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APR to APY Calculator — Nominal ↔ Effective Annual Rate

Convert nominal APR to effective APY (and back) at any compounding frequency — daily, monthly, quarterly, or continuous. Two-way, instant, browser-only.

  • Runs locally
  • Category Calculator
  • Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.
Quick scenarios
Conversion direction
You type this
%
Calculated
%
Compounding frequency
Result
APR (nominal)
5.00%
APY (effective)
5.1162%
Spread (APY − APR)
0.1162%
The gap is what intra-year compounding adds. It widens with the rate and with how often interest compounds.
Formula
APY = (1 + 5/12)^12 − 1 = 5.1162%
n = 12 periods/year

What this tool does

Free APR to APY calculator that converts a nominal annual rate (APR) into the effective annual yield (APY) you actually earn or pay once compounding is folded in — and converts back the other way too. Type an APR, pick how often interest compounds (daily, monthly, quarterly, semi-annually, annually, or continuous), and read the APY instantly; flip the direction and the tool solves the inverse, giving you the nominal APR that produces a target APY. It uses the exact closed-form math: APY = (1 + APR/n)^n − 1 for n compounding periods per year, e^APR − 1 in the continuous limit, and the reverse APR = n × ((1 + APY)^(1/n) − 1). The result panel shows both rates side by side plus the spread between them, so you can see exactly how much intra-year compounding adds — the gap that turns a 24.99% credit-card APR into roughly a 28.4% real cost, or a 5% savings APR into a 5.12% APY. Three one-click scenarios cover the cases people actually hit: a 5% monthly savings account, a 24.99% daily-compounding credit card, and a 6.5% monthly mortgage. Every conversion runs 100% in your browser — no signup, no network call, nothing logged — and the shareable URL reproduces your exact rate and frequency so you can paste a settled comparison straight into a chat or email. Built for savers comparing bank promo rates, anyone reading the fine print on a loan or card, finance students learning why the stated rate and the effective rate diverge, and analysts who need the conversion right the first time.

Tool details

Input
Numbers
The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output
Live result + Copy
The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy
Browser-side processing
The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share
Shareable URL state
Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget
Initial JS <= 12 KB
No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit
Calculator · Finance
Category and role tags drive related tools, internal links, and quick fit checks.

How to use

  1. 1. Input

    Paste or drop your content into the tool panel.

  2. 2. Process

    Click the button. All processing is local in your browser.

  3. 3. Copy / Download

    Copy the result or download to disk in one click.

How APR to APY Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

  • Getting a realistic range before a purchase, plan, workout, or schedule decision.
  • Comparing scenarios by changing one input at a time.
  • Turning rough assumptions into a number you can discuss.

Calculation checks

  • Double-check units, dates, rates, and rounding assumptions.
  • Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
  • Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

  1. 1 Compound Interest Calculator Compound interest calculator — see how money grows over time, with monthly contributions, charts, and breakdown. Open
  2. 2 Simple Interest Calculator I = P × r × t — solve for interest, principal, rate, or time, plus total and a simple-vs-compound gap — browser-only Open
  3. 3 Rule of 72 Calculator Estimate doubling time from a rate (72 ÷ r), or the rate from a target time — side by side with the exact ln(2)/ln(1+r) figure — browser-only Open

Real-world use cases

  • Compare two savings accounts quoted in different units

    Bank A advertises a 4.95% APY. Bank B advertises a 4.9% APR compounded daily. Which one actually pays more? Drop Bank B's 4.9% into the APR → APY direction with daily compounding and you get ~5.02% APY — Bank B wins, despite the smaller headline number. Converting both to the same unit (APY) is the only way to compare deposits honestly, and it takes two clicks here.

  • See the real cost of a credit-card APR

    Your card statement says 24.99% APR, but issuers compound daily, so the rate you truly pay if you carry a balance is the APY. Enter 24.99 with daily compounding and read 28.39% APY — a 3.4 point premium the APR alone hides. That difference on a $5,000 balance is about $170 a year you would not have predicted from the stated rate.

  • Back out the nominal rate a target yield requires

    You want a product to deliver a clean 5% APY and need to know what nominal APR a monthly-compounding account must quote to hit it. Switch to APY → APR, type 5, pick monthly, and the tool returns ~4.889% APR. Useful when you are structuring a promo rate, writing a term sheet, or checking whether an advertised APR is consistent with the APY in the same disclosure.

  • Settle a finance-class question on effective rates

    The textbook asks for the effective annual rate of a 6% nominal rate compounded quarterly. Type 6, pick quarterly, and the formula line spells out APY = (1 + 6%/4)^4 − 1 = 6.1364% so you can check your hand-work and see the exact substitution, not just a final number. The continuous option covers the e^APR − 1 limit problems too.

  • Pick the compounding frequency that matters

    Cycle a single 10% APR through every frequency to feel how much compounding frequency alone moves the needle: 10.25% APY semi-annually, 10.47% quarterly, 10.4713% monthly, 10.5156% daily, 10.5171% continuous. The jump from annual to monthly is large; the jump from daily to continuous is almost nothing — a concrete demonstration of diminishing returns that's far more convincing than a paragraph of theory.

Common pitfalls

  • Comparing an APR against an APY directly. A 4.9% APR and a 4.95% APY are not what they look like — convert both to the same unit first. Quoting one product in APR and another in APY is exactly how a worse rate gets dressed up as the better deal.

  • Forgetting to set the compounding frequency before reading the result. The same APR gives a different APY at daily vs monthly vs annual compounding, and the default may not match your product. Pick the frequency the disclosure actually uses, or the number is meaningless.

  • Assuming continuous compounding for a normal bank product. Almost nothing compounds continuously — it is a theoretical ceiling. Use daily or monthly for real accounts and reserve continuous for coursework and derivatives math.

Privacy

The APR ↔ APY math (the (1 + APR/n)^n − 1 power, its inverse root, and the continuous e^APR − 1 / ln(1 + APY) forms) is plain JavaScript that runs entirely in your browser tab. No rate is ever sent to a server, there is no analytics on the values you enter, and nothing is logged. The one privacy caveat: the shareable URL state encodes your current rate, direction, and compounding frequency in the query string, so if you paste a share link into a chat or email, that destination's access log will record those values. For ordinary rates that is fine; for a confidential rate, copy the result text manually instead of sharing the URL.

FAQ

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Made by Toolora · 100% client-side · Updated 2026-06-12