APY Calculator
Convert APR to APY (or APY back to APR) for any compounding frequency, see how a deposit grows, and compare the same rate compounded annually, monthly, daily or continuously.
Convert
Add a deposit amount (optional)
Compare compounding frequencies
| Frequency | Times/year | APY |
|---|
The rate or deposit was above the allowed range and was capped for this calculation.
This is an arithmetic calculation, not financial, investment or tax advice.
Every calculation runs in your browser — nothing is sent to a server.
Why a 5% Rate Isn't Always a 5% Rate
Banks and lenders can describe the exact same product using two different percentages, and the gap between them is entirely explained by compounding. APR (annual percentage rate) is the simple, nominal yearly rate — no compounding included. APY (annual percentage yield), sometimes called EAR (effective annual rate), is what actually happens to your money over a year once the compounding schedule is applied. A savings account paying "5% APR compounded monthly" doesn't earn exactly 5% in a year — it earns 5.116%, because each month's interest is added to the balance and starts earning interest of its own before the year is out.
How to use this calculator
- Choose a direction: APR → APY if you have a stated nominal rate and want the real effective yield, or APY → APR if a bank advertised an APY and you want the underlying nominal rate to compare elsewhere.
- Enter the rate as a percentage (5 for 5%, not 0.05).
- Pick the compounding frequency — annually, semi-annually, quarterly, monthly, daily, or continuously (the theoretical limit of compounding infinitely often).
- Optionally enter a deposit amount and currency to see exactly what that money grows to in one year.
- Open Compare compounding frequencies to see the same underlying APR turned into an APY at every compounding schedule side by side.
The formulas
n is the number of times interest compounds per year (12 for monthly, 365 for daily). As n grows without bound, the formula converges to the continuous-compounding limit APY = eAPR − 1.
This is the same formula solved for the nominal rate. For continuous compounding, it simplifies to APR = ln(1 + APY).
Three worked examples
Same 5% APR, six compounding schedules
The table below shows how much a flat 5% APR turns into at each compounding frequency — exactly what the "Compare compounding frequencies" section of the calculator produces automatically for whatever rate you enter:
| Compounding | Times per year | APY on a 5% APR |
|---|---|---|
| Annually | 1 | 5.00% |
| Semi-annually | 2 | 5.06% |
| Quarterly | 4 | 5.09% |
| Monthly | 12 | 5.12% |
| Daily | 365 | 5.13% |
| Continuously | ∞ | 5.13% |
Common mistakes with APR and APY
- Comparing a loan's APR to a savings account's APY directly. They're measured on different bases; convert one to match the other first — that's exactly what this calculator's APY → APR mode does.
- Assuming a higher APR always means more return. As Example 2 shows, a lower APR compounded more often can out-earn a higher APR compounded less often.
- Forgetting that APY already assumes a full year. If you withdraw early or a promotional rate only lasts a few months, the actual amount earned won't match the quoted APY.
- Typing the rate as a decimal instead of a percentage. Enter 5 for 5% — the calculator handles the ÷100 conversion internally.
What this calculator doesn't cover
This tool converts a stated rate into its effective yield (or back) and shows a plain one-year growth example — it doesn't model account fees, minimum-balance requirements, tiered interest rates that change with your balance, promotional "teaser" rates that expire, taxes on interest income, or deposit insurance limits. Always check a specific bank's official rate disclosure — usually printed right next to the word "APY" — before treating a number from any calculator as the rate you'll actually receive.
Sources & further reading
Frequently asked questions
What's the difference between APR and APY (or EAR)?
APR (annual percentage rate) is the nominal, stated yearly interest rate before compounding is taken into account. APY (annual percentage yield) — also called EAR (effective annual rate) — is what you actually earn or pay in a year once compounding is factored in, since interest starts earning its own interest. Whenever the rate is above 0% and compounding happens more than once a year, APY is always a little higher than APR; they're equal only when compounding is annual or the rate is 0%. That's why US banks are required to advertise APY on savings accounts and CDs so you can compare products fairly, while loans and credit cards are usually quoted in APR.
What's the exact APY formula, with a worked example?
The formula is APY = (1 + APR/n)^n − 1, where APR is entered as a decimal and n is the number of compounding periods per year. Worked example: a 5% APR compounded monthly (n = 12) gives APY = (1 + 0.05/12)^12 − 1 ≈ 5.116%. The same 5% APR compounded daily (n = 365) gives about 5.127%, and compounded continuously — the mathematical limit as n approaches infinity, APY = e^APR − 1 — gives about 5.127% too, showing that beyond daily compounding, adding more compounding periods barely moves the result.
How do you convert the other way, from APY back to APR?
Solve the same formula for APR: APR = n × ((1 + APY)^(1/n) − 1), or APR = ln(1 + APY) for continuous compounding. This matters because US savings accounts are usually advertised by APY alone, so if you want to compare that rate against a loan or another product quoted as a nominal APR, you need to convert it back. Example: an advertised 5% APY compounded monthly corresponds to a nominal APR of about 4.889% — noticeably lower than the headline number, because the APY already includes a year of monthly compounding.
Why does compounding frequency matter, and when does it stop mattering?
More frequent compounding means each bit of interest starts earning its own interest sooner, so for the exact same APR, APY rises as the compounding frequency increases: annual < semi-annual < quarterly < monthly < daily < continuous. The gap narrows quickly, though — the difference between daily and continuous compounding is usually a few thousandths of a percentage point, so once a rate compounds daily, a theoretically continuous rate makes almost no practical difference. The comparison table above this FAQ shows exactly how much (or how little) each step adds for the rate you entered.
Is my rate or deposit amount sent anywhere, and is this financial advice?
No. Every calculation — the APR/APY conversion, the compounding comparison table, and the balance growth example — runs entirely in your browser using ordinary math; nothing you type is uploaded, logged, or sent to a server, and your last entry is only kept in your own browser's local storage so it's there next time you visit. This tool performs arithmetic only: it isn't financial, investment or tax advice, and real accounts can carry fees, minimum balances, tiered rates or promotional periods that this simple calculator doesn't model — always check an account's official disclosure before relying on any number here.