How this calculator works
APR and APY both describe annual rates, but they answer different questions. APR is a nominal annual rate—it does not, by itself, reflect interest compounding within the year. APY is an effective annual rate that includes compounding, showing what the nominal rate becomes when interest is added more than once per year.
This converter moves between nominal APR and effective APY using the compounding frequency you select: daily, monthly, quarterly, or annually. Enter APR to see APY, or enter APY to see the nominal APR behind it. The math assumes a constant rate and a fixed compounding schedule—no fees, promotional periods, or balance tiers.
When comparing financial products, mixing APR on one account with APY on another skews results. Savings accounts are often quoted with APY because it reflects compounding. Loans may emphasize APR under regulatory disclosure rules. Converting both sides to the same measure—usually APY for deposits and APR for borrowing comparisons—puts products on equal footing for rate math.
This tool handles the conversion only. For long-term growth projections after converting a savings rate, use the compound interest calculator. For installment payment amounts on a loan, use the loan payment calculator.
The relationship between APR and APY is deterministic once compounding frequency is known. Daily compounding applies interest 365 times per year in the standard convention; monthly applies 12 times. Each intra-year accrual period slightly raises the effective annual yield above the nominal APR when the rate is positive.
What affects the result
Three inputs control the conversion. The gap between APR and APY widens with higher rates and more frequent compounding.
- Nominal APR or APY is the quoted annual figure you are converting. Enter whichever measure the product provides and read the complementary result.
- Compounding frequency must match the account or loan terms. Daily compounding is common on high-yield savings; monthly is common on many loans and CDs. Using the wrong frequency produces a correct formula with the wrong assumptions.
- Direction of conversion determines whether you are finding effective yield from nominal rate or nominal rate from effective yield. Both directions use the same underlying relationship.
At low rates the APR–APY spread looks small. At higher nominal rates with daily compounding, the difference becomes material over multi-year horizons even though the one-year gap may still look modest in percentage points.
Regulatory loan APR on mortgages and some consumer loans attempts to include certain fees in the borrowing cost. This converter does not add fees—it converts rate math only. Read official loan disclosures for borrowing decisions.
Zero or negative rates collapse the APR–APY spread. At 0%, both measures align. This converter handles positive rate conversions used in typical savings and loan quotes.
Real-world examples
Comparing two savings accounts. Bank A quotes 4.25% APR compounded daily. Bank B quotes 4.30% APY directly. Convert Bank A to APY with daily compounding, then compare APY to APY. A higher nominal APR with less frequent compounding can still lose to a lower-quoted APY product.
Understanding a CD quote. A 12-month certificate lists 5.00% APY with monthly compounding. Convert to APR if you need the nominal rate for a spreadsheet model or to compare against a loan priced in APR terms.
Loan nominal rate vs. true annual cost. An installment loan advertises 8.5% APR compounded monthly. Converting to APY shows the effective annual cost of that compounding schedule—useful when comparing against a line of credit or credit card priced differently. Pair with the loan payment calculator to see payment and total interest on the actual balance and term.
Credit card context. Revolving cards compound daily on balances carried month to month. Nominal APR understates the effective cost of carrying debt compared with simple annualization. For payoff timelines, the credit card payoff calculator models balance reduction; this converter clarifies rate terminology.
Teaching simple vs. compound growth. After converting APR to APY, project multi-year balances in the compound interest calculator. Contrast with the simple interest calculator when explaining non-compounding contracts.
Money market vs. high-yield savings. Account A: 4.50% APR compounded daily. Account B: 4.55% APY stated directly. Convert A to APY before choosing. A nominally lower APR with daily compounding can beat a slightly lower quoted APY on another product depending on frequency.
Spreadsheet validation. Financial models sometimes store nominal APR while reports display APY. Use this converter to verify formula cells before presenting rate comparisons to clients or family members.
Common mistakes
Comparing APR on one product to APY on another without converting. This is the most frequent apples-to-oranges error in rate shopping.
Selecting the wrong compounding frequency. If terms say daily compounding, choosing monthly understates APY relative to the true effective yield.
Assuming loan APR includes every cost. Disclosure rules vary by product. Origination fees, insurance, and third-party charges may or may not be reflected depending on the loan type and jurisdiction.
Treating promotional rates as permanent. Introductory APY on savings or teaser APR on cards revert to standard rates. Convert the long-run rate you will actually earn or pay.
Using this converter for investment returns with volatility. APY here assumes a fixed nominal rate compounding on schedule. Market investments do not behave that way.
Ignoring tax impact on savings yields. APY is pre-tax unless you adjust externally. Tax-equivalent yield analysis is outside this tool.
Confusing APR on credit cards with daily balance cost. Cards compound on average daily balance. Payoff behavior matters as much as the nominal APR—use the credit card payoff calculator alongside rate conversion.
Assuming quarterly compounding when terms say monthly. Always match the product disclosure. A one-frequency error is small at low rates but systematic across comparisons.
When to use this calculator
Use this converter when you need to normalize rate quotes across products, explain APR vs. APY to someone comparing accounts, or verify spreadsheet formulas against a trusted implementation. It is ideal for savings account shopping, CD comparisons, and clarifying nominal vs. effective rates before longer projections.
Use the compound interest calculator after converting a deposit rate to project balances over time. Use the loan payment calculator or personal loan calculator when the decision depends on monthly payment, not just rate terminology. For broader context, see the guide on APR vs. APY.
Do not use this tool as the sole basis for mortgage selection, credit card cost analysis, or regulatory compliance. It excludes fees, tiered rates, penalties, and changing rates.
Keep a record of compounding frequency assumptions when comparing products over time. Banks occasionally change compounding conventions on deposit products—reconvert when terms update rather than relying on stale APY memories.
When building a personal finance spreadsheet, store both APR and compounding frequency as inputs and derive APY with the same formula this calculator uses. That prevents drift between manual cells and bank statements when rates change mid-year.
Related calculators
- Compound interest calculator — Project balance growth after you convert a savings rate to APY.
- Simple interest calculator — Estimate non-compounding interest for contracts that use principal-only calculations.
- Loan payment calculator — Compute monthly payments and total interest on installment loans.
- Credit card payoff calculator — Model revolving payoff timelines where daily compounding affects carrying costs.
- Savings goal calculator — Solve for monthly contributions needed to reach a target using a return assumption.
FAQ
Why is APY usually higher than APR?
When interest compounds more than once per year, APY includes the effect of interest earning interest. APR is the nominal annual rate before that compounding effect is expressed as an effective yield.
Which compounding frequency should I choose?
Choose the frequency used by the account or loan terms—daily for many savings accounts, monthly for many loans and CDs, or as stated in the product disclosure.
Does this converter include fees?
No. It only converts between nominal and effective rates based on compounding frequency. Loan fees and account charges are not included.
Should I compare loans using APR or APY?
Loans are often quoted with APR. Compare APR to APR when evaluating borrowing costs, but read disclosures to see which fees are included. For savings accounts, compare APY to APY.
Why do two accounts with the same APR have different growth?
Different compounding frequencies produce different effective yields. Daily compounding typically yields slightly more than monthly at the same nominal APR. Convert both to APY for an apples-to-apples comparison.
Can I convert APY back to APR?
Yes. Enter APY and select compounding frequency to solve for the nominal APR that produces that effective yield.
Does compounding frequency matter at low rates?
The APR–APY gap is smaller at low rates but still nonzero with frequent compounding. At higher rates or over long horizons, the difference becomes more meaningful.
Is APY the same as CAGR on an investment?
APY here assumes a fixed nominal rate with scheduled compounding. Investment CAGR reflects actual start and end values and may include volatility not captured by this converter.
How does this relate to credit card APR?
Cards quote APR but compound daily on carried balances. Converting to APY clarifies effective annual cost, though payoff planning also requires balance and payment inputs.
Should I use this for mortgage rate shopping?
Mortgage APR disclosures include specific fee treatments under regulatory rules. Use this converter for rate math only and rely on official Loan Estimates for borrowing decisions.