APY ↔ APR Calculator — Convert Compound Interest Rates Instantly
Convert between APR and APY for any compound frequency: annually, semi-annually, quarterly, monthly, weekly, daily, or continuous. See how the same APR produces different effective yields depending on how often interest compounds. A quick reference for DeFi staking, savings accounts, and crypto lending.
How to use this tool
- Select a direction: APR to APY, or APY to APR.
- Enter the rate and select the compound frequency.
- See the converted rate and a comparison table across all frequencies.
10.00% APR compounds to 0.1047% APY
| Frequency | APY |
|---|---|
| Continuous | 10.5171% |
| Daily (365×/year) | 10.5156% |
| Weekly (52×/year) | 10.5065% |
| Monthly (12×/year) | 10.4713% |
| Quarterly (4×/year) | 10.3813% |
| Semi-annually (2×/year) | 10.2500% |
| Annually (1×/year) | 10.0000% |
About APY ↔ APR Calculator
The APY ↔ APR Calculator converts between two ways of quoting an interest rate: APR (Annual Percentage Rate), the simple stated yearly rate, and APY (Annual Percentage Yield), the effective yearly return once compounding is included. Choose a direction, enter a rate, and pick a compounding frequency, and the tool computes the equivalent figure and shows a reference table of the resulting APY at every frequency from annual to continuous.
The math is standard compound-interest mathematics. Converting APR to APY uses APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year: 1 for annual, 2 semi-annual, 4 quarterly, 12 monthly, 52 weekly, and 365 daily. Continuous compounding is the limit of that formula and uses APY = e^(APR) − 1. The reverse direction inverts the same relationship: APR = n × ((1 + APY)^(1/n) − 1), and for continuous compounding APR = ln(1 + APY). Because compounding earns interest on previously earned interest, APY is always greater than or equal to APR, and they are equal only when interest compounds exactly once per year.
This is useful when comparing offers that are quoted differently. DeFi protocols, crypto lending platforms, and staking dashboards often advertise APY, while loans and some savings products quote APR. Converting both to the same basis lets you compare them fairly, and the all-frequencies table makes it easy to see how much more frequent compounding adds at a given headline rate. It is also a quick way to understand why a 10% APR can be marketed as a slightly higher APY.
The calculator assumes a constant rate and ideal, uninterrupted compounding over a full year. Real products differ: fees, variable rates, lockup periods, minimum balances, partial-year holding, and changing token prices all affect what you actually earn. The figures here are a mathematical conversion of one rate quotation into another, not a projection of returns, and the all-frequencies table is intended to build intuition about how compounding affects effective yield. This tool is an educational reference rather than financial advice, and you should verify the compounding terms of any specific product against its own disclosures. All calculations run locally in your browser.
Frequently Asked Questions
- What is the difference between APR and APY?
- APR is the simple annual rate with no compounding applied, while APY is the effective annual return after compounding is taken into account. For the same APR, compounding more often during the year produces a higher APY because each period earns interest on the interest already credited.
- How is APY calculated from APR?
- The tool uses APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. For continuous compounding it uses APY = e^(APR) − 1, which is the mathematical limit as the number of periods grows without bound. Daily compounding is already very close to continuous in practice.
- How does it convert APY back to APR?
- It inverts the compounding formula: APR = n × ((1 + APY)^(1/n) − 1) for a finite frequency, and APR = ln(1 + APY) for continuous compounding. This tells you the simple stated rate that would produce a given effective yield at the chosen compounding frequency.
- Why is APY always equal to or higher than APR?
- Because compounding lets earned interest itself earn interest within the year. The only case where APY equals APR is annual compounding, where interest is credited just once and there is no intra-year balance to compound. Every more frequent option produces APY greater than APR.
- What does continuous compounding mean?
- Continuous compounding is the theoretical case of compounding at every instant, the limit of making n infinitely large. It uses the exponential formula and gives the highest APY for a given APR. The difference between daily and continuous compounding is tiny, so daily is a good real-world approximation.
- Why do DeFi and staking platforms quote APY instead of APR?
- Many crypto lending, staking, and yield platforms compound rewards frequently, so quoting APY shows the effective return a user can expect over a year. Converting an advertised APY to APR, or comparing two offers on the same basis, helps you judge whether a higher headline number reflects a better rate or just more frequent compounding.
- Are these numbers a guarantee of what I will earn?
- No. The calculator performs an exact rate conversion assuming a fixed rate and uninterrupted compounding for a full year. Real returns depend on fees, variable rates, lockups, holding period, and, for crypto, token price changes. Treat the output as an educational reference, not financial advice or a forecast.
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