APR & APY Converter

Turn a nominal annual rate (APR) into its effective yield (APY) — or work back the other way — for any compounding frequency, and see the rate per period plus how much compounding adds.

Rate to convert
Direction
Converted rate
Effective annual yield (APY)
Rate per period
APY − APR gap
Enter a rate and choose how often it compounds to convert it.

Every conversion runs in your browser — the rates you enter never leave your device.

FAQ

How do you convert between APR and APY?

The effective yield comes from the nominal rate and how often it compounds: APY = (1 + APR/n)^n − 1, where n is the number of compounding periods in a year. To go the other way, APR = n × ((1 + APY)^(1/n) − 1). For example, 12% APR compounded monthly works out to about 12.6825% APY.

What is the difference between APR and APY?

APR is the plain yearly rate before compounding; APY is what you actually earn or pay once interest compounds through the year. Because each period earns interest on the period before it, APY is always a little above APR, and the gap widens with a higher rate or more frequent compounding. The two are equal only when interest compounds once a year.

How does compounding frequency change the result?

The more often interest compounds, the further the effective yield pulls ahead of the nominal rate — so for one APR, daily beats monthly beats yearly. Continuous compounding is the theoretical limit, the most APY a given APR can reach, found with APY = e^APR − 1. It marks the ceiling rather than what a real account usually pays.

Will this match my bank or lender’s figures?

Not always. This converts a pure nominal rate, whereas a real loan APR can fold in fees and an advertised APY may round off or assume a particular day count. Use it to compare rates on the same footing, and confirm the provider’s own numbers before you commit.

Written and reviewed by the BroBroGo editorial team.Last updated:

The Fundamental Difference Between APR and APY

In financial decision-making, understanding the distinction between nominal and effective interest rates is essential. The nominal annual rate, or Annual Percentage Rate (APR), represents the plain yearly interest rate before compounding is factored in. In contrast, the Effective Annual Yield (APY) represents the actual interest earned or paid over a year once compounding is taken into account.

Because interest earned in one period generates its own interest in subsequent periods, the APY is higher than the APR for any compounding frequency greater than once per year. The two rates are equal only when interest compounds exactly once a year. Understanding this difference allows individuals to evaluate the true cost of a loan or the actual return on an investment.

How Compounding Frequency Impacts the Effective Yield

Compounding frequency determines how often interest is calculated and added to the principal balance. As the frequency of compounding increases, the effective yield pulls further ahead of the nominal rate. This occurs because interest is calculated on an increasingly larger balance throughout the year.

The tool defaults to converting 12% APR compounded monthly to 12.6825% APY. If the compounding frequency changes, the resulting APY will shift:

  • Annually: Interest compounds once per year, meaning APR and APY are identical.
  • Semi-annually: Interest compounds twice per year.
  • Quarterly: Interest compounds four times per year.
  • Monthly: Interest compounds 12 times per year.
  • Semi-monthly: Interest compounds 24 times per year.
  • Biweekly: Interest compounds 26 times per year.
  • Weekly: Interest compounds 52 times per year.
  • Daily: Interest compounds 365 times per year.
  • Continuous: Interest compounds constantly, representing the theoretical limit of compounding frequency.

The difference between the nominal rate and the effective yield is represented as the "APY − APR gap". This gap widens when you have a higher nominal rate or more frequent compounding periods.

Mathematical Formulas Behind APR and APY Conversions

The mathematical relationship between APR and APY depends on the number of compounding periods in a year, represented by the variable n.

Converting APR to APY

To calculate the effective annual yield from a nominal annual rate, use the following formula:

APY = (1 + APR/n)ⁿ − 1

Converting APY to APR

To perform the reverse calculation and find the nominal annual rate from a known effective annual yield, use this formula:

APR = n × ((1 + APY)^(1/n) − 1)

Continuous Compounding

When compounding occurs continuously, the frequency n approaches infinity. In this theoretical limit, the conversion relies on the mathematical constant e (approximately 2.71828):

APY = e^APR − 1

When using the converter for continuous compounding, the output for "Rate per period" is not displayed because there are no discrete compounding periods. For all other frequencies, the tool calculates and displays the "Rate per period" alongside the converted rate.

Comparing Financial Products on an Equal Footing

Different financial institutions advertise rates using different standards. A savings account might advertise an APY, while a credit card or car loan might disclose an APR. To make an accurate comparison, you must convert these rates to the same metric.

This tool allows you to perform conversions in both directions:

  • APR → APY: Useful when you know the nominal rate of an investment or loan and want to find its effective yield.
  • APY → APR: Useful when you want to calculate the nominal rate that would be required to achieve a specific effective yield.

By converting all options to a single standard, you can compare the true financial impact of different products. However, these conversions treat APR as a plain nominal rate and do not include external fees. Consequently, the calculated values may not exactly match a bank's advertised APY or a lender's disclosed APR, which may incorporate origination fees, closing costs, or specific day-count conventions. The results are for reference only and do not constitute investment, tax, or financial advice.

Using the APR & APY Converter

The tool accepts numerical values for the "Rate to convert". The input rate must be 0% or more. The interface processes your inputs in real time and displays the following outputs based on your selected direction and compounding frequency:

  • Nominal annual rate (APR)
  • Effective annual yield (APY)
  • Rate per period (not shown for continuous compounding)
  • APY − APR gap

Error Handling

If you enter invalid data, the tool will display specific error messages:

  • Entering a negative number will display: "Enter a rate of 0% or more."
  • Entering non-numerical text will display: "Enter a valid number to convert."
  • Entering an excessively high rate will display: "That rate is too large to convert."

Privacy and Processing

Every conversion runs in your browser, and the rates you enter never leave your device. No data is uploaded to external servers.

Frequently Asked Questions

How do you convert between APR and APY?

The effective yield comes from the nominal rate and how often it compounds: APY = (1 + APR/n)ⁿ − 1, where n is the number of compounding periods in a year. To go the other way, APR = n × ((1 + APY)^(1/n) − 1). For example, 12% APR compounded monthly works out to about 12.6825% APY.

What is the difference between APR and APY?

APR is the plain yearly rate before compounding; APY is what you actually earn or pay once interest compounds through the year. Because each period earns interest on the period before it, APY is always a little above APR, and the gap widens with a higher rate or more frequent compounding. The two are equal only when interest compounds once a year.

How does compounding frequency change the result?

The more often interest compounds, the further the effective yield pulls ahead of the nominal rate — so for one APR, daily beats monthly beats yearly. Continuous compounding is the theoretical limit, the most APY a given APR can reach, found with APY = e^APR − 1. It marks the ceiling rather than what a real account usually pays.

Will this match my bank or lender’s figures?

Not always. This converts a pure nominal rate, whereas a real loan APR can fold in fees and an advertised APY may round off or assume a particular day count. Use it to compare rates on the same footing, and confirm the provider’s own numbers before you commit.

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