APR to APY Calculator
APR to APY Calculator
Compounding Frequency Comparison
Enter an APR and convert to compare effective APY across common compounding frequencies.
| Compounding | Periods/year | APY from APR | Periodic rate |
|---|---|---|---|
| Run an APR to APY conversion to fill this table. | |||
Balance Growth Mode
Compare Two Offers
Formulas: $$\text{APY}=(1+\tfrac{\text{APR}}{m})^{m}-1 \quad;\quad \text{APR}=m\left((1+\text{APY})^{1/m}-1\right)$$ Continuous: $$\text{APY}=e^{\text{APR}}-1 \quad;\quad \text{APR}=\ln(1+\text{APY})$$
Formula: $$\text{CAGR}=\left(\frac{\text{Ending}}{\text{Beginning}}\right)^{1/n}-1$$
APR vs APY: What’s the Difference?
APR is a nominal yearly rate without intra-year compounding. APY/AER/EAR is the effective yearly rate that includes compounding. With m periods/year, \( \text{APY} = (1 + \text{APR}/m)^m - 1 \).
| Metric | Best for | Includes compounding? |
|---|---|---|
| APR | Quoted loan or nominal annual rate | No |
| APY/AER/EAR | Savings yield and apples-to-apples rate comparison | Yes |
| CAGR | Smoothed multi-period growth | Yes, across periods |
CAGR is the smoothed multi-period growth rate: \( \left(\frac{\text{Ending}}{\text{Beginning}}\right)^{1/n} - 1 \).
- Daily compounding: Choose 365 or 360 based on convention.
- Continuous compounding: \( \text{APY} = e^{\text{APR}} - 1 \).
- CAGR caveat: Ignores interim volatility and cash flows.
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Release Updates
v1.1 (May 21, 2026)
- Added a compounding frequency comparison table for annual, semiannual, quarterly, monthly, weekly, daily 365, daily 360, and continuous compounding.
- Added shareable result URLs, a copy result button, balance growth projection, and two-offer APR/APY comparison mode.
APY to APR Calculator
Use the conversion dropdown above to switch from APR to APY into APY to APR mode. APY, AER, and EAR are effective annual rates, so the reverse calculation removes the compounding effect and returns the nominal APR for the selected frequency.
APR vs APY: Quick Difference
| Term | Meaning | Use it when |
|---|---|---|
| APR | Annual Percentage Rate. A nominal annual rate before intra-year compounding. | You need the quoted nominal cost or base interest rate. |
| APY | Annual Percentage Yield. The effective annual return after compounding. | You compare savings accounts, CDs, deposits, or yield offers. |
| AER | Annual Equivalent Rate. Common UK/EU term for effective annual yield. | You compare interest-bearing accounts in markets that use AER. |
| EAR | Effective Annual Rate. Another name for the compounded annual rate. | You want a finance-textbook equivalent of APY/AER. |
APR to APY Formula
For discrete compounding, divide APR by the number of compounding periods per year, compound that periodic rate for one year, then subtract 1: $$ \text{APY} = \left(1 + \frac{\text{APR}}{m}\right)^m - 1. $$ Here, m is the number of compounding periods per year, such as 12 for monthly or 365 for daily.
APY to APR Formula
To convert APY back to nominal APR, solve the same relationship for APR: $$ \text{APR} = m\left((1+\text{APY})^{1/m}-1\right). $$ For continuous compounding, use \( \text{APY}=e^{\text{APR}}-1 \) and \( \text{APR}=\ln(1+\text{APY}) \).
Compounding Frequency Comparison
The same APR produces a higher APY as compounding becomes more frequent. Annual compounding uses one period per year; quarterly uses 4; monthly uses 12; weekly uses 52; daily commonly uses 360 or 365. Continuous compounding is the mathematical limit where compounding happens constantly.
Examples
Example: 5% APR compounded monthly
\( (1 + 0.05/12)^{12} - 1 \approx 5.1162\% \) APY.
Example: 12% APR compounded daily
With a 365-day basis, \( (1 + 0.12/365)^{365} - 1 \approx 12.7475\% \) APY.
Example: Convert 5% APY to APR
With quarterly compounding, \( 4((1+0.05)^{1/4}-1) \approx 4.9089\% \) APR.
Daily 360 vs Daily 365
Daily 365 treats the year as 365 compounding periods. Daily 360 treats the year as 360 periods, a convention often seen in banking, money-market, and loan contexts. The difference is usually small, but it matters when comparing disclosures that use different day-count bases.
AER, EAR, and APY: Are They the Same?
Yes for practical comparison purposes. APY, AER, and EAR all refer to an effective annual rate that includes compounding. The label changes by region and context: APY is common in the US, AER is common in the UK and EU, and EAR is common in finance education.
When Should You Use APR vs APY?
- Savings accounts and CDs: Compare APY/AER because it includes compounding.
- Loans and credit cards: APR shows the nominal quoted rate, but the effective cost depends on compounding and fees.
- Investments: Use CAGR for long-run growth summaries, and pair it with volatility, deposits, withdrawals, and fees.
- Offer comparisons: Convert both offers to APY/EAR to compare equivalent annual value.
Frequently Asked Questions
What is the difference between APR and APY?
APR is the nominal annual rate without compounding. APY is the effective annual yield including compounding. With m periods per year, APY = (1 + APR/m)m - 1.
Do you support daily and continuous compounding?
Yes. Daily uses 365 or 360 days per year. Continuous uses APY = eAPR - 1 and APR = ln(1 + APY).
How do you calculate CAGR?
CAGR = (Ending / Beginning)1/n - 1, where n is the number of years or periods.
Is my data private?
Yes. Everything runs entirely in your browser; nothing is uploaded or stored.
This page is for education only and is not financial advice.