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APY vs APR Calculator

U.S. only tools

A savings account quotes its rate and often a second, higher number — the annual percentage yield. The gap is not a marketing trick: it is what compounding does to a quoted rate within a year. This page converts between the two in either direction, so you can see exactly what a quoted APR pays in a year, and what annual percentage yield a stated rate is really offering.

APY vs APR Calculator - Danfio

https://danfio.com/tools/apy-vs-apr/ - printed from this page

Currency: USD ($) - display only, nothing was converted

The rate the account quotes, before compounding is counted.

How often interest is credited within a year.

Results update as you type. Nothing leaves your device.

Currency symbol

Symbol only - nothing is converted and no exchange rate is used. Figures quoted in the explanation text stay as the sources publish them.

Annual percentage yield (APY)

5.12%

A quoted 5% APR compounding 12 times a year earns this as an effective annual yield.

The same APR, compounded differently

CompoundingAPYInterest per $10,000 in a year
Annually5%$500
Twice a year5.06%$506
Quarterly5.09%$509
Monthly5.12%$512
Daily5.13%$513

More frequent compounding raises the APY without raising the quote. Over a year the differences are small; they are shown because advertisers only ever quote the APY.

APR and APY are only equal when interest compounds once a year. Anything that compounds more often makes the APY the number that describes what you actually end up with, which is why savings accounts advertise it.

Pick a direction, enter the rate and how often interest compounds, and the page gives the other number — along with a table of how the same quoted rate behaves across compounding schedules, because that is the part adverts leave out.

About this apy vs apr calculator

Across a single year, compounding turns a quoted annual rate into a larger effective one, and the size of that gap depends only on how often interest is credited. Savings accounts advertise the effective figure because it flatters them; lenders quote the nominal one. This page converts between the two in either direction, so the arithmetic is visible rather than implied.

One formula drives both directions and its inverse undoes it, so the page never mixes two approximations of the same idea. Enter a rate, choose how often interest compounds, and the other figure appears with a table of schedules beside it. It runs with no account and no sign-up, and nothing you type is stored or shared.

Compare the effective yield for anything you save and the quoted rate for anything you borrow, because the two sides advertise the number that favors them. The page assumes a plain compounding relationship and does not fold in loan fees, which can push a borrowing APR above the APY. Read it as an estimate from the numbers you enter, not a rate quote from a bank.

How this apy vs apr calculator works

The relationship between the two

APR is the quoted annual rate, stated before anything inside the year is compounded. APY is the effective annual yield: what that rate actually earns once interest is credited and then earns interest on itself. The two numbers agree only when interest compounds once a year, and the gap widens with every additional compounding date, because each credit lands on a balance that has already grown a little.

Both directions on this page run on that single definition, so the numbers you get are inverses of each other rather than two independent approximations. One caveat about the word APR: on a loan, the disclosed APR can include fees, and one built that way may sit above an APY calculated from the same note rate. The clean one-way relationship - APY at or above APR - holds for fee-free deposit accounts, which is the case this page prices.

The formula in the APR-to-APY direction

For a nominal rate r compounded n times a year, the effective annual yield is (1 + r/n)^n − 1. A 5% APR compounded monthly is (1 + 0.05/12)^12 − 1, which works out to about 5.12% - roughly $512 of interest on $10,000 in a year instead of the $500 the quote suggests. The page applies that formula directly, with no linear shortcut, so the answer is the definition rather than an estimate of it.

The table beside the answer prices the same quoted rate under all five schedules the field offers - annually, twice a year, quarterly, monthly and daily - and shows both the APY and what a $10,000 balance would earn. Two guards keep a stray link from producing nonsense: the compounding count is rounded to a whole number between 1 and 365, and rates are held between 0% and 1000% so an extreme value cannot overflow the power function.

Backwards, from the yield to the quote

Reversing the formula gives the quoted rate behind a stated yield: n × ((1 + APY)^(1/n) − 1). It is the useful direction for borrowing, where an account advertises a monthly or daily rate and you want the annual figure it adds up to. A 5.5% APY compounded monthly backs out to an APR of about 5.37%, and the page solves it with the inverse rather than subtracting one number from the other.

This direction prints the APR and a short note, and stops there - there is no schedule table, because the question it answers is a single rate rather than a comparison across frequencies. An APY of zero returns a warning instead of a figure: nothing positive sits behind it to invert, and printing 0% as a quoted rate would suggest the page had done arithmetic it had not.

When they are the same number

If interest compounds once a year there is nothing to compound within the year, so APR and APY are the same figure. That is why the table keeps an annually row as the reference every other schedule is measured against. At realistic rates the spread between monthly and daily compounding is only a few basis points - a 5% quote moves from about 5.12% to 5.13% - while the rate itself moves in whole percentage points.

So compare the level of the rate first and the schedule second, and do not accept a visibly lower quote for the sake of more frequent compounding. Compare APY when you are saving, because that is what you actually earn, and APR when you are borrowing, because that is what the lender discloses. Read the output as arithmetic on the numbers you entered, not as a rate quote from any institution.

Where the two numbers get misquoted

Three mistakes account for most of the confusion. The first is treating a monthly rate as a twelfth of the annual figure: an account paying 0.4% a month is not 4.8% a year, it is 4.907% once each month earns on the last. The second is quoting a daily rate as if it were paid out 365 times and kept: a 0.01% daily rate compounds to 3.72% a year, not 3.65%, and the difference is the interest on interest. The third is comparing an APR on a loan that carries fees with an APY on a deposit that does not - the fee-inclusive APR is a borrowing cost, not a yield, and the two are only comparable after the fee is taken out.

The practical rule: use the APY column for anything you hold and the APR column for anything you owe, and when a page or an advert shows only one of them, convert it before comparing. The gap looks small in basis points at low rates and grows with the rate, which is exactly when the comparison matters most. A 5% quote differs from its yield by 12 basis points; a 20% quote differs by more than a full percentage point, because 20% compounded monthly is 21.94% a year.

Worked examples

Each example below was run through the calculator on this page when the site was built, so the numbers match what you see when you enter the same inputs.

Monthly compounding on a quoted APR

Which conversion: APR to APY (quoted → effective) · Annual percentage rate (APR): 5% · Interest compounds: Monthly

Annual percentage yield (APY)

5.12%

A quoted 5% APR compounding 12 times a year earns this as an effective annual yield.

Daily compounding on the same APR

Which conversion: APR to APY (quoted → effective) · Annual percentage rate (APR): 5% · Interest compounds: Daily

Annual percentage yield (APY)

5.13%

A quoted 5% APR compounding 365 times a year earns this as an effective annual yield.

Backing out the APR from a quoted APY

Which conversion: APY to APR (effective → quoted) · Interest compounds: Monthly · Annual percentage yield (APY): 5.5%

Annual percentage rate (APR)

5.37%

5.5% of effective yield, compounding 12 times a year, corresponds to this quoted APR.

When APR equals APY

Which conversion: APR to APY (quoted → effective) · Annual percentage rate (APR): 6% · Interest compounds: Annually

Annual percentage yield (APY)

6%

A quoted 6% APR compounding once a year earns this as an effective annual yield.

Annual compounding makes the two numbers identical.

Frequently asked questions

What is the difference between APR and APY?

APR is the quoted annual rate before compounding; APY is the effective annual yield after compounding within the year is counted. They are equal only when interest compounds once a year. Savings accounts advertise the APY because it is the higher, more honest number; loans quote the APR.

Why is the APY always higher than the APR?

Because the APY counts the interest earned on interest. A 5% APR compounding monthly means 5/12% interest twelve times a year, and each credit is a little bigger than the last, so the yield lands at about 5.12%. APR is the flat quote; APY is the compounding total.

Can APR be higher than APY?

Yes, for loans that charge fees or interest in advance — the APR on a mortgage or credit card includes certain fees, so it can exceed the simple APY of the same quoted rate. On a plain savings account with no fees, this page’s one-way relationship holds: APY is always at least the APR.

Which number should I compare when choosing an account?

Compare APY for savings, because it is the effective yield you actually earn. Compare APR for borrowing, because it is the quoted rate that includes the loan’s fees and is the number lenders disclose. Comparing apples to apples means picking the right one for each side of the transaction.

Does compounding more often always win?

At the same quoted APR, yes — daily compounding beats annual, but only slightly: the table shows the differences are small over realistic rates. The rate itself dwarfs the compounding schedule, so a slightly lower APR that compounds more often is not automatically the better deal.

Assumptions and sources

  • The APR-to-APY relationship follows the standard compound-interest rule.
  • Federal Reserve consumer guidance on the difference between nominal and effective (annual percentage yield) interest rates.
  • Truth in Savings Act (Regulation DD), which requires deposit accounts to disclose an annual percentage yield rather than a nominal rate.

Last reviewed 2026-09-25. Not investment or insurance advice; quotes come from a licensed provider. Read the full disclaimer.

Where a figure on this page comes from an official agency — HUD, IRS, FICO or a state body — the site keeps a dated snapshot of the source page in its sources library, and a scheduled job re-checks that snapshot, so the number can be traced back to the document it came from.

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