How to use
- Move the price ratio slider (r = P₁/P₀): r = 1.00 means no change, r = 2.00 means the price doubled, r = 0.50 means it halved.
- Set the initial deposit amount.
- The cards show the impermanent loss percentage, hold value, and pool value.
- The chart visualizes the IL curve across the range r ∈ [0.1, 10] with the current point highlighted.
- The calculation assumes a 50/50 pool (constant product AMM, x·y = k). Hold value is calculated for a volatile token / stablecoin pair, where r is the price ratio of the volatile asset.
LP net return = IL + swap fees
This calculator shows impermanent loss only. Real LP PnL = IL + swap fees earned (and sometimes + incentive rewards). Over long horizons in low-volatility pairs, accumulated fees can fully offset IL; in high-volatility pairs, IL often dominates. Always compare IL against the expected fee APR for the pool before providing liquidity.Scope: Uniswap v2-style CPMM only
The formula IL(r) = 2√r/(1+r) − 1 applies strictly to 50/50 constant-product pools (Uniswap v2, SushiSwap, PancakeSwap v2, and similar x·y = k designs). It does not apply to:
- Uniswap v3 concentrated liquidity — IL is higher than v2 inside the chosen price range (amplified by the range-tightness leverage factor) and the position rebalances to 100% of one asset outside the range.
- Curve stableswap — near-zero IL for same-peg assets (stable↔stable, LST↔ETH) while the peg holds; the stableswap invariant blends constant-sum and constant-product.
- Balancer weighted pools — different formula:
IL = ∏(rᵢ^wᵢ) / (∑ wᵢ·rᵢ) − 1. Reduces to v2 only when weights are 50/50.
IL reference table (CPMM, 50/50)
| Price ratio r | IL | Price ratio r | IL |
|---|---|---|---|
| 1.00 | 0.00% | 2.00 | −5.72% |
| 1.25 | −0.62% | 4.00 | −20.00% |
| 1.50 | −2.02% | 5.00 | −25.46% |
| 1.75 | −3.79% | 10.00 | −42.50% |
| — | — | 100.00 | −80.20% |
By symmetry IL(r) = IL(1/r): r = 0.10 also gives −42.50%, r = 0.01 gives −80.20%.
Calculator
Impermanent Loss Calculator (constant product AMM)
Impermanent loss
0.00%
If held
$10,000.00
If in pool
$10,000.00
Difference (Pool − Hold)
$0.00
Formulas
IL(r) = 2 × sqrt(r) / (1 + r) - 1
- r — price ratio P₁/P₀ (dimensionless). r = 2.00 means the price doubled, r = 0.50 means it halved, r = 1.00 means no change
- P₀ — asset price at the time of entering the pool
- P₁ — current asset price
- IL(r) — impermanent loss (computed), always ≤ 0; applies to Uniswap v2-style 50/50 CPMM only
Pool_value = Hold_value × (1 + IL)
- Hold_value — position value if held outside the pool (computed)
- IL — impermanent loss (fraction, negative number)
- Pool_value — position value inside the pool (computed)