The formulas behind every calculator.

Weighted impermanent loss

Used by the impermanent loss calculator. The weighted-pool result against the matching hold basket is:

ILw(k) = kʷ ÷ (w·k + 1 − w) − 1

Where:

• w — token A’s entry weight.
• k — relative price ratio, calculated as (A₁/A₀) ÷ (B₁/B₀).

At w = 0.5, the result reduces to the 50/50 formula. Assumptions: a two-token full-range constant-mean pool, aligned marginal price, no fees inside the IL term, and a hold basket with the same entry weights.

Concentrated-liquidity range

Used by the Uniswap v3 and concentrated-liquidity calculator and by the range mode in the IL calculator. In-range token balances are:

x = L(1/√P − 1/√Pᵦ); y = L(√P − √Pₐ)

Where:

• L — position liquidity.
• P — current price.
• Pₐ — lower price bound.
• Pᵦ — upper price bound.
• x and y — base and quote token amounts.

Price is clamped to the bounds for one-sided inventory. The entry inventory is the hold benchmark. Fee income multiplies volume, fee rate, position share, time in range, and days, then is added after divergence is shown.

Liquidity-pool fees and rewards

Used by the liquidity pool calculator. Net period income keeps fees and incentives separate before costs:

net = V·f·q·t·d + C·r·d/365 − gas

Where:

• V — routed daily volume.
• f — pool fee tier.
• q — position share, C/(active liquidity + C).
• t — time in range.
• d — days held.
• C — deployed capital.
• r — incentive APR.
• gas — entered transaction costs.

Volume and liquidity must describe the same pool and band. Reward APR is an input, not a prediction.

LP profit against holding

Used by the LP profit and return calculator. The complete benchmark ledger is:

net vs hold = pool value − hold value + fees + rewards − costs

Where:

• pool value — rebalanced position value at exit.
• hold value — original inventory marked at exit prices.
• fees and rewards — observed income.
• costs — entered operating expenses.

Net return divides this result by entry capital. Annualization describes the entered period; it does not forecast a repeat.

Meteora DLMM discrete bins

Used by the Meteora DLMM calculator. Each bin has a geometric price and constant-sum liquidity:

Pᵢ = P₀(1+s/10,000)ⁱ; Lᵢ = Pᵢxᵢ + yᵢ

Where:

• i — relative bin ID.
• s — bin step in basis points.
• Pᵢ — fixed price of bin i.
• Lᵢ — constant-sum liquidity value.
• xᵢ and yᵢ — token reserves in that bin.

Spot is uniform. Curve uses a Gaussian with standard deviation equal to one quarter of the bin span; Bid-Ask uses inverse density. Token X and Y allocations are normalized separately on their respective sides, matching the SDK helper before integer rounding.

Meteora DLMM fee rates

The calculator keeps program-precision base and variable rates separate:

fee = min(B·s·10·10ᵖ + ceil(A·(v·s)²/10¹¹), 10%)

Where:

• B — base factor.
• s — bin step.
• p — base-fee power factor.
• A — variable-fee control.
• v — volatility accumulator.
• 10% — maximum total fee.

Raw rates use 1e9 precision. Fee income uses entered volume and competing liquidity for the modeled active bin, then applies time in range and LP share. An out-of-range endpoint earns zero in the endpoint scenario.

Shared exclusions and verification

All calculators run locally and make no wallet or external API calls. They exclude contract risk, token transfer taxes, approval or signing risk, slippage, MEV, tax, liquidation, oracle failure, and any price path not represented by the inputs. Endpoint IL also excludes loss-versus-rebalancing accumulated along the route. Results are educational scenarios, not financial advice.

The source implementation and tests are public in the calculator library on GitHub. Primary references are the Uniswap v2 whitepaper, the Uniswap v3 whitepaper, Balancer weighted-pool documentation, and Meteora’s official DLMM formulas and strategy definitions.

Calculator explanations and guide content follow the same editorial policy: drafts may use AI assistance, material claims are checked against cited primary sources, and the SudoAI team reviews the work before publication. Corrections are handled through the contact route published there.