LOANS & DEBT
APR to APY Calculator — Convert Between APR and APY
By Worldtickers ·
Convert a nominal APR into its effective APY for any compounding frequency, or work backward from an advertised APY to the underlying APR. This page deliberately combines the APR calculator and APY calculator into one tool, since the two are simply inverse conversions of the same underlying relationship. See both formulas, worked examples across monthly, quarterly, and daily compounding, and why APY is always at least as high as APR.
This apr to apy calculator — convert between apr and apy tool focuses on convert a nominal APR into its effective APY for any compounding frequency, or work backward from an advertised APY to the underlying APR. This page deliberately combines the APR calculator and APY calculator into one tool, since the two are simply inverse conversions of the same underlying relationship. See both formulas, worked examples across monthly, quarterly, and daily compounding, and why APY is always at least as high as APR. Use it to compare borrowing costs, monthly payments, interest charges, payoff timelines, and refinance or repayment choices by changing the rate, term, balance, and payment assumptions.
APR to APY Calculator
APR to APY Calculator
Enter a nominal APR and how many times per year it compounds to find the effective annual yield (APY).
What Are APR and APY?
APR (Annual Percentage Rate) and APY (Annual Percentage Yield) both describe an annual interest rate, but they answer slightly different questions. APR is the nominal, stated rate — the number printed on a loan disclosure or a savings account's fine print before accounting for how often interest compounds within the year. APY is the effective rate — what you actually earn or pay once compounding is folded in.
Because these two numbers are simply two sides of the same conversion — APY is what APR becomes after compounding, and APR is what you get by unwinding a known APY back to its nominal form — this single calculator handles both directions instead of splitting them across two separate pages. Toggle between "APR → APY" to find the effective yield of a stated rate, or "APY → APR" to back out the nominal rate behind an advertised effective yield.
This distinction matters most when comparing offers: a 12% APR credit card compounding daily costs meaningfully more over a year than a simple 12% flat charge would suggest, and a savings account advertising 5% APY is already telling you the effective, compounded figure — no further adjustment needed on your end.
How to Use This Calculator
The calculator has two modes for the two directions of the same conversion.
APR → APY
Use this mode when you have a nominal APR (from a loan, credit card, or savings account disclosure) and want to know the effective annual yield. Enter the Nominal APR and the Compounding Frequency — how many times per year interest compounds (12 for monthly, 4 for quarterly, 365 for daily, 1 for annual) — and click calculate.
APY → APR
Use this mode when you already know an advertised effective APY (common on savings accounts and CDs) and want to back out the underlying nominal APR for comparison against a loan or another rate quoted as APR. Enter the Effective APY and the Compounding Frequency, and click calculate.
The Formulas Explained
APR to APY: APY = (1 + APR/100/n)^n − 1, then multiplied by 100 to express as a percentage, where n is the compounding frequency (times per year).
APY to APR: APR = n × [(1 + APY/100)^(1/n) − 1], again multiplied by 100 for a percentage. This is the algebraic inverse of the first formula — solving the APR-to-APY equation for APR instead of APY.
As compounding frequency n increases, APY rises for any fixed positive APR, because interest is compounded — added to the balance and then itself earning interest — more often within the year. As n approaches infinity, this converges to continuous compounding, where APY = e^(APR/100) − 1. For a 12% APR, that continuous-compounding ceiling works out to approximately 12.75%, only about 0.002 percentage points above the daily-compounding (n = 365) figure of roughly 12.7475% — showing how quickly the curve flattens out once compounding is already frequent.
Worked Examples
Example 1: Monthly Compounding
A 12% nominal APR compounded monthly (n = 12): APY = (1 + 0.12/12)^12 − 1 = (1.01)^12 − 1 ≈ 12.68%. This is the classic example that shows how a "12% rate" actually pays out slightly more than 12% once monthly compounding is included.
Example 2: Comparing Compounding Frequencies on the Same APR
Take that same 12% nominal APR and vary only the compounding frequency: quarterly (n = 4) gives an APY of approximately 12.55%; monthly (n = 12) gives approximately 12.68%; daily (n = 365) gives approximately 12.75%; and annual (n = 1) gives exactly 12.00%— identical to the APR, since there's no intermediate compounding to boost it. Notice how the increases get smaller as n grows larger, illustrating diminishing returns from more frequent compounding.
Example 3: A High-Rate Credit Card
Credit cards often compound daily but are commonly quoted with monthly compounding assumptions for simplicity; using monthly compounding on a 24% APR credit card (n = 12): APY = (1 + 0.24/12)^12 − 1 ≈ 26.82% — a meaningfully larger effective cost than the headline 24% APR suggests, which is exactly why understanding this conversion matters when carrying a credit card balance.
Example 4: Working Backward From an Advertised APY
A savings account advertises a 5.00% APY, compounded daily (n = 365). Working backward: APR = 365 × [(1.05)^(1/365) − 1] ≈ 4.88%. This is the nominal rate the bank is actually crediting each day before compounding brings it up to the advertised 5.00% effective yield.
Tips and Limitations
Always Compare APY to APY, and APR to APR
When shopping for a savings account, compare APY figures directly — they already account for each bank's compounding frequency, so a higher APY is genuinely a better rate regardless of how often each bank compounds. When comparing loan offers, compare APR, since that's the figure regulated for disclosure and often includes fee adjustments that APY alone would not reflect.
Rounding Can Cause Tiny Round-Trip Differences
If you convert a 12% APR to APY (getting 12.6825%) and then round that to a displayed 12.68% before converting back to APR, you'll get approximately 11.9978% instead of exactly 12.00% — a difference of about 0.002 percentage points. This isn't an error in the formula; it's simply the effect of rounding an intermediate figure before reversing the calculation. For precise round-trips, carry as many decimal places as possible.
APR on Loans May Already Include Fees
Some APR disclosures (especially on mortgages) bundle in origination fees, points, or other closing costs spread over the loan term, meaning the APR is already higher than the loan's raw interest rate — a separate adjustment from the compounding conversion this calculator performs. Don't assume APR here is purely a compounding artifact; check what the quoted APR already includes before comparing.
Use This Alongside Loan Comparison Tools
Converting rates to a consistent basis is especially useful when comparing loan offers quoted with different compounding conventions. Pair this calculator with our Loan Comparison Calculator to see the full monthly-payment and total-cost picture side by side.
Frequently Asked Questions
What is APR?
APR stands for Annual Percentage Rate — the nominal, stated yearly interest rate on a loan or the yearly rate quoted before accounting for compounding. On loans, APR often also bundles in certain fees, giving a more complete picture of a loan's cost than the bare interest rate alone. On its own, however, APR does not tell you the actual annualized return or cost once compounding within the year is factored in — that's what APY is for.
What is APY?
APY stands for Annual Percentage Yield — the effective annual rate you actually earn or pay once compounding is taken into account. If interest is credited or charged more than once a year (monthly, daily, and so on), each compounding period's interest itself starts earning or costing interest, so the true annual rate ends up higher than the simple nominal APR. Banks are required to advertise APY on savings products specifically because it reflects the real return you'll experience.
Why is APY always higher than APR when compounding more than once a year?
Because compounding means interest is calculated on a growing balance rather than just the original amount. Once the first compounding period's interest is added, the next period's interest is calculated on that larger balance too — interest earning interest. The more frequently this happens within a year (monthly versus daily versus annually), the more those small boosts accumulate, so APY rises as compounding frequency increases, even though the nominal APR stays the same.
Why are APR and APY equal when compounding annually?
When interest compounds only once per year (n = 1), there is no intermediate compounding period where interest can earn additional interest within that same year — the single annual calculation is the whole story. In that specific case, the formula APY = (1 + APR/100/1)^1 − 1 simplifies directly back to APR/100, so the two percentages are numerically identical. The gap between APR and APY only opens up once compounding happens more than once per year.
Which one matters more for a savings account vs. a loan?
For savings accounts and CDs, APY is what you actually earn and is the number worth comparing across banks, since it already accounts for compounding frequency. For loans and credit cards, APR is more commonly quoted and regulated (in the U.S., lenders are legally required to disclose APR under Truth in Lending rules), but the effective APY tells you the true annualized cost if interest compounds within the year, which matters most on revolving debt like credit cards that compound daily or monthly.
Is APR the same as interest rate?
Not exactly. A loan's interest rate is the base rate applied to the principal, while APR often includes certain fees (like origination fees or mortgage points) spread over the loan term, giving a more complete apples-to-apples cost figure required for comparing loan offers. Two loans can have the identical interest rate but different APRs if one carries more upfront fees. APR itself still doesn't reflect compounding within the year — that's the separate step this calculator performs to get to APY.
How does compounding frequency affect the difference between APR and APY?
The more often interest compounds, the bigger the gap between APR and APY, though the gap grows more slowly than most people expect. A 12% APR compounded monthly (n=12) gives an APY of about 12.68%. Compounded daily (n=365), it rises to roughly 12.75%. Compounded quarterly (n=4), it's a bit lower at about 12.55%. As compounding frequency increases toward continuous compounding, the APY approaches a mathematical ceiling — for a 12% APR, that ceiling (using e^APR − 1) is about 12.75%, barely above the daily-compounding figure.
Can APR and APY be negative, or represent a loss?
The formulas themselves work the same way regardless of sign, but in practice APR and APY as conventionally used describe the cost of borrowing or the yield on savings, and both are typically shown as positive rates. A "negative return" scenario (like an investment losing value) is usually expressed through a different metric, such as a rate of return or CAGR, rather than APR/APY, which are specifically standardized disclosures for loans, deposits, and interest-bearing products.