APR vs APY converter

An APR is a nominal annual rate: a per period rate multiplied up to a year, containing no compounding within that year by construction. An APY is an effective annual yield, the total interest a balance earns or costs across 365 days once the interest already credited starts earning too. Regulation DD is explicit about the split. At 12 CFR 1030.2 it defines the annual percentage yield as a percentage rate reflecting the total amount of interest paid on an account, based on the interest rate and the frequency of compounding for a 365 day period, and the interest rate as the annual rate of interest paid on an account which does not reflect compounding.

That has a consequence people miss: a rate with no compounding schedule attached is not yet a number. Twelve percent means one thing compounded annually and another compounded daily, and only the frequency turns a nominal rate into a quantity two offers can be compared on. That is why the APR vs APY Converter asks for the schedule before it will answer.

US law decides which number goes on the poster. Regulation DD at 12 CFR 1030.8(b) says that if an advertisement states a rate of return, it shall state the rate as an annual percentage yield using that term, and that the interest rate may be stated in conjunction with, but not more conspicuously than, the annual percentage yield to which it relates. A US bank advertisement therefore leads with the APY by law, while a card or a loan leads with the APR. The two sides of your balance sheet are quoted in different units and nobody converts them for you.

Annual compounding is the only case where the two agree, and it agrees exactly: the periodic rate is the annual rate, nothing is credited part way through the year for the balance to earn on, and the APR and APY match to every decimal place. Every other schedule pushes the APY above the APR, and the gap widens with both the rate and the frequency.

APR to APY, the formula is APY = (1 + r / n) raised to the power n, minus 1, where r is the nominal annual rate as a decimal and n is the number of compounding periods in a year. At 24.99 percent compounded daily, r is 0.2499, n is 365, the periodic rate r / n is 0.00068466, and the result is 28.379 percent. Continuous compounding has no n to divide by, so the formula becomes e to the power r, minus 1, which is 28.390 percent. That is the ceiling: no schedule beats it, and daily captures 99.96 percent of it.

The other way, from an advertised APY back to the nominal rate, it inverts to APR = n multiplied by ((1 + APY) raised to the power 1 / n, minus 1). A 4.50 percent APY compounded monthly is 12 multiplied by (1.045 to the power one twelfth, minus 1), which is 4.410 percent. This is the direction a saver needs and the one most calculators skip: you want it to model a single month, reconcile a statement line, or compare an advertised yield against a note quoted nominally.

A third formula is worth knowing because the regulation publishes it. Appendix A to 12 CFR Part 1030 gives APY as 100 multiplied by ((1 + Interest / Principal) raised to the power 365 divided by days in term, minus 1). Principal is the amount assumed deposited at the beginning of the account, Interest is the total dollar interest earned on it for the term, and days in term is the actual number of days. The appendix works it through: $30.37 of interest on a $1,000 principal over 182 days is an annual percentage yield of 6.18 percent. That version starts from dollars rather than a rate, and this page's test suite reproduces its 6.18 percent exactly.

One warning about doing this in a spreadsheet. Both formulas end by subtracting 1 from a number very close to 1, and at low rates with daily compounding that subtraction quietly destroys about four significant digits. This page uses the exponential and logarithm forms that never build the intermediate value, which is why converting a rate and converting it back returns what you typed.

Regulation Z defines the APR at 12 CFR 1026.14(a) as a measure of the cost of credit, expressed as a yearly rate. For open end credit, which is what a credit card is, 12 CFR 1026.14(b) says the annual percentage rate to be disclosed shall be computed by multiplying each periodic rate by the number of periods in a year. That is a nominal calculation by design, and it is why 12 CFR 1026.6(b)(4)(i) requires the rate to be disclosed as a periodic rate and a corresponding annual percentage rate: the same fact stated twice, once per period and once per year, with no compounding in between.

Meanwhile the card compounds. A statement quoting a daily periodic rate is telling you that unpaid interest joins the balance every day and accrues interest of its own from the next. The disclosed 24.99 percent and the 28.379 percent you accrue over a year of revolving are both correct; they answer different questions, and nothing on the statement performs the second one for you.

This matters at real rate levels. The Federal Reserve's G.19 release of 7 August 2026 puts the average rate on credit card plans at 20.94 percent for all accounts in the second quarter of 2026 and 22.15 percent on accounts assessed interest. Compounded daily those are 23.286 percent and 24.786 percent, so a cardholder revolving a balance pays roughly 2.3 to 2.6 percentage points a year more than the agreement says.

One asymmetry cuts the other way. On a closed end loan the Regulation Z APR is not a bare rate at all: 12 CFR 1026.4(a) defines the finance charge as the cost of consumer credit as a dollar amount, any charge imposed by the creditor as an incident to or a condition of the extension of credit, with points and loan fees among the listed examples. A loan APR therefore sits above the note rate because it swallows origination fees, while a card APR sits below the true annual cost because it ignores compounding. This page converts rates and does not model fees, so enter a loan APR as the rate it already is.

The percentage gap is why this gets ignored and the dollar gap is why it should not be. At 4.50 percent on $10,000 the whole spread between annual and daily compounding is $10.25 over a year. At 24.99 percent on the same balance it is $338.87. The gap grows roughly with the square of the rate, so compounding frequency matters in proportion to how expensive the money already is.

So chasing a compounding schedule is almost always the wrong move on the deposit side. At the FDIC national average savings rate of 0.38 percent, effective 17 August 2026, the difference between the two ways of stating that rate is about seven cents a year on $10,000. Moving to the 0.63 percent money market average on the same date is worth about $25, roughly 350 times more. If you came here to choose between daily and monthly compounding on a business savings account, the honest answer is that it does not matter.

On the borrowing side the same arithmetic argues the opposite way, because the balance is larger and the rate several times higher. On a $25,000 revolving balance at 22.15 percent compounded daily, compounding alone is worth $659.09 a year. Know it before you compare a card against a term loan quoted nominally: lining up two APRs without restating them on one schedule flatters whichever one compounds more often.

That is what the restate mode in the APR vs APY Converter is for. It takes a nominal rate on one schedule and finds the nominal rate on another that pays out exactly the same: 24.99 percent compounded daily, for instance, restates to 25.243 percent compounded monthly. If both offers already carry an APY, no conversion is needed. Compare the APYs and stop.

This is a payments site, so the commonest misuse of this page is worth stating plainly. A merchant cash advance is priced with a factor rate, a flat multiplier with no time in it: a 1.30 factor on $50,000 means you repay $65,000, and that $15,000 charge is the same whether repayment takes six months or eighteen. There is no periodic rate to compound and no schedule to convert, so typing 1.30, or 30, into the APR vs APY Converter returns a number that is arithmetically valid and financially meaningless.

The missing variable is the one that decides the price. Because the charge is fixed at signing, the annualized cost depends entirely on how fast the money comes back. The same 1.30 factor on $50,000 is roughly 111 percent APR when a 10 percent holdback clears it in about 137 banking days, and roughly 37 percent when the same $65,000 is stretched over eighteen months. One factor rate, two completely different prices, and nothing on the term sheet says which one you signed.

The right tool is the merchant cash advance calculator, which solves for the rate that makes the cash you actually received equal the stream of daily payments, the way the actuarial method in Appendix J to 12 CFR Part 1026 does. Once it gives you an APR you can bring that back here for the APY. The same warning already sits on this site's compound interest and simple interest calculators, for the same reason.

Two other payments figures do not belong here either. A processing effective rate is a fee on a transaction, not a rate on a balance over time, so there is nothing to annualize; use the effective rate calculator. A rolling reserve does sit idle earning nothing under almost every US merchant agreement, but its real cost is having less cash on hand, not the forgone interest.