APR vs APY on Aave
Aave contracts store interest as an APR that compounds every second, while the app shows APY. See the formula, a worked example and why the gap is often small.
Updated
Look up a rate in Aave's smart contracts and then in the Aave app, and you will see two slightly different numbers. Neither is wrong. The contract stores an APR, the app shows an APY, and the gap between them is compounding.
What Aave stores: an APR that compounds every second
For every asset the protocol keeps a current borrow rate, written as a yearly percentage. That is the APR, or annual percentage rate. It is the raw output of the interest rate curve.
Interest on debt is not added once a year or once a month. It accrues every second, and each second's interest joins the balance that earns interest in the next second. That is compounding, and it means a loan left alone for a year grows by a little more than the APR.
What the app shows: APY
APY, or annual percentage yield, answers a practical question: if the rate stayed exactly where it is for a full year, by what percentage would the balance grow? The formula is:
APY = (1 + APR / 31,536,000) ^ 31,536,000 - 1
The number 31,536,000 is the count of seconds in a 365-day year. Because the compounding steps are so small, the result is almost identical to the continuous compounding formula, which is easier to type into a calculator:
APY = e ^ APR - 1
Both formulas take the APR as a decimal, so 4% goes in as 0.04.
A worked example
In September 2026 we read a borrow rate of 4.337% APR for USDC straight from the Ethereum Core contract. Running it through the formula:
e ^ 0.04337 - 1 = 0.04432, which is 4.432% APY.
At the same moment the Aave app showed 4.43%. It is the same rate written two ways. Here is how the gap grows as rates rise:
| APR | APY | Gap |
|---|---|---|
| 1% | 1.005% | 0.005 points |
| 4.337% | 4.432% | 0.10 points |
| 10% | 10.52% | 0.52 points |
| 14.4% | 15.49% | 1.09 points |
| 50% | 64.87% | 14.87 points |
Why the gap is small at low rates
A handy rule of thumb: the gap between APY and APR is roughly half the APR squared. At 4% that is 0.04 x 0.04 / 2 = 0.0008, or 0.08 percentage points. At 10% it is about half a point. At very high rates the shortcut falls short, because interest on interest snowballs, which is why the last row of the table is so large.
For everyday stablecoin rates the two numbers are close enough that mixing them up costs little. During rate spikes the difference becomes noticeable.
Which one should you use?
- Comparing rates: compare APY with APY, or APR with APR. The Aave app shows APY, and so does every rate on this site.
- Estimating cost: APY is the better guide to what a loan costs over a year if you never pay the interest down along the way. Try the borrow cost calculator.
- Averaging over time: average the APR first, then convert to APY. APRs add up correctly over time and APYs do not. That is how the daily averages in our USDC borrow rate history are built.
The same maths applies on the supply side: the contract stores a supply APR and the app shows a supply APY. For deposits the contract adds interest in simple steps between pool updates and compounds at each update. On a busy pool that happens many times an hour, so the outcome is practically the same.
Common questions
Is APY always higher than APR?
Yes, whenever the rate is above zero. APY includes the effect of interest earning interest, so it is always a little higher than the APR it is calculated from.
Does the Aave app show APR or APY?
The Aave app shows APY for both supplying and borrowing. The smart contracts store the underlying APR.
How do I convert an Aave APR to APY?
Write the APR as a decimal and calculate e to the power of the APR, minus 1. For example, an APR of 0.04337 gives 0.04432, or 4.432% APY.
Does a 5% borrow APY mean I will pay exactly 5% this year?
No. APY assumes the current rate stays fixed for a year. Aave rates are variable and change with utilization, so your actual cost depends on how the rate moves.