APR to APY Calculator

Convert between APR and APY at any compounding frequency, and see what the difference is actually worth.

APR and APY are not two rates. They are one rate written down twice, and the only thing that separates them is an assumption about how often the money is put back to work. A protocol paying 69.38% nominal and one advertising 100% APY compounded daily are quoting the identical arrangement, so what an APR to APY calculator really does is strip that assumption out: a reader comparing those two headline figures side by side is comparing compounding conventions rather than generosity.

Formula: APY = (1 + APR / n)^n - 1, for n compounding periods a year

Your figures

Conversion direction

APR is the nominal rate before compounding; APY is what the same rate becomes once it is compounded.

Rate to convert

The rate as quoted, in percentage points. Negative rates are accepted — a funding rate or a borrow position can be one.

Compounding frequency

How often the rate is applied to a balance that already includes what it paid. Continuous is the limit of compounding ever more often, and is what most lending-rate models quote.

Results

APY

12.7475%

from 12.0000% APR compounded daily

APR — the nominal rateThe rate before compounding: the periodic rate multiplied by the number of periods, which is not what a balance actually grows by.: 12.0000%
APY — the effective rateWhat one year at that nominal rate compounded daily actually returns.: 12.7475%
DifferenceAPY less APR. Zero at annual compounding, where the two are the same number by definition.: +0.7475 percentage points
Compounding's share of the APYHow much of the headline effective figure comes from restaking rather than from the rate itself.: 5.864%
Effective daily rateThe rate that compounds up to the APY over 365 days. An effective annual yield is defined over a calendar year, so this uses 365 whatever frequency is selected.: 0.032877%
Compounding usedBoth headline figures depend on this. The same nominal rate at another frequency is a different APY.: Daily · 365 periods a year
Compounded annually0.0000 percentage points above the nominal rate · 1.00 becomes 1.120000 after a year.: 12.0000%
Compounded semi-annually+0.3600 percentage points above the nominal rate · 1.00 becomes 1.123600 after a year.: 12.3600%
Compounded quarterly+0.5509 percentage points above the nominal rate · 1.00 becomes 1.125509 after a year.: 12.5509%
Compounded monthly+0.6825 percentage points above the nominal rate · 1.00 becomes 1.126825 after a year.: 12.6825%
Compounded weekly+0.7341 percentage points above the nominal rate · 1.00 becomes 1.127341 after a year.: 12.7341%
Compounded daily+0.7475 percentage points above the nominal rate · 1.00 becomes 1.127475 after a year · the frequency selected above.: 12.7475%
Compounded continuously+0.7497 percentage points above the nominal rate · 1.00 becomes 1.127497 after a year.: 12.7497%

What this means

12.0000% nominal, compounded daily, is 12.7475% effective — a difference of +0.7475 percentage points, which is 5.864% of the effective figure. The table underneath holds that nominal rate still and walks every frequency, because a quoted APY answers two questions at once without saying which is which: how much the rate pays, and how often it is assumed to be restaked. Continuous compounding bounds the table from above, since it is the limit of compounding ever more often.

APR and APY are the same rate stated two ways. Neither is more correct than the other, and comparing an APR from one protocol with an APY from another compares the compounding assumptions as much as the rates.
An APY assumes every reward is restaked at the same rate the moment it is paid. Where rewards are claimed by hand, or claiming costs gas, or the rate moves as more capital arrives, the realised figure is the APR end of this pair rather than the APY end.
Negative rates convert exactly as positive ones do. The arithmetic stops meaning anything at −100%, where the balance is gone and there is nothing left to compound.
This converts a rate. It says nothing about whether the rate will be paid, for how long, or by whom.

The link reopens this calculator with the same numbers. Nothing you enter is sent to a server.

Continue with these figures

About the APR to APY calculation

This converter runs both directions, so it is an APY to APR calculator as readily as the other way round. Give it a nominal rate and a compounding frequency and it returns the effective yield; give it an effective yield and the frequency it was built on and it returns the nominal rate underneath. The two conversions are exact inverses of each other, so putting a rate through one and then the other at the same frequency returns the number you started with.

The output worth reading is not either headline figure but the table beneath them, which is where the page doubles as a compounding frequency calculator. It holds the nominal rate still and walks every frequency from annual to continuous, which separates the part of a quoted APY that is yield from the part that is nothing but the restaking assumption. On the example below that split is 69.38 points of yield and 30.62 points of assumption.

That split matters because the assumption is often the part that does not survive contact with reality. Any effective annual rate calculator, this one included, has to presume that every reward is restaked at the same rate the instant it is paid, because that presumption is precisely what an APY is. Where rewards are claimed by hand, where claiming costs gas, or where the rate falls as more capital arrives, what actually lands in the account is closer to the APR end of the pair than the APY end.

APR to APY formula

n periods a year
  APY = (1 + APR ÷ n)^n − 1
  APR = n × ((1 + APY)^(1 ÷ n) − 1)

continuous compounding
  APY = e^APR − 1
  APR = ln(1 + APY)

difference          = APY − APR              in percentage points
compounding's share = (APY − APR) ÷ APY
effective daily     = (1 + APY)^(1 ÷ 365) − 1
growth factor       = 1 + APY                what 1.00 becomes

APR: The nominal annual rate: the rate charged or paid in one period multiplied by the number of periods in a year. It is a piece of bookkeeping rather than a description of how a balance grows.
APY: The effective annual rate: what one unit actually becomes after a year of that nominal rate being applied to a balance that already contains what it paid.
n: Compounding periods a year — 1 annually, 2 semi-annually, 4 quarterly, 12 monthly, 52 weekly, 365 daily. Continuous compounding has no finite n and uses the exponential form instead.
e: The base of natural logarithms, roughly 2.71828. It appears because e is the limit of (1 + 1 ÷ n)^n as n grows without bound, which is what continuous compounding means.
ln: The natural logarithm — the inverse of e^x, and therefore the only way back from a continuously compounded effective rate to the nominal rate underneath it.
growth factor: One plus the APY, expressed as a multiplier. A concrete reading of an effective rate: at a growth factor of 2.00, one coin becomes two over a year.

The conversion is a power rather than a multiplication because each period pays on a balance that already includes what the previous period paid. Applying 1% twelve times is not 12%, it is 1.01 to the twelfth, which is 12.6825% — and the extra 0.6825 points are the interest that the first eleven payments themselves earned. An APR is what you get by deliberately ignoring that and simply adding the periodic rate up, which is a legitimate thing to quote as long as everybody knows that is what it is.

Going the other way is a root, for the same reason in reverse. If a year at n periods multiplies the balance by 1 + APY, then one period multiplies it by the n-th root of that, and the nominal rate is n times what that root leaves over 1. Writing both directions as a matching pair of pure conversions is what makes the round trip exact by construction: converting an APR to an APY and straight back at the same frequency returns the rate that was typed in, rather than something a rounding step away from it.

Continuous compounding is the ceiling on the whole table, because it is the limit of (1 + r ÷ n)^n as the periods get shorter without bound, and that limit is e^r. What surprises people is how little of the gain sits at the top end. On the example below, moving from annual to quarterly compounding buys 20.23 of the 30.75 percentage points that are available at all, and moving from daily all the way to continuous buys 0.13 of them. Compounding more often than daily is a rounding decision, not a strategy.

The share of the APY that is compounding rather than yield is the number this page exists to produce. A quoted effective rate answers two questions at once and never says which is which: how much the protocol pays, and how often it assumes the reward goes back in. Splitting them lets you check the second assumption against what you would actually do — and negative rates split the same way, since a funding cost or a borrow rate compounds by identical arithmetic, right down to the point at −100% where there is no balance left to compound.

APR to APY: a worked example

A pool whose documentation advertises a 100% APY and states that it is compounded daily, converted back to the nominal rate underneath and then walked across every other compounding frequency.

DirectionAPY to APR, at n = 365
APR365 × (2^(1 ÷ 365) − 1) = 69.3806%
Round trip check(1 + 0.693806 ÷ 365)^365 − 1 = 100.0000%
Difference100 − 69.3806 = 30.6194 percentage points
Compounding's share30.6194 ÷ 100 = 30.6194%
Effective daily rate2^(1 ÷ 365) − 1 = 0.190084%
Same nominal rate, annually69.3806%, and 1.00 becomes 1.6938
Quarterly(1 + 0.693806 ÷ 4)^4 − 1 = 89.6097%
Monthly(1 + 0.693806 ÷ 12)^12 − 1 = 96.3031%
Weekly(1 + 0.693806 ÷ 52)^52 − 1 = 99.2157%
Continuouslye^0.693806 − 1 = 100.1318%

The pool pays a nominal 69.3806%, and 30.6194 percentage points of the 100% headline are the assumption that every reward goes straight back in, every day, at the same rate. That one nominal rate is quotable as 69.38%, 81.41%, 89.61%, 96.30%, 99.22%, 100.00% or 100.13% depending only on the compounding stated beside it, which is why two protocols cannot be ranked on headline figures alone. Note also that the share and the gap read as the same number here purely because the APY happens to be exactly 100 — at any other yield they differ.

How to use the APR to APY calculator

Pick the direction first. Choose APR to APY when you hold a nominal rate and want to know what a year of it is worth; choose APY to APR when a platform has quoted an effective figure and you want the rate underneath it.
Enter the rate exactly as it was quoted to you, in percentage points rather than as a decimal. Negative values are accepted, because a funding rate or the cost of a borrow position can legitimately be one.
Set the compounding frequency to what the quote assumes, not to what you intend to do. If the documentation does not say, the conversion is ambiguous and the table below is the honest answer rather than any single figure in it.
Read the table as a like-for-like comparison. Every row holds the same nominal rate and changes only the restaking assumption, so the spread across the rows is the entire size of the assumption.
Carry the nominal rate, not the effective one, into the staking or yield farming pages. Both of those compound the rate you give them, so handing them an APY compounds the same effect a second time.

Limitations of the APR to APY calculator

Every calculation makes assumptions. These are the ones that matter here.

Converts a rate and nothing else. It says nothing about whether that rate will be paid, for how long, by whom, or with what left over after the platform has taken its share.
An APY assumes every reward is restaked the moment it is paid, at the same rate, with no transaction cost. Where claiming costs gas or is done by hand, the realised figure sits nearer the APR end of the pair.
Weekly is treated as 52 periods and monthly as 12, which are the conventional counts rather than 365 ÷ 7 and 365 ÷ 30. That is what a reader gets when they check the sum in a spreadsheet.
The effective daily rate uses 365 days regardless of the frequency selected, because an effective annual yield is defined over a calendar year and its 365th root is the only reading of daily that compounds back to it.
Fixed rates are the only case this handles cleanly. A pool rate that falls as capital arrives is a sequence of different rates, and no single conversion describes it.
The arithmetic stops meaning anything at or below −100%, where the balance is gone and there is nothing left for a further period to act on.

Frequently asked questions about APR to APY

In an APR vs APY comparison, which figure is the correct one to quote?

Neither is more correct than the other; they are the same rate stated with different assumptions attached. What causes trouble is mixing them, because comparing one protocol's APR against another's APY compares the compounding assumptions at least as much as the rates. The safest habit is to convert everything to one convention before ranking anything.

Why does compounding more often stop helping?

Because the gain from each extra period is earned on the interest paid by the periods before it, and that quantity shrinks as the periods get shorter. In the worked example, going from annual to quarterly adds 20.23 percentage points, going from monthly to daily adds 3.70, and going from daily all the way to the continuous limit adds 0.13. The ceiling is e^APR − 1 and no frequency can pass it.

What does continuous compounding actually mean in practice?

It is the mathematical limit of compounding ever more often, not a schedule any chain runs on. It exists on this page because a handful of protocols and most lending-rate models quote it, and because it bounds the table from above — if a headline figure exceeds the continuous row for a given nominal rate, something other than compounding is being counted.

Can I convert a negative rate?

Yes, and the arithmetic is unchanged. A negative funding rate or a borrow cost compounds exactly as a positive rate does, with the effective figure sitting further from zero than the nominal one rather than nearer to it. The one boundary is −100%, at which the balance is exhausted and no further period can act on anything.

Why does my APY differ slightly from the platform's own figure?

Usually the period count. A platform compounding on 360 days, or treating a month as 30 days and a year as twelve of them, will land a fraction of a point away from these figures on the same nominal rate. Some platforms also quote an APY net of their own fee while the rate you were given is gross, which is a larger difference than any day-count convention.

Does a higher APY mean more money?

Only if the rate behind it is real and the restaking assumption holds. A 100% APY compounded daily and a 100.13% APY compounded continuously are the same nominal rate, and a headline that is mostly compounding assumption converts to cash only for someone who actually restakes on that schedule and pays nothing to do it.

Last reviewed 29 August 2026. See our methodology and editorial policy.

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