial products do not offer continuous compounding, but the concept explains why daily compounding is essentially the practical ceiling for most savings accounts. The APR vs APY calculator covers the five standard frequencies used by banks and lenders.

How does the APR vs APY comparison change at higher interest rates?

The absolute gap between APR and APY widens as rates increase because compounding is multiplicative rather than additive. At 2% APR with monthly compounding the difference is about 0.02 percentage points, while at 10% APR the gap grows to roughly 0.47 percentage points and at 20% APR it exceeds 1.95 percentage points. This means the APR vs APY distinction matters more during high-interest-rate environments, both for savers choosing between deposit accounts and for borrowers evaluating expensive credit products like credit cards or payday loans.

Is the APY disclosed on bank accounts the same as what the APR vs APY calculator produces?

It should be, assuming the bank is using standard compounding. Under Regulation DD, banks are required to calculate and disclose APY using the same formula that this APR vs APY calculator applies. If the APY on your account statement differs from what the calculator shows for the stated APR and compounding frequency, the discrepancy usually means the bank is applying fees, a tiered rate structure, or a different compounding convention than you assumed. Double-checking your bank's deposit agreement and Truth in Savings disclosures is the best way to resolve any mismatch.

How do I use the APR vs APY calculator to compare a savings account to a CD?

Start by converting both the savings account APY and the CD APY back to APR using the reverse mode, then compare those APRs on a common compounding basis. Alternatively, if both products already disclose APY, you can compare them directly without the calculator; APY is already standardized for compounding. The calculator becomes most valuable when one product discloses APR (common for loans) and another discloses APY (common for deposits), since those two figures are not directly comparable. For a full side-by-side analysis that models dollar outcomes, the CD vs savings calculator on this site extends the APR vs APY conversion into a complete earnings comparison.

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