How do I convert APR to APY?

Use APY = (1 + APR/m)^m − 1 for m compounding periods per year, or APY = e^APR − 1 for continuous compounding.

How do I convert APY to APR?

Use APR = m × ((1 + APY)^(1/m) − 1) for m periods per year, or APR = ln(1 + APY) for continuous compounding.

Which is better for comparing accounts, APR or APY?

APY. It already includes compounding and enables apples-to-apples comparisons.

APR ↔ APY Converter Calculator

Q: Does APY include fees?

No. APY reflects interest compounding; fees reduce realized yield.

Inputs

Conversion

Compounding

APR (nominal)

%

APR is the nominal rate tied to a compounding schedule. APY is the effective one-year yield including compounding. Continuous compounding uses e.

Results

Enter inputs to convert.

How to use the converter

Select APR → APY or APY → APR.
Pick the compounding schedule (daily, monthly, quarterly, semiannual, annual, or continuous).
Enter the known rate.
Read the equivalent rate and review the formula steps.
Use APY for apples-to-apples deposit comparisons; use APR to interpret loans.

Results interpretation

For the same APR, more frequent compounding → higher APY.
To compare deposit accounts fairly, convert everything to APY.
Continuous compounding gives APY = e^APR − 1 (theoretical upper bound).
Use APR when lenders quote nominal rates linked to compounding (e.g., monthly).

How this converter works

Formulas, steps, assumptions

For discrete compounding with m periods/year and nominal APR r, the effective annual yield is APY = (1 + r/m)^m − 1. Rearranging yields APR = m × ((1 + APY)^(1/m) − 1).

For continuous compounding, APY = e^r − 1 and APR = ln(1 + APY).

Assumptions: fixed rate for one year, no fees, no tiering. Real accounts may use daily balances or fees that change realized yield.

Use cases & examples

Example 1 — Savings accounts: Bank A quotes APR 5.00% monthly. Convert to APY to compare with Bank B’s APY 5.12%.

Example 2 — CDs: A CD advertises APY 5.10% (daily). Convert to nominal APR to understand the underlying rate.

Example 3 — Continuous comp: For modeling, switch compounding to continuous and observe APY = e^APR − 1.

APR vs. APY: Convert Rates Correctly and Compare Fairly

A clear APR ↔ APY converter helps you compare rates across banks and products without guesswork. APR (annual percentage rate) is a nominal rate that must be paired with a compounding schedule—monthly, quarterly, or annually—to describe what you actually earn in one year. APY (annual percentage yield) is the effective one-year return that already includes compounding. Converting between them ensures your comparisons are apples-to-apples, reveals when “5%” at one bank isn’t the same as “5%” at another, and prevents marketing from hiding the real number that matters.

Why APY is the comparison standard

Two accounts can both advertise “5%,” yet the one compounding monthly will deliver slightly more than the one compounding annually. APY captures this difference by folding compounding into a single one-year figure. If you only have APR, you can reconstruct APY using (1 + APR/m)^m − 1, where m is periods per year. Once everything is in APY terms, choosing the better offer is straightforward.

APR still matters—especially for loans

For loans and many disclosures, rates are quoted as APR tied to a compounding schedule (often monthly). APR integrates neatly into amortization formulas and payment systems. But if you’re comparing consumer deposit accounts (savings, CDs), APY communicates the outcome more directly: “What did I earn over a year?”

Continuous compounding in context

Continuous compounding is a mathematical ideal where interest accrues at every instant. It simplifies relationships to APY = e^r − 1, offering intuition and a theoretical upper bound compared with discrete schedules. While real products use discrete compounding, the continuous case provides a useful reference point.

A quick checklist for comparing rates

Normalize to APY before comparing deposit accounts.
Confirm compounding whenever you see an APR (monthly, daily, etc.).
Account for fees; they reduce realized yield even if APY looks identical.
Match your horizon—APY is a one-year metric; for shorter terms, use a term-specific calc.

With a quick conversion, you’ll see through marketing gloss, weigh offers fairly, and select the rate that truly pays more over your time frame.

APR ↔ APY — FAQ

Is APY always higher than APR?

For positive rates with discrete compounding, yes—APY ≥ APR. With continuous compounding, APY = e^APR − 1.

What compounding should I assume if none is listed?

Ask the provider. Monthly is common for deposits, but don’t compare until you know.

Does APY include fees?

No. APY reflects interest compounding only. Fees reduce realized yield.

Can I convert for any time period?

This tool normalizes to one year. For shorter terms, compute the term’s effective rate.

Do loans use APY?

Loans typically use nominal APR with a compounding schedule; some disclosures show effective rates too.