APR Calculator From APY: Convert Savings Yield

An APR calculator from APY converts an annual percentage yield into an approximate annual percentage rate by removing the effect of compounding. Enter the APY and the number of times interest compounds per year to see the equivalent APR; the conversion is mathematical and does not include loan fees or other costs.

Formula

The calculator solves for the nominal annual rate that produces the entered APY at the specified compounding frequency. It first converts APY to a decimal, takes the frequency-th root of one plus that decimal, subtracts one, then multiplies by the number of periods and converts back to a percentage:

APR = m × [(1 + APY / 100)^1/m − 1] × 100

• APY is the annual percentage yield, entered as a percentage.
• m is the number of compounding periods per year, such as 12 for monthly or 365 for daily.
• APR is the equivalent nominal annual rate, expressed as a percentage.
• APR minus APY is the difference in percentage points, not a separate interest rate.

The calculation assumes the same periodic rate is applied in every period and interest compounds at the stated frequency. It does not reverse-engineer fees, changing rates, irregular deposit timing, or a product’s specific disclosure method.

Worked Example

With the calculator’s defaults, APY is 5% and compounding occurs 12 times per year. First convert APY to a decimal: 5 / 100 = 0.05. Then calculate the monthly periodic rate that yields 5% over 12 periods:

Monthly rate = (1 + 0.05)^1/12 − 1 ≈ 0.0040741238.

Multiply that rate by 12 and convert to a percentage:

APR = 12 × 0.0040741238 × 100 ≈ 4.8890%.

The second output is 4.8890% − 5.0000% = −0.1110 percentage points. The negative difference reflects that the nominal APR is lower than the APY when positive interest compounds during the year.

How APR and APY Differ

APR is generally a nominal annual rate: it states an annualized rate without expressing the full effect of compounding in the same way APY does. APY reflects the annual outcome when interest compounds. For a positive rate compounded more than once a year, the APY is higher than the equivalent nominal APR.

For example, quoting “5%” alone is ambiguous unless you know whether it means APR or APY and what compounding assumption applies. A 5% APY compounded monthly corresponds to an APR of about 4.889%, not 5%. Conversely, a 5% APR compounded monthly produces an APY of about 5.116%, using the same assumptions.

The terms also depend on context. Deposit accounts commonly present yield using APY, while borrowing products may disclose APR that can incorporate certain costs under applicable disclosure conventions. This calculator only performs the rate conversion; it cannot determine what a financial product’s legally required APR or APY should be.

When to Use This Conversion

Use the calculator when one figure is stated as APY and you want the equivalent nominal annual rate under a clear compounding assumption, or when you need to compare rate conventions on a like-for-like mathematical basis. It is not a complete comparison of savings accounts, investments, credit products, or loans.

• Use the APY shown in the relevant account or product information, not a promotional headline whose meaning is unclear.
• Enter the compounding frequency that matches the rate definition. Monthly is 12; quarterly is 4; semiannual is 2; annual is 1.
• Read the first result as the equivalent nominal APR. The second result simply reports how many percentage points that APR is above or below the entered APY.
• Check product documents for fees, minimum-balance conditions, variable-rate terms, and other details that this conversion does not model.

Compounding Choices and Limits

The selected frequency matters because the conversion treats compounding as a fixed number of equal periods per year. For annual compounding, m = 1, so APR and APY are equal under this formula. As compounding becomes more frequent, the nominal APR equivalent to a given positive APY generally becomes lower.

The input accepts APY from 0% to 100% and a frequency from 1 to 365 periods per year. These are calculator limits for a bounded numerical entry, not a claim that a particular product offers those terms. For unusually structured rates, continuous compounding, leap-year conventions, daily balance methods, or varying rates, a simple fixed-frequency conversion may not reproduce the product’s actual calculation.

Results are rounded to four decimal places for display. That rounding is useful for comparing the conversion but does not change the underlying rate or guarantee that a provider will display the same number of digits.

Common Mistakes

• Entering APR as APY: The input specifically expects APY. Reversing the two can produce a different answer.
• Using the wrong frequency: Monthly compounding means 12 periods, not 30 or 365. Daily compounding is represented here as 365 periods.
• Confusing percentage with decimal: Enter 5 for 5%, not 0.05. The formula converts the percentage to a decimal internally.
• Treating the difference as a fee: APR minus APY is a rate-convention difference, not a charge or dollar amount.
• Assuming the converted rate captures borrowing costs: Fees and other charges may affect a loan’s disclosed APR, and are not inferred from APY here.

Frequently Asked Questions

How do I calculate APR from APY?
Use APR = m × [(1 + APY/100)^1/m − 1] × 100, where m is the number of compounding periods per year.

Is APR always lower than APY?
Under this conversion, with a positive rate and more than one compounding period per year, the equivalent nominal APR is lower than APY. With annual compounding, they are equal.

What compounding frequency should I enter?
Use the frequency stated in the product’s terms: for example, 12 for monthly, 4 for quarterly, or 365 for daily. If it is not specified, the calculator cannot determine the product’s exact convention.

Can I convert a loan APR into APY with this calculator?
This calculator runs from APY to equivalent nominal APR. The same relationship can be rearranged for a fixed periodic rate, but a loan’s disclosed APR may include costs or conventions that a simple compounding conversion does not cover.

Does this show how much interest I will earn?
No. It converts annual rate formats only. The amount earned depends on the balance, timing of deposits and withdrawals, rate changes, and the account’s calculation rules.

This conversion is an estimate of rate equivalence; consult the product disclosure for the exact figures and calculation terms.

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in apy | Annual percentage yield (APY) | % | 5 | 0 | 100
in freq | Compounding periods per year | - | 12 | 1 | 365
out apr | Equivalent nominal APR | % | freq * ((1 + apy / 100) ^ (1 / freq) - 1) * 100 | 4
out diff | APR minus APY | percentage points | apr - apy | 4