APY to APR Calculator
Convert an APY back to a nominal APR.
12 = monthly, 365 = daily
Results update as you type.
How it works
Sometimes you know the effective annual yield of an account but need the underlying nominal rate, and this calculator converts an APY back to a nominal APR. You enter the annual percentage yield and how many times per year interest compounds, and it returns the equivalent nominal annual rate. This is the inverse of the usual APY calculation: instead of adding the effect of compounding to a nominal rate, it strips compounding out to recover the stated rate. The nominal rate it produces is always lower than the APY whenever compounding happens more than once a year, because the APY already includes the extra earnings from interest compounding on itself. The conversion is useful when comparing a savings account quoted in APY against a product or formula that uses a nominal rate, when reverse-engineering the periodic rate for amortization or spreadsheet calculations, or when a lender or platform mixes the two conventions. For example, a 5.12 percent APY compounded monthly corresponds to a nominal rate of about 5 percent. Keep in mind that here APR means the simple nominal annual rate; a loan's advertised APR may also fold in fees, which this pure rate conversion does not. Enter the APY and compounding frequency to find the nominal rate.
APR = n · ((1 + APY)^(1/n) − 1)
To reverse APY into a nominal rate, take one plus the APY, raise it to the power of one over the number of compounding periods, subtract one, and multiply by the number of periods. This undoes compounding, giving the nominal annual rate that, compounded at that frequency, produces the given APY. More frequent compounding makes the nominal rate lower than the APY.
Source:Finance (nominal vs effective rate)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter annual percentage yield (apy) and compounds per year.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Nominal rate (APR) updates instantly as you type — no button to press.
Frequently asked questions
How do I convert APY to APR?
Take one plus the APY, raise it to the power of one divided by the number of compounding periods per year, subtract one, and multiply by that number of periods. This reverses compounding to give the nominal rate. The calculator does this instantly when you enter the APY and compounding frequency.
Why is the nominal rate lower than the APY?
The APY includes the extra earnings that come from interest compounding on itself during the year, so it is higher than the underlying nominal rate. Converting back removes that compounding boost, producing a lower nominal figure. The more frequently interest compounds, the larger the gap between the APY and the nominal rate.
When would I need this conversion?
It is useful when comparing an account quoted in APY against one using a nominal rate, when you need the periodic rate for an amortization schedule or spreadsheet, or when a product mixes conventions. Converting to a common basis, whether nominal or effective, ensures you are comparing rates fairly rather than being misled by different quoting methods.
Is APR here the same as a loan's advertised APR?
Not exactly. Here APR means the pure nominal annual interest rate that, when compounded, gives the APY. A loan's advertised APR often also includes fees and costs, making it higher than the pure interest rate. This calculator handles only the rate conversion between effective and nominal, not fee-inclusive loan APR.
Does compounding frequency matter for the result?
Yes. The same APY corresponds to different nominal rates depending on how often interest compounds. More frequent compounding means a lower nominal rate produces the same APY. So you must enter the correct compounding frequency, whether monthly, daily, or otherwise, to get the right nominal rate from a given APY.