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APY • APR • COMPOUNDING

APY Calculator

Convert APR and APY with annual, semiannual, quarterly, monthly, daily or continuous compounding, and project how a balance can grow with recurring contributions.

Effective APY—
Equivalent nominal APR—
Effective monthly rate—
Projected final balance—
Total contributed—
Growth / interest earned—
APY uplift vs APR—

What this means

Compounding comparison

See how the same annual rate changes when compounding frequency changes.

APR ↔ APY

Annual projection

Projected balance and accumulated contributions at each year end.

Total contributedBalance

Year-by-year projection

Projected balance and accumulated contributions at each year end.

YearBalanceTotal contributedGrowth earned
Important: APY assumes reinvestment and a stable stated rate. Real savings, investment, staking or lending returns can change, and taxes, fees, platform risk and withdrawal conditions are not modeled unless you include them separately.

Method, example and assumptions

Discrete compounding. With a nominal APR as a decimal r and n compounding periods per year, the effective APY is (1 + r/n)n − 1; the reverse conversion is APR = n × ((1 + APY)1/n − 1).

Continuous compounding. As the number of periods grows without limit, the effective yield approaches APY = er − 1, and the reverse conversion is APR = ln(1 + APY). Continuous compounding gives the highest possible APY for a given nominal APR.

Example: a 5% APR compounded monthly gives APY = (1 + 0.05/12)12 − 1 ≈ 5.116%; compounded continuously it gives e0.05 − 1 ≈ 5.127%.

Projection: the balance projection converts the effective APY to an equivalent monthly rate, applies recurring contributions on their chosen schedule (beginning or end of period), and assumes the rate stays constant. It is a scenario tool, not a forecast.

Method reviewed August 24, 2026.

How to calculate APY from APR

Annual Percentage Yield (APY) measures the effective annual return after compounding. Annual Percentage Rate (APR) is a nominal annual rate that does not itself include the effect of intra-year compounding. This calculator converts between the two and shows how compounding frequency changes the effective result, from annual through daily to continuous compounding (APY = er − 1, with r the APR as a decimal).

Use the growth projection to model an initial balance and recurring contributions. It is a scenario tool rather than a forecast: the calculation assumes the selected rate remains constant over the projection period.

Frequently asked questions

What is the difference between APR and APY?

APR is a nominal annual rate. APY includes the effect of compounding, so with a positive rate and more than one compounding period per year, APY is usually higher than APR.

Does more frequent compounding always increase APY?

For the same positive nominal APR, more frequent compounding increases APY, although the incremental benefit becomes smaller as frequency rises.

Can I use this calculator for savings, staking or investments?

Yes for rate-conversion and scenario planning. The math can model a stated yield, but it does not account for changing rates, token-price changes, taxes, fees, lockups or platform-specific risks.

What is continuous compounding and how does it affect APY?

Continuous compounding credits interest an infinite number of times per year. For a nominal APR r as a decimal, APY = er − 1, the highest APY any compounding frequency can produce for that APR. Select the Continuous option to see it.

How do I calculate daily compound APY?

Enter the nominal APR, choose Daily compounding, and the calculator computes APY = (1 + APR/365)365 − 1. Daily compounding is close to the continuous-compounding ceiling for typical rates.

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