APR vs APY vs DPR: What the Difference Means for Your Crypto Yield

The Three Rate Definitions You Need to Know

Crypto yield products — staking, lending, liquidity pools, DeFi protocols, and CEX savings accounts — advertise returns using three different rate formats that are frequently confused and sometimes deliberately used interchangeably to make offers appear more attractive than they are. Understanding the difference is not optional; it directly affects how you compare products and calculate your real returns.

• APR (Annual Percentage Rate): Simple interest for a year. If you deposit $10,000 at 20% APR and do nothing else, you receive $2,000 at the end of the year. No compounding. Your principal stays $10,000 throughout.
• APY (Annual Percentage Yield): Compound interest — the actual yield you receive if earnings are continuously reinvested. At 20% APR with daily compounding, the APY is higher than 20% because each day's earnings generate their own earnings on subsequent days.
• DPR (Daily Percentage Rate): The return per day. Particularly useful in DeFi where some protocols display rates on a daily basis, and in perpetuals trading where funding rates are charged or paid three times daily (or continuously).

Why APY Is Always Higher Than APR

APY is always greater than or equal to APR (equal only when there is no compounding — i.e., annual compounding at a frequency of 1). The more frequently compounding occurs, the larger the gap between APY and APR.

The formula connecting APR to APY with daily compounding:

APY = (1 + APR / 365)^365 - 1

Worked example at 20% APR with daily compounding:

• Daily rate = 20% / 365 = 0.05479% per day
• APY = (1 + 0.0005479)^365 - 1 = 1.2213 - 1 = 22.13%

The difference is 2.13 percentage points — meaningful for large capital. At 100% APR (common in high-yield DeFi during bull markets), the APY with daily compounding is approximately 171%. The absolute gap grows non-linearly with the rate.

Converting Between APR, APY, and DPR

The three conversion formulas:

• APR to DPR: DPR = APR / 365 (for simple daily rate) or DPR = (1 + APR/365)^(1/365) - 1 (for the compound equivalent)
• DPR to APY: APY = (1 + DPR)^365 - 1
• APY to APR: APR = ((1 + APY)^(1/365) - 1) × 365
• APY to DPR: DPR = (1 + APY)^(1/365) - 1

Worked example — DeFi pool showing 0.1% DPR:

• APR = 0.1% × 365 = 36.5%
• APY = (1 + 0.001)^365 - 1 = 1.4402 - 1 = 44.02%

The same 0.1% daily rate looks very different depending on which metric you use to present it. Always convert everything to APY before comparing products — it is the only apples-to-apples comparison when compounding frequencies differ.

DeFi vs CEX: Which Rate Is Being Shown?

This is where most confusion occurs in practice. DeFi protocols and CEXes typically display rates differently:

• DeFi protocols (Aave, Compound, Uniswap V3, etc.) almost always show APY, because they assume you are continuously compounding by auto-reinvesting. When you provide liquidity or lend on these platforms, your position compounds automatically every block. The displayed APY is the effective annual return if rates stay constant.
• CEX staking products (Binance Earn, OKX Savings, etc.) frequently show APR — the simple annual rate — and distribute payouts daily, weekly, or at maturity. Whether you compound depends entirely on whether you manually reinvest those payouts. If you do not reinvest, you actually earn the APR, not the APY.
• Liquidity pools display APY assuming 100% reinvestment. In practice, you must harvest and reinvest manually (or use an auto-compounder). If you harvest weekly instead of daily, your effective APY drops slightly.

Practical rule: when comparing a DeFi APY to a CEX APR, convert the CEX APR to APY first. A Binance Earn product showing 5% APR becomes 5.13% APY with daily compounding — marginally different, but the comparison is now fair.

Real-World Yield Examples

These examples use rates representative of long-term stable yields — high-yield DeFi rates change constantly and cannot be reliably quoted:

• Binance BNB flexible staking at 5% APR (daily compounding): APY = (1 + 0.05/365)^365 - 1 = 5.13%. Difference: 0.13 percentage points — small at low rates.
• Ethereum staking at 3.5% APR: APY ≈ 3.56%. Again, small gap at single-digit rates. ETH staking rewards are distributed at the consensus layer and do not auto-compound — you must manually trigger compounding by adding to your stake.
• DeFi liquidity pool at 80% APY (auto-compounding): What is the equivalent DPR? DPR = (1 + 0.80)^(1/365) - 1 ≈ 0.163% per day. This means 0.163% of your position value is added each day through compounding. At $10,000 capital, that is approximately $16.30 per day at the outset, growing as the position compounds.
• A lending protocol showing 0.05% DPR: APR = 18.25%, APY = 20.02%. The APY is nearly 2 percentage points above the naive APR — worth knowing when choosing between platforms.

Important Warnings About High-Yield Products

Before chasing high APY, understand what it reflects:

• Impermanent loss is not included in APY. A liquidity pool showing 80% APY may be offset significantly by impermanent loss if the two assets in the pool diverge in price. The net return can be far below the advertised yield — or even negative.
• Rates change constantly. DeFi APYs are market-driven and can drop from 80% to 10% in days as capital floods in. The rate you see today is not guaranteed tomorrow.
• High APY often signals high risk. Yields substantially above the risk-free rate (e.g., T-bill rates) compensate for counterparty risk, smart contract risk, token price risk, or liquidity risk. There is no free lunch in yield.
• Tax treatment: In most jurisdictions, yield income from staking and lending is taxable as ordinary income at the time of receipt, not at sale. The APY is your pre-tax return — factor your marginal tax rate into the net comparison.