APY from APR Calculator
Solve the compounding relation APY = (1 + APR / n)n − 1 for any of its three unknowns — the effective yield, the nominal rate, or the compounding frequency — with step-by-step maths, a live yield diagram, and a full staking projection.
APR and APY are not interchangeable
A platform advertising "12% APR" and one advertising "12% APY" are offering different products. At daily compounding, 12% APR is worth 12.7475% APY — nearly three-quarters of a percentage point more. On a $10,000 stake that is an extra $74.75 per year. When comparing staking opportunities, always convert to a common basis: APY is the number that reflects what you actually earn over a year with reinvestment.
Compounding has a hard ceiling
No matter how often you compound, APY cannot exceed eAPR − 1. At 12% APR the limit is 12.7497% APY. Daily compounding already captures 12.7475% of that, so moving from daily to continuous adds only 0.0022 percentage points. This is the most important practical fact about compounding frequency: the first few compounds do almost all the work, and increasing n beyond daily is essentially cosmetic.
The first compound matters most
Going from annual (n = 1) to monthly (n = 12) at 12% APR raises APY from 12.00% to 12.6825% — a gain of 0.68 percentage points. Going from daily to continuous adds only 0.0022 points. The curve is steep at the left and flat at the right. That means the choice between annual and monthly compounding is genuinely important, while the choice between daily and hourly is not.
High APY usually carries hidden cost
An APY far above the market rate is rarely free money. It is usually funded by token emissions, which dilute the token's supply, or by fees paid by other users, or by new depositors' capital. When emissions slow, the rate falls. The yield may also be paid in a token whose price declines faster than the yield accrues. The APY formula tells you what you earn in units, not what those units are worth when you sell them.
How to Use This Calculator
The compounding relation links three quantities: the nominal rate, the effective yield, and how often rewards are reinvested. Choose which one the tool should solve, then fill in the rest.
1. Choose what to solve for
Pick APR, APY, or n from the toggle. The calculator rearranges APY = (1 + APR / n)n − 1 automatically for whichever you choose. Solving for n uses a numerical search because the formula cannot be inverted in closed form.
2. Match the compounding frequency
Use the platform's actual credit schedule: daily is n = 365, weekly is n = 52, per epoch varies. If the platform compounds continuously, pick the ∞ preset. If it only credits rewards when you claim them, the effective n is however often you claim and restake.
3. Enter a principal (optional)
The principal field scales the projected dollar earnings. It does not affect APR, APY, or n. Set it to your actual stake to see what the yield is worth in dollars over a year.
4. Read the result and verdict
The result card shows the solved value plus the compounding gain in percentage points. A colour-coded verdict classifies the yield from very low through savings, moderate, attractive, high, very high, extreme and implausible — with a reminder that higher yield usually means higher risk.
5. Check the schematic and the first chart
The schematic puts the nominal rate and the effective rate side by side as bars, with a bracket showing the compounding gain. The chart plots APY against the compounding frequency on a logarithmic axis for three different APRs.
6. Switch to Advanced for the full picture
Advanced mode adds a chart of APY against APR at three fixed frequencies, a sensitivity check on +1% moves, and companion metrics including the per-period rate, the continuous limit, the remaining headroom, time to double, and projected earnings on your principal.
What This Tool Offers
Built around the classic compounding relation APY = (1 + APR / n)n − 1, the fundamental link between a quoted rate and the yield you actually earn.
Three-way solving
Solve for the effective yield, the nominal rate, or the compounding frequency. The calculator rearranges the formula for whichever you choose, using a numerical solver when n is the unknown.
Compounding presets
One click for annual, monthly, weekly, daily, hourly, minutely, and continuous compounding — covering every schedule you will meet on a staking platform.
Yield schematic
APR and APY drawn as scaled bars with a dashed reference line at the nominal rate and a bracket showing exactly how much compounding adds.
Staking projection
Enter a principal and the calculator projects the value after one year, the dollar earnings, the implied daily rate, and the time to double.
Dual comparison charts
APY against compounding frequency on a log axis for three APRs, plus an advanced chart of APY against APR at annual, monthly, and daily compounding.
Reference tables
A three-way APR / APY / n converter, a yield lookup grid across rates and frequencies, and a full variable reference with typical staking values.
Reference Tables & Conversions
A three-way rate converter, a yield lookup grid across rates and frequencies, and a reference table of the variables involved.
APR ⇄ APY ⇄ n converter
APY Lookup — APY = (1 + APR / n)n − 1
Rows are nominal APR; columns are compounding frequency. Each cell is the resulting effective APY.
| APR ↓ / n → | 1 annual | 4 quarterly | 12 monthly | 52 weekly | 365 daily | ∞ continuous |
|---|
Compounding Frequencies in Crypto Staking
What each common schedule means and how much it actually adds at 12% APR.
| Schedule | n per year | Rate per period | APY at 12% APR | Gain over APR |
|---|---|---|---|---|
| Annual | 1 | 12.0000% | 12.0000% | +0.0000 pp |
| Semi-annual | 2 | 6.0000% | 12.3600% | +0.3600 pp |
| Quarterly | 4 | 3.0000% | 12.5509% | +0.5509 pp |
| Monthly | 12 | 1.0000% | 12.6825% | +0.6825 pp |
| Weekly | 52 | 0.2308% | 12.7341% | +0.7341 pp |
| Daily | 365 | 0.0329% | 12.7475% | +0.7475 pp |
| Hourly | 8,760 | 0.00137% | 12.7496% | +0.7496 pp |
| Continuous | ∞ | — | 12.7497% | +0.7497 pp |
Variable Reference
| Symbol | Meaning | Typical staking range | Units |
|---|---|---|---|
| APR | Nominal annual rate | 0.5% – 100%+ | % per year |
| APY | Effective annual yield | 0.5% – 150%+ | % per year |
| n | Compounding periods per year | 1 – 525,600 | count |
| i | Rate per compounding period | — | APR / n |
| P | Staked principal | 0 – 10⁹+ | USD or token units |
| t₂ | Time to double the stake | — | ln(2) / ln(1 + APY) years |
What Does APY = (1 + APR / n)n − 1 Measure?
The APY formula converts a nominal rate — the simple rate a platform quotes — into the effective rate you actually earn once rewards are reinvested. It does this by splitting the nominal rate into n equal pieces, compounding each piece forward, and then subtracting the original unit to leave only the gain. The result is a single number that is directly comparable across platforms regardless of how often they compound.
The distinction matters because "12% APR" and "12% APY" are different offers. The first pays 12% of your principal over a year if you never reinvest. The second pays 12% on a base that is continuously growing as rewards are added back. At daily compounding, a 12% APR is worth 12.7475% APY. On a $10,000 stake that is $74.75 of extra yield per year — a small but real difference, and one that compounds further the longer you stay staked.
The APY Formula
The defining relationship is:
Where APR is expressed as a decimal fraction. The term APR / n is the rate applied in each compounding period, and the exponent n is how many of those periods fit into a year. Rearranged to solve for the other two unknowns:
n → solved numerically, since the formula cannot be inverted in closed form
As n grows without bound, the expression approaches its continuous limit:
This limit is the theoretical maximum yield for a given nominal rate. No compounding schedule can exceed it.
APY Variables
| Symbol | Meaning | Notes |
|---|---|---|
| APR | Nominal annual rate | The simple rate the platform quotes; no reinvestment assumed |
| APY | Effective annual yield | What you earn over a year with reinvestment; always ≥ APR |
| n | Compounding periods per year | 365 for daily, 52 for weekly, 1 for annual, ∞ for continuous |
| i | Rate per period | Equal to APR / n; the rate applied each compounding step |
| P | Principal | Scales the dollar earnings; does not affect APR, APY or n |
| t₂ | Doubling time | ln(2) / ln(1 + APY) years; the time for the stake to double |
How Compounding Frequency Changes the Yield
The relationship between n and APY is steep at the beginning and flat at the end. At 12% APR, moving from annual to monthly compounding adds 0.68 percentage points of yield. Moving from monthly to daily adds only 0.065 points. Moving from daily to continuous adds 0.0022 points. This is a direct consequence of the exponential: the first few compounds capture most of the available gain, and each additional compound operates on an already-inflated base.
The practical implication is that the choice between annual and monthly compounding genuinely matters, while the choice between daily and hourly compounding is essentially cosmetic. A platform offering "daily compounding" versus one offering "continuous compounding" at the same APR is offering nearly identical products — the difference on a $10,000 stake at 12% APR is about 22 cents per year. Focus on the APR and on how often you can actually claim and restake, not on the marketing language around compounding frequency.
There is also a second, subtler point. The compounding the formula assumes only happens if rewards are actually reinvested. If a platform credits rewards but you leave them unclaimed, your effective compounding frequency is not the platform's credit frequency but your claiming frequency. Someone who claims and restakes daily at a platform that credits daily earns the full daily-compounded APY; someone who claims monthly at the same platform earns the monthly-compounded APY instead, which at 12% APR is 0.065 percentage points lower.
Yield Calculation Examples
APY = ( 1 + 0.12 / 365 )365 − 1 = ( 1.00032877 )365 − 1
APY = 0.127475 = 12.7475%
APY = ( 1 + 0.12 / 12 )12 − 1 = ( 1.01 )12 − 1
APY = 0.126825 = 12.6825%
APY = e0.12 − 1 = 1.127497 − 1 = 12.7497%
APR = 365 × ( ( 1.127475 )1/365 − 1 ) = 365 × 0.00032877 = 12.0000%
Find n such that ( 1 + 0.12 / n )n − 1 = 0.126825
n = 12 (monthly compounding)
Value = 10,000 × ( 1 + 0.127475 ) = $11,274.75
Earnings = $1,274.75
Frequently Asked Questions
Three reasons, and only one is innocent. First, APR is the rate the platform actually applies to each period — if it credits 0.032877% per day, the natural thing to quote is the annualised simple rate, which is 12% APR. Second, APR is the number that goes into the per-period calculation the smart contract performs; the APY is a derived display figure. Third, and less innocently, APR is numerically smaller than APY at the same nominal rate, so a platform advertising "12% APR" appears to offer less than one advertising "12.75% APY" even when the underlying product is identical. When comparing platforms, always convert to APY first.
Less than the marketing suggests, but not nothing. At 12% APR the difference between annual and daily compounding is 0.7475 percentage points — meaningful. The difference between daily and continuous is 0.0022 points — about 22 cents per year on a $10,000 stake. The curve flattens very quickly. In practice, the frequency that matters is how often you can claim and restake, because that is the frequency at which your rewards actually start earning. A platform that credits daily but requires you to claim manually gives you continuous compounding only if you claim continuously, which nobody does.
Continuous compounding is the mathematical limit as the compounding interval shrinks to zero. The formula becomes APY = eAPR − 1. No platform literally compounds at every instant, but several approximate it very closely: a protocol that accrues rewards per block on a chain with sub-second blocks is effectively continuous, and a lending market that updates an interest index on every interaction behaves the same way. The practical difference between per-block accrual and true continuous compounding is negligible — at 12% APR, per-second compounding differs from continuous by about 0.0000001 percentage points.
Look at how often the platform credits rewards to your balance. If the balance grows every day, n = 365. If it grows every week, n = 52. If it only grows when you claim, then n is your claiming frequency, not the platform's accrual frequency. If the platform shows a continuously rising balance within a block explorer — common for lending markets — use the continuous setting. When in doubt, compute both the daily and the continuous APY: the difference is at most a few thousandths of a percentage point, so the choice rarely changes a decision.
Because sustainable yield has to come from somewhere. Real sources of yield are: trading fees paid by users, interest paid by borrowers, and MEV or block rewards. Those sources produce yields in the single digits to low double digits in most markets. A 200% APY is almost always funded by token emissions — the protocol printing new tokens and giving them to depositors. That dilutes the token's supply, which pushes its price down, which reduces the dollar value of the yield. In the worst cases the yield is funded by new depositors' principal, which is the definition of a Ponzi scheme. High APY is not automatically fraudulent, but it demands an explanation of where the money comes from.
This matters more than the headline rate. If you stake token A and earn more token A, the yield is denominated in the same asset and its dollar value moves with that asset's price. If you stake token A and earn token B, you are taking on the price risk of B as well. Some platforms pay in a governance token that has no liquid market, in which case the "yield" is not realisable until a market appears. The APY formula tells you the growth rate in units; it says nothing about what those units will be worth. Always check the denomination before treating a yield as income.
Not in the staking sense. Staking rewards are additive — the balance grows or stays flat. A negative APY would mean the balance shrinks, which happens only if the protocol charges a fee larger than the reward, or if there is a slashing event that removes part of the stake. Slashing is a penalty, not a negative yield, and it is usually a one-time event rather than a rate. The formula here assumes a non-negative APR, which covers essentially every staking product.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| APY | Annual percentage yield | |
| APR | Nominal annual percentage rate | |
| n | Compounding periods per year |
What it means
APR (Annual Percentage Rate) is the simple interest rate without compounding, while APY (Annual Percentage Yield) includes the effect of compounding. This formula converts APR to APY based on the compounding frequency n. For staking, if rewards are compounded daily (n=365), APY is higher than APR. This is used to compare staking platforms and to understand the true return on staked assets. Understanding the difference between APR and APY is essential for accurately evaluating yield‑generating opportunities in DeFi and staking.
Worked example
APY from APR – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| APR (%) | 8.0 |
| Compounding Frequency (n/year) | 365 |
| Parameter | Value |
|---|---|
| APR | 12.0 |
| Compounding Frequency | 12 |
Common mistakes
- APR vs APY: APR is the nominal rate; APY includes compounding.
- n: The number of compounding periods per year (e.g., 365 for daily).
- Result: APY is always ≥ APR for n>1.
- Variable rates: This formula assumes a constant APR; real staking rates may change.
Applications
APY from APR (crypto staking) converts a nominal annual percentage rate (APR) to an effective annual percentage yield (APY) by accounting for compounding frequency. This is essential because staking rewards are often compounded daily or hourly, and APY provides a true annualised return. Investors use this formula to compare staking products with different compounding intervals and to understand the real earning potential. It also helps in evaluating the impact of compounding on total returns over time. By using this conversion, investors can make apples‑to‑apples comparisons across various staking and yield‑farming opportunities. Understanding APY is crucial for maximising returns and for selecting the most profitable staking strategies.
- Comparing staking and yield‑farming APYs across protocols
- Evaluating the effect of compounding frequency on returns
- Estimating annual earnings from staking rewards
- Decision‑making between different reward structures
- Financial planning and goal setting
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