APR and EAR Calculator: Compare Annual Interest Rates

This APR and EAR calculator converts a quoted annual percentage rate (APR) into its effective annual rate (EAR), showing the effect of compounding during the year. Enter the APR and the number of compounding periods per year to see the equivalent annual rate and the difference between the two rates.

Formula

The effective annual rate is the annual growth produced by applying the nominal annual rate in equal compounding periods:

EAR = 100 × [(1 + APR ÷ (100 × n))ⁿ − 1]

• APR is the nominal annual percentage rate entered as a percentage, such as 8 for 8%.
• n is the number of compounding periods in one year: 1 for annual, 4 for quarterly, 12 for monthly, or 365 for daily compounding.
• EAR is the effective annual percentage rate after compounding is included.

The calculator’s second result is EAR − APR, measured in percentage points. A positive difference shows how much the annualized effect of compounding exceeds the nominal APR. This result is a rate comparison, not a dollar cost or return.

Worked Example

Using the defaults, APR = 8% and n = 12 monthly periods:

1. Convert the APR to a decimal: 8 ÷ 100 = 0.08.
2. Find the monthly rate: 0.08 ÷ 12 = 0.0066666667.
3. Apply monthly compounding for 12 periods: (1 + 0.08 ÷ 12)¹² − 1 ≈ 0.0829995068.
4. Convert back to a percentage: 0.0829995068 × 100 ≈ 8.2999% EAR.
5. Subtract the nominal APR: 8.2999 − 8 = 0.2999 percentage points.

Results are rounded to four decimal places for display. Intermediate steps use unrounded values, so a hand calculation rounded earlier can differ slightly in its last digit.

Assumptions

• The APR is a nominal annual rate divided into equal compounding periods.
• Interest compounds once per period at APR ÷ n; the calculation assumes no variation in the rate during the year.
• The calculator does not include fees, taxes, payment timing, balances, or cash flows. It compares rates only.
• The selected period count is treated as the number of equal periods in a year. Actual financial products may use a different day-count or accrual convention.

APR and EAR: What the Difference Means

APR and EAR both describe annual interest, but they answer different questions. A nominal APR is an annual rate before adjusting for the effect of compounding within the year. EAR, also called the effective annual rate or annual percentage yield in some deposit contexts, expresses the result of applying that periodic interest repeatedly over a full year.

For example, a nominal 8% APR compounded monthly does not simply produce exactly 8% growth over a year if interest is retained and itself earns interest. The calculator’s example produces about 8.2999% effective annual growth under its stated mathematical assumptions. With annual compounding, by contrast, EAR equals APR because there is only one compounding period.

For a positive APR, more frequent compounding generally produces a higher EAR, since interest is added to the balance more often. This comparison isolates compounding; it does not establish which loan or deposit has the lower total cost or higher realized return. Fees, required payments, introductory periods, variable rates, and how a balance changes can matter to the full financial outcome.

How to Use the Calculator

• Enter the nominal APR as a percentage, not a decimal. For an 8% APR, enter 8—not 0.08.
• Enter the number of compounding periods per year. Use 12 for monthly compounding or 4 for quarterly compounding, if that matches the product’s terms.
• Read the first output as the effective annual percentage rate.
• Read the second output as the percentage-point difference between EAR and APR; it is not a percent change.

The allowed range for periods is 1 to 365, which covers common whole-period conventions and daily compounding. It does not model continuous compounding or fractional periods. If a disclosure uses a specific daily accrual rule, check its definition rather than assuming that a simple 365-period calculation reproduces every detail.

Common Mistakes and Limits

A frequent mistake is treating APR and EAR as interchangeable. They match under annual compounding, but generally differ when interest compounds multiple times a year. Another is entering a rate in decimal form: entering 0.08 means 0.08%, not 8%.

Do not confuse the percentage-point difference with a percentage increase. In the example, EAR exceeds APR by 0.2999 percentage points. The relative increase compared with the APR would be a different calculation and is not the calculator’s second output.

Most importantly, an APR shown in a financial disclosure may incorporate or present charges according to a specific product definition, while this calculator treats the entered APR simply as a nominal rate divided evenly across periods. It does not add fees or recreate a lender’s APR methodology. It also does not compute a monthly payment, total interest on a loan, investment profit, or the amount of interest earned on a changing balance. Use the actual terms and disclosures for those figures; rates and fees are inputs to verify with the provider, not values this tool can look up.

Frequently Asked Questions

What is the difference between APR and EAR?
APR is the nominal annual rate before accounting for intra-year compounding. EAR is the annualized result after compounding at the stated frequency.

How do I calculate EAR from APR?
Convert APR to a decimal, divide it by the number of compounding periods per year, add 1, raise that result to the number of periods, subtract 1, and convert the result to a percentage.

Is EAR always higher than APR?
For a positive rate compounded more than once a year, EAR is higher than APR. With annual compounding they are equal. The exact relationship depends on the rate and compounding convention.

What compounding frequency should I enter?
Use the frequency stated in the account or loan terms: for example, 12 for monthly or 4 for quarterly compounding. If the terms use a special day-count method, this simplified calculator may not match it exactly.

Does this calculator include fees?
No. It converts a nominal rate using compounding alone. It does not calculate a regulated or product-specific APR from fees, cash flows, or payment timing.

Is EAR the same as APY?
They are closely related annualized measures of compounded growth, but terminology and disclosure calculations can depend on product and applicable conventions. Check the provider’s stated definition when comparing actual products.

This result is an estimate, and the lender’s disclosure gives the exact figures.

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in apr | Nominal annual rate (APR) | % | 8 | 0.01 | 100
in n | Compounding periods per year | - | 12 | 1 | 365
out ear | Effective annual rate (EAR) | % | 100 * ((1 + apr / (100 * n)) ^ n - 1) | 4
out diff | EAR minus APR | percentage points | ear - apr | 4