Impermanent Loss Formula: From Price Ratio to Dollar Gap

For a 50/50 full-range constant-product pool, the LP-to-HODL value ratio is 2√r ÷ (1+r), where r is the relative Token A to Token B price multiplier. Impermanent loss is that ratio minus one; a positive loss magnitude is one minus the ratio.

Define both asset growth factors

Let gA be Token A exit price divided by entry price and gB the equivalent factor for Token B. The relative multiplier is r = gA ÷ gB. Using both prices avoids the false assumption that one asset must be stable.

Value HODL and the fee-free pool

For starting value V with equal value in each token, HODL is V(gA+gB)/2 and the arbitraged fee-free pool is V√(gAgB). Dividing the second by the first yields 2√r/(1+r). The weighted constant-mean extension uses V(gA^w)(gB^(1−w)) versus V(wgA+(1−w)gB).

Apply the percentage to ending HODL value

If Token A doubles while Token B is unchanged, a $10,000 starting deposit produces $15,000 HODL and $14,142.14 LP value. The 5.7191% gap equals $857.86 because the percentage applies to $15,000, not the original $10,000.

Understand reciprocal symmetry

A 2× relative move and a 0.5× move produce the same IL percentage. A +50% move and a −50% move are not reciprocals: their multipliers are 1.5 and 0.5. Compare ratios, not signed percentage changes.

Carry full precision

Do not round token growth, square roots, or pool value before the final display. For extreme ratios, a logarithmic form can improve numerical stability. Public fixtures should include no divergence, reciprocal moves, joint moves, and large divergence.

Use this information

Apply the method in the Impermanent Loss & LP Break-Even Calculator. Keep the entered assumptions with the result so another reader can reproduce it.

Return to the cluster guide or continue to fee break-even for the next decision.

Frequently asked questions

Can this guide replace a written contract or professional review?

No. It explains a reproducible planning method and the questions to verify; the applicable contract, official source, or qualified adviser controls.

Why are the assumptions shown instead of hidden defaults?

Financial results can change materially with tax, price, risk, cost, time, and responsibility assumptions. Visible inputs make the answer auditable.

How often should I revisit the result?

Recalculate whenever a quoted rate, fee, price, contract term, source rule, or risk allocation changes.

Sources

Sources and methodology reviewed 2026-09-25. Results are planning estimates, not a lender quote, tax opinion, investment recommendation, legal opinion, or provider proposal.