finance

APY Calculator

Calculate the Annual Percentage Yield (APY) from the nominal interest rate and compounding frequency. APY reflects the true annual return including the effect of compound interest.

Reviewed by Christopher FloiedUpdated April 16, 2026

This free online apy calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Nominal Interest Rate (%)

The stated annual interest rate as a percentage.

Compounding Periods per Year

How many times interest is compounded per year (12 = monthly, 365 = daily).

How to Use This Calculator

Enter your input values

Fill in all required input fields for the APY Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

Read the results

The APY Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

APY Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

•Use the APY Calculator when comparing financial options side-by-side — such as different loan terms or investment returns — to make more informed decisions.
•Use it to quickly estimate costs or returns before making purchasing, investment, or borrowing decisions.
•Use it for financial education and planning to understand how compound interest, fees, or tax affects the real value of money over time.
•Use it when building or reviewing a budget to verify that projections and calculations are mathematically correct.

About This Calculator

The APY Calculator is a free financial calculation tool designed to help individuals and businesses understand key financial concepts and estimate costs, returns, and loan parameters. Calculate the Annual Percentage Yield (APY) from the nominal interest rate and compounding frequency. APY reflects the true annual return including the effect of compound interest. The calculations are based on standard financial mathematics formulas. Results are for informational and educational purposes only and should not be considered financial, investment, or tax advice. Consult a qualified financial professional before making financial decisions. All calculations are performed in your browser — no personal financial data is stored or transmitted.

About APY Calculator

The Annual Percentage Yield (APY) calculator converts a nominal (stated) interest rate into the true effective annual rate by accounting for compound interest. Banks are required by the Truth in Savings Act to disclose APY so consumers can fairly compare savings accounts, CDs, and money market products. The APY is always higher than the nominal rate when interest compounds more than once a year, because earned interest itself starts earning interest. The more frequently interest compounds, the higher the APY. Understanding APY helps you maximize returns on savings and accurately compare financial products from different institutions.

The Math Behind It

APY is defined as (1 + r/n)^n - 1, where r is the nominal annual rate and n is the number of compounding periods per year. As n approaches infinity, the APY approaches e^r - 1, representing continuous compounding. For example, a 5% nominal rate compounded monthly yields an APY of (1 + 0.05/12)^12 - 1 = 5.116%, while continuous compounding gives e^0.05 - 1 = 5.127%. The difference between APY and the nominal rate increases with higher rates and more frequent compounding. In the US, the Truth in Savings Act requires banks to display APY prominently. On the borrowing side, the equivalent concept is APR (Annual Percentage Rate), which may include fees and uses different compounding assumptions. When comparing savings products, always use APY rather than the nominal rate. For investments with variable rates, the APY calculation applies to each period separately. The effective annual rate (EAR) is mathematically identical to APY but the term is more common in corporate finance and academic contexts.

Formula Reference

APY Formula

APY = (1 + r/n)^n - 1

Variables: r = nominal annual rate (decimal); n = compounding periods per year

Worked Examples

Example 1: Monthly compounding savings account

A savings account offers 5% nominal rate compounded monthly.

Step 1:r = 0.05, n = 12.

Step 2:APY = (1 + 0.05/12)^12 - 1.

Step 3:= (1.004167)^12 - 1 = 0.05116.

The APY is 5.116%, slightly above the 5% stated rate.

Example 2: Daily compounding CD

A CD pays 4.5% compounded daily.

Step 1:r = 0.045, n = 365.

Step 2:APY = (1 + 0.045/365)^365 - 1.

Step 3:= 0.04603.

The APY is 4.603%.

Common Mistakes & Tips

!Comparing nominal rates across products with different compounding frequencies instead of comparing APY.
!Confusing APY with APR; APR is used for loans and may include fees, while APY is for deposits.
!Assuming daily and monthly compounding produce significantly different APYs; the difference is usually small.

Related Concepts

Simple Interest

Interest calculated only on the principal, without compounding.

Rule of 72

A quick estimation method for how long it takes to double money at a given interest rate.

Used in These Calculators

Calculators that build on or apply the concepts from this page:

CD Calculator

Simple Interest Calculator

Frequently Asked Questions

Is APY the same as the interest rate?

No. The interest rate (nominal rate) is the stated rate before compounding. APY includes the effect of compounding and is always equal to or higher than the nominal rate.

Which is better: higher compounding frequency or higher nominal rate?

A higher nominal rate almost always wins. The effect of more frequent compounding is relatively small. For example, 5% compounded daily vs. monthly differs by only about 0.01%.

What is continuous compounding?

Continuous compounding is the theoretical limit of compounding infinitely often. The formula is APY = e^r - 1. In practice, daily compounding is very close to continuous.