How this calculation works
Start with equal fiat value in two tokens. Apply their separate ending/start price ratios. Under an idealized fee-free full-range constant-product model aligned by arbitrage, compare LP value with retaining the original token quantities.
LP = V√(ab); hold = V(a+b)/2; relative difference = LP/hold − 1A worked example
If token A doubles and token B is unchanged, a 100,000 starting value becomes about 141,421.36 in the idealized LP, compared with 150,000 from holding. Relative divergence is approximately −5.719096%.
Good to know
A scenario from entered prices, quantities and assumptions. No live prices, wallet connection, trade execution, return forecast or tax determination. Decimal arithmetic is used; displayed values are rounded. Examples are arithmetic demonstrations, not market rates or recommendations. Fee-free, full-range, two-token 50/50 constant-product model only. Not concentrated liquidity, stable-swap or a forecast. Excludes fee income, incentives, costs, token-transfer effects, rebalancing and protocol risks.
Reference: Uniswap v2 documentation: constant-product returns (opens in a new tab) ↗
The comparison is with holding, not with the starting deposit
An idealized 50/50 full-range constant-product pool changes its token quantities as relative prices move and arbitrage aligns the pool. The relevant divergence comparison keeps the original token quantities as a holding benchmark.
If token A doubles and token B is unchanged, a starting value of 100,000 becomes approximately 141,421.36 in the fee-free LP model. The original tokens held separately would be worth 150,000. The LP has grown from its start while still falling short of holding.
For price multipliers a and b, LP value is V√(ab) while holding value is V(a+b)/2. The square root makes the symmetry visible: exchanging the two token multipliers produces the same relative comparison.
Identify the pool model before using the formula
Equal relative movement produces no divergence. If both tokens double, both the idealized LP and holding value double. What matters for relative divergence is the change in their price ratio, not a shared movement in the fiat unit.
Trading fees and incentive rewards are excluded rather than assumed to offset the shortfall. This full-range formula does not apply unchanged to concentrated liquidity, a selected price range, stable-swap curves or a pool with unusual token-transfer behavior.
The constant-product swap scenario calculator examines one trade against entered reserves. This divergence model instead compares ending LP value after a price movement with a holding benchmark. Neither model predicts future prices, fee income or protocol safety.
A few questions, answered
Is divergence the same as losing money from the start?
No. It is a relative difference from holding. Both strategies can gain or lose fiat value while the LP still has a relative shortfall.
Does this include pool fees?
No. It is an idealized fee-free comparison.
Can I use it for a concentrated range?
No. A range-specific position has different inventory behavior and needs a suitable model.