APY Calculator
Calculate the Annual Percentage Yield (APY) from the nominal APR, or vice-versa, and see projections with compounding.
Type in your APR or APY — changing one automatically calculates the other based on compounding frequency.
Click "Calculate" to view results.
Advertised Rate
Real Rate of Return
Compounding edge
Enter an initial deposit or regular deposit to generate a savings projection chart.
Enter an initial deposit or regular deposit to generate a year-by-year growth table.
| Year | Deposits Added | Interest Earned | Year End Balance |
|---|---|---|---|
APY & APR Formulas
Nominal rate (APR) and Effective yield (APY) are related through the compound interval. Since compounding adds interest back to your balance, the yield is always higher than the APR.
Where: r = nominal APR as a decimal, n = compound periods per year (e.g. 12 for monthly), and APY is expressed as a decimal.
Your Step-by-Step Calculation
3. Substitute: APY = (1 + / ) - 1
4. Calculate: APY = () - 1
5. Result: APY = → %
3. Substitute: APR = × [(1 + )1/ - 1]
4. Calculate: APR = × [ - 1]
5. Result: APR = → %
What Is the APY Calculator?
The APY Calculator converts a stated Annual Percentage Rate (APR) into the true Annual Percentage Yield (APY) based on your compounding frequency. While banks advertise APR, the actual return you earn depends on how often interest compounds — making APY the more accurate measure for comparing savings products.
The Truth in Savings Act (TISA) in the United States requires financial institutions to disclose APY on deposit accounts, ensuring consumers can make fair comparisons. This calculator helps you verify those disclosures and compute APY for any compounding schedule.
The APY Formula
APY = (1 + APR/n)^n - 1
where APR is the nominal annual rate (as a decimal) and n is the number of compounding periods per year. The more frequently interest compounds, the higher the APY relative to APR.
How to Use the APY Calculator
Using this calculator is straightforward. Enter your known values into the fields below, and the solver will compute the result immediately. Here is what each input represents:
Worked Example: Converting a 4.5% APR Savings Account to APY
Problem: Your bank offers a savings account with a 4.5% APR, compounded daily (365 times per year). What is the actual APY you will earn?
1. Identify the Variables
APR = 4.5% = 0.045 (decimal). Compounding periods per year (n) = 365.
2. Calculate the Periodic Rate
Divide APR by the number of compounding periods: 0.045 / 365 = 0.00012329.
3. Apply the APY Formula
APY = (1 + 0.00012329)^365 − 1 = 1.04603 − 1 = 0.04603.
4. Convert to Percentage
0.04603 × 100 = 4.603%. The daily compounding adds an extra 0.103% yield over the stated 4.5% APR.
How to Calculate APY Step-by-Step
Understanding the underlying solution workflow helps build mathematical intuition:
Real-World Applications of APY Calculator
Comparing High-Yield Savings Accounts
Online banks and credit unions advertise different APRs and compounding schedules. Converting all offers to APY lets you identify which account truly pays the highest return.
Certificate of Deposit (CD) Ladder Planning
When building a CD ladder with different maturities and rates, APY ensures you compare the actual yield of each rung, not just the advertised rate.
Understanding DeFi Yield Farming Returns
Crypto yield farming platforms often quote APR. Converting to APY reveals the true return when rewards auto-compound hourly or daily.
Common Pitfalls & Mistakes to Avoid
Comparing APR from One Account to APY from Another
Always convert both accounts to APY (or both to APR) before comparing. Mixing the two metrics will give misleading results.
Assuming Higher Compounding Frequency Always Matters
The APR-to-APY gap narrows as rates decrease. At 0.5% APR, the difference between monthly and daily compounding is negligible — focus on the rate itself.
Ignoring Introductory Rate Expirations
Some banks offer promotional APYs that revert to a lower rate after 6-12 months. Calculate the blended effective APY across the full period.
Key Terminology Glossary
Expert Tips for APY Calculator
- If you're comparing savings accounts, always compare the APY rather than the APR. APY is the true reflection of what you'll earn.
- The more frequently interest is compounded, the higher the APY will be relative to the nominal APR.
- Bidirectional conversion: Type in APR to find APY, or type in APY to find the APR needed.
- Consider regular deposits: Adding even a small regular deposit makes compounding grow your balance significantly faster.
About the APY Calculator
The APY Calculator is maintained by Basic Math Tools, an educational platform committed to providing accurate STEM and financial computing tools. Every tool processes calculations transparently in your browser for privacy and speed.
If you have suggestions or request additional features, please review our Editorial Policy or contact our math team.