Liquidity Pool Simulator: Impermanent Loss and Staking APY

Impermanent loss vs staking yield: formula and worked example

In a 50/50 constant-product liquidity pool, impermanent loss equals 2√k ÷ (1 + k) − 1, where k is the ratio between the new and old price of the volatile token. A 75% rise costs 3.79% compared with simply holding, a doubling costs 5.72%. The tool weighs that loss against the rewards earned over the period.

Formulas

• k = 1 + token A price change ÷ 100 (floor of 0.01), with token B as the stable reference.
• Impermanent loss = 2√k ÷ (1 + k) − 1.
• Value if simply held (HODL) = capital ÷ 2 + capital ÷ 2 × k.
• Pool value before rewards = HODL value × (1 + impermanent loss).
• Rewards = initial capital × ((1 + rate ÷ 365)^days − 1).

Default example

$5,000 deposited for 180 days at 14.5%, token A up 75%: holding would be worth $6,875 and the pool $6,614 before rewards, a loss of $261 (3.79%). Rewards add $371, so the final position reaches $6,985, $110 above HODL. If the token doubles, the loss grows to $429 (5.72%) and the pool ends $58 below HODL. A 50% drop gives the same percentage loss as a doubling, because the formula is identical for k and 1/k.

What the calculation actually does

• The rate you enter is compounded daily: 14.5% yields 15.6% over 365 days, so it behaves as a nominal rate (APR). If your platform shows an APY, which already includes compounding, the tool slightly overstates the gains; an APY of 14.5% corresponds to about 13.54% to enter.
• Rewards are calculated on the initial capital, not on the pool value as prices move.
• The formula applies to a 50/50 constant-product pool (Uniswap v2 model); concentrated-liquidity, weighted or stableswap pools behave differently.
• Gas fees, tax and smart-contract risk are excluded.

This is an indicative simulation, not investment advice.

Frequently Asked Questions

How do you calculate impermanent loss in a liquidity pool?

For a 50/50 constant-product pool, loss = 2√k ÷ (1 + k) − 1, where k is the ratio of new to old price. Benchmarks: +25% or −20% gives 0.62%, +50% gives 2.02%, a doubling or halving 5.72%, a fivefold move about 25.46%.

Is impermanent loss permanent?

It only becomes real if you withdraw your tokens while prices have diverged. If the price ratio returns to its starting level, k equals 1 and the loss falls back to 0. Fees and rewards earned in the meantime are kept.

What yield is needed to offset impermanent loss?

Rewards over the period must exceed the loss in value. On $5,000 over 180 days, a 75% rise costs $261 while a 14.5% yield earns $371, so the pool comes out ahead. If the token doubles, the loss reaches $429 and a rate of about 16.7% would be needed to cover it.

Should I enter the APR or the APY in the simulator?

The tool compounds the rate you enter daily, so it expects an APR: entering 14.5% gives 15.6% over a year. If your platform shows a 14.5% APY, enter about 13.54% to get the right result.

Is this tool really free?

Yes, all tools on Kristools are 100% free and accessible without registration.

Is my data protected?

Yes. All processing is performed directly and securely inside your browser. No personal data is sent to our servers.