What this APY vs APR Calculator does
APR (Annual Percentage Rate) is the nominal yearly rate lenders are required to disclose under Regulation Z. APY (Annual Percentage Yield) is the effective rate that accounts for compounding — what you actually earn or owe over a year. The gap between them grows with compounding frequency: a 5% APR compounded daily produces a 5.127% APY, while the same rate compounded annually stays exactly 5% APY. This English-language version of the calculator converts in both directions — APR → APY and APY → APR — for daily, monthly, quarterly, semiannual, and annual compounding. It also surfaces the per-period rate (APR ÷ n) so you can verify the math on any bank statement or loan amortization schedule yourself. 100% client-side — your data never leaves your browser. No uploads, no tracking, no server logs.
Features
- Bidirectional conversion. Switch between APR → APY and APY → APR in one click. Most online tools only go one way and leave you doing the reverse algebra yourself.
- Five compounding frequencies. Daily, monthly, quarterly, semiannual, and annual — the full range used by U.S. consumer financial products, from HYSAs to CDs to mortgages.
- Cross-frequency comparison table. Enter any APR and instantly see what APY it produces at all five compounding cadences side by side, so you can compare CD or savings offers on equal footing.
- Per-period rate display. The calculator shows APR ÷ n explicitly — the actual rate the bank applies each day or month — so you can reconcile your statements without guessing.
- Runs entirely in your browser. All math executes client-side in JavaScript. No form submissions, no server logs, no third-party data sharing — just instant results as you type.
- Regulation-aware note panel. A built-in reference explains when each rate type applies: Reg Z for loan APR disclosures and Reg DD for savings APY disclosures, with context on why the two metrics exist.
How to use the APY vs APR Calculator
The calculator updates in real time as you change any input — no submit button needed.
- Choose a conversion direction. Select APR → APY if you have a loan or savings rate quoted as a nominal annual rate. Select APY → APR if you know the effective yield and need the nominal rate — useful when comparing a bank's advertised APY back to the underlying APR for amortization checks.
- Enter the rate. Type the percentage value in the Rate field (e.g., 5.25). The field accepts decimals. If you're pulling a rate programmatically, the underlying formula is
APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. - Select the compounding frequency. Pick the frequency your bank or lender uses. HYSAs and most CDs compound daily. Most consumer loans amortize monthly. If you're unsure, check the account agreement or Loan Estimate — the compounding cadence must be disclosed under Reg Z and Reg DD.
- Read the results and comparison table. The primary result shows the converted rate plus the per-period rate. Scroll to the comparison table to see what that same APR yields at every other compounding frequency — handy when a CD at one bank compounds monthly while another compounds daily at the same headline rate.
Common use cases
- Comparing HYSA offers. A San Francisco-based bank advertises 5.00% APY; a Boston fintech lists 4.95% APR with daily compounding. Enter 4.95% APR with daily compounding — the result is 5.072% APY, so the second offer actually pays more despite the lower headline number.
- Translating credit card APR to daily rate. A card at 22.99% APR compounds daily. The per-period rate field shows 0.06299% per day, and the effective APY is 25.83%. That's the real annual cost of carrying a balance — the figure most cardholders never see.
- Deciding between CD compounding schedules. Two CDs both advertise 4.80% APR. One compounds monthly (APY: 4.907%), the other quarterly (APY: 4.893%). The monthly compounding CD earns about $14 more per year on a $100,000 deposit — a difference the comparison table makes immediately visible.
- Verifying a loan amortization. A mortgage note rate is 6.75% — not the APR on the Loan Estimate, which folds in origination fees. Enter 6.75% with monthly compounding to get the per-period rate (0.5625%/mo) used in the amortization schedule, confirming the payment math on closing documents.
- Teaching first-time savers why compounding matters. The Rule of 72 shows that money growing at 7% roughly doubles in about 10 years. Walking a new saver through the APR-to-APY conversion at different frequencies makes that compounding intuition concrete and numerical rather than abstract.
Frequently asked questions
Is any of my data sent to a server?
No. Every calculation runs locally in your browser using JavaScript. Nothing is transmitted, stored, or logged. You can verify this by opening your browser's network tab — no requests are fired when you change the rate or frequency.
Why does a mortgage show a higher APR than the interest rate?
A mortgage's Loan Estimate APR includes most origination fees (points, origination charges, mortgage insurance) spread over the loan's full term, which pushes the APR above the note rate. The note rate — not the APR — is what the bank uses to calculate your monthly payment in the amortization schedule. This is a Regulation Z disclosure requirement, not a quirk of the lender.
Are APR and APY ever equal?
Yes — at annual compounding (n = 1), the formula (1 + APR/1)^1 − 1 reduces to exactly APR, so APY equals APR by definition. For all higher compounding frequencies, APY exceeds APR, with the gap widening as frequency increases.
What is continuous compounding and why isn't it in the calculator?
Continuous compounding is the mathematical limit as n → ∞, expressed as APY = e^(APR) − 1. At typical consumer rates the difference versus daily compounding is under 0.001 percentage points — effectively irrelevant. Consumer banks never offer continuous compounding; it appears in academic finance and options pricing, not savings accounts or loans. Omitting it keeps the tool focused on the five frequencies you'll actually encounter.
How do I compare savings accounts when one quotes APY and another quotes APR?
Always convert to APY before comparing savings products. Enter the APR offer into this calculator with its compounding frequency to get the true APY, then compare APY-to-APY. Regulation DD requires savings institutions to disclose APY, so if a product only quotes APR, ask the bank for the APY — they are legally required to provide it. For loans, compare APR-to-APR at the same compounding cadence, typically monthly for consumer products.
Can I use this calculator for non-U.S. products?
The math is universal — the APR ↔ APY conversion formulas apply to any nominal/effective rate pair regardless of country. The regulatory framing (Reg Z, Reg DD) is U.S.-specific, but the compounding arithmetic works identically for a Canadian GIC or a European savings account. Just ignore the regulatory notes and focus on the rate conversion and comparison table.