APY to APR calculator: convert both ways

APY includes compounding and APR doesn't, so the same return shows up as two different numbers. The calculator converts either way for any compounding schedule, down to every Ethereum block, and shows why a vault's 7-day and 30-day APY rarely match.

An APY to APR calculator turns one way of quoting a return into the other. APR (annual percentage rate) is the simple yearly rate, while APY (annual percentage yield) adds the interest earned on interest as it compounds, so an APY is always equal to or higher than the APR behind it. At 5% APY with daily compounding, the matching APR is about 4.88%. The gap grows as rates rise and as compounding gets more frequent, which is why crypto products that compound constantly show a visible difference between the two figures.

Enter a rate in either box below and the other updates. The table underneath shows the same APR at every common compounding frequency.

How to convert APY to APR

The formula runs the compounding backwards: APR = n × ((1 + APY)^1/n − 1), where n is the number of compounding periods in a year. A 5% APY compounded daily (n = 365) works out to 365 × (1.05^1/365 − 1), or about 4.879% APR. For continuous compounding, the limit as n grows without bound, the formula becomes APR = ln(1 + APY), which gives about 4.879% for the same 5% APY. The two answers match to three decimal places because daily compounding is already very close to continuous.

How to convert APR to APY

Going the other way, APY = (1 + APR / n)ⁿ − 1. An APR of 10% compounded monthly becomes (1 + 0.10/12)¹² − 1, or about 10.47% APY, and compounded daily it becomes about 10.52%. The SEC's compound interest calculator runs the same arithmetic for a balance over several years.

At low rates the choice of compounding schedule barely matters. At 20% APR the gap between monthly and daily compounding is almost 0.2 percentage points, and the gap between APR and APY is more than two points.

APY vs APR in crypto

Lending markets and vaults usually quote APY, because onchain interest accrues continuously. A lending market like Aave accrues interest by the second, and Ethereum produces a slot every 12 seconds, according to ethereum.org, which is about 2.6 million compounding periods a year. At that frequency the APY matches the continuous-compounding figure to several decimal places. Borrow costs are often shown as APR, and some centralised platforms quote APR for staking or savings products that pay out daily or weekly.

The difference matters most when comparing products that quote differently. A savings product at 5% APR paid daily and a vault at 5% APY aren't the same return, because the first works out to about 5.13% APY. Converting both to APY puts them on the same basis. Our explainer on what APY means in crypto covers the benchmark rates for each asset and why sites show different APYs for the same product.

Why a vault's 7-day and 30-day APY differ

A vault doesn't pay interest in the usual sense. Its earnings raise the price of its share token, and the APY shown on a vault page is annualised from how much that share price moved over a lookback window. A 7-day APY takes the last week's change and compounds it over a year, while a 30-day APY does the same with the last month, so the two windows capture different stretches of performance.

When a strategy's returns pick up, the 7-day figure moves first and sits above the 30-day figure, and when returns slow, the 7-day figure drops below it. A short window reacts faster and is noisier, since one strong or weak day carries more weight, while a longer window is steadier and slower to change. The second half of the calculator takes three share prices and shows both figures side by side. Upshift vaults report a trailing APY built from the vault's share price in this way, and the vault guide explains how the share token works.

Neither window is a forecast. A trailing APY describes what the vault earned in the past, and the rate going forward depends on lending rates, funding rates and the strategy's positions. Always make sure to do your own research and be aware of the above and any other risks before depositing.

Frequently asked questions

What is the formula to convert APY to APR?

APR = n × ((1 + APY)^1/n − 1), where n is the number of compounding periods per year. For continuous compounding, APR = ln(1 + APY).

Is 5% APY the same as 5% APR?

No. A 5% APY with daily compounding equals about 4.88% APR, and a 5% APR compounded daily equals about 5.13% APY.

Is APY always higher than APR?

APY is equal to APR when interest compounds once a year and higher whenever it compounds more often. It's never lower for a positive rate.

Why do crypto platforms show APY?

Onchain interest accrues continuously, often every block, so APY describes what a depositor actually earns over a year if the rate holds. It's also the larger of the two numbers.

How is a vault's APY calculated?

From the change in its share price over a window, such as 7 or 30 days, annualised with compounding. The result depends on the window, which is why the same vault can show different APYs on different pages.

Keep reading

• What is APY in crypto? Benchmark rates by asset and why sites disagree.
• T-bill calculator. Compare a Treasury bill with onchain yield over the same term.
• DeFi lending. How lenders earn and how they get their money out.