> ## Documentation Index > Fetch the complete documentation index at: https://docs.meteora.ag/llms.txt > Use this file to discover all available pages before exploring further. # DBC Formulas > Understand the product math behind DBC price movement, universal curve segments, migration thresholds, trading fees, surplus, protocol migration fees, and leftover tokens. DBC uses concentrated-liquidity style math to create a customizable bonding curve. You do not need to understand every implementation detail to use the product, but the formulas below explain the main economic levers behind a launch. On-chain fee numerators use a denominator of `1,000,000,000`. For example, `2,500,000` is `0.25%`, and `990,000,000` is `99%`. ## Curve Segment Formula Each DBC curve segment behaves like a constant-product price range. ```math theme={"system"} x \times y = k ``` In DBC product terms: * `x` represents the base token side of the curve. * `y` represents the quote token side of the curve. * `L` represents virtual liquidity. * `sqrt_price` represents the square root of the token price. The curve is built from one or more price ranges. Each range has a lower price, an upper price, and a liquidity value. ## Base Tokens Sold Through a Segment The amount of base token available across a curve segment is: ```math theme={"system"} \text{Base Amount} = L \times \left(\frac{1}{\sqrt{P_\text{lower}}} - \frac{1}{\sqrt{P_\text{upper}}}\right) ``` In product terms, this tells you how much launched token can be sold while the price moves through that segment. If a segment has more liquidity, more quote tokens are needed to move price through the segment. If it has less liquidity, price moves faster. ## Quote Tokens Collected Through a Segment The amount of quote token needed to move through a segment is: ```math theme={"system"} \text{Quote Amount} = L \times (\sqrt{P_\text{upper}} - \sqrt{P_\text{lower}}) ``` In product terms, this tells you how much buying demand is needed to move from one curve price to the next. ## Migration Quote Threshold The migration quote threshold is the amount of quote reserve needed before the launch can graduate. For a multi-segment curve, the total quote amount is the sum of the quote amount across each segment up to the migration price: ```math theme={"system"} \text{Migration Quote Threshold} = \sum_i L_i \times (\sqrt{P_i} - \sqrt{P_{i-1}}) ``` The pool becomes migration-ready when: ```math theme={"system"} \text{Quote Reserve} \ge \text{Migration Quote Threshold} ``` ## Migration Price The migration price is the price reached when the quote reserve hits the migration threshold. DBC derives this price from the curve and uses it to initialize the migrated DAMM pool. ```math theme={"system"} \text{Migration Price} = \left(\sqrt{P_\text{migration}}\right)^2 ``` This matters because the post-migration DAMM pool should open around the price discovered by the bonding curve, not an unrelated price chosen after the fact. ## Total Trading Fee DBC trading fees have two layers: ```math theme={"system"} \text{Total Trading Fee} = \text{Base Fee} + \text{Dynamic Fee} ``` The base fee is always present. The dynamic fee is optional and becomes zero when disabled. The total fee numerator is capped at `990,000,000`, or `99%`. ## Base Fee The base fee is the default trading fee behavior. DBC supports fee scheduler and rate limiter behavior: | Base Fee Mode | Product Meaning | | ------------- | ----------------------------------------------------------------------------- | | Fee scheduler | Fee can stay fixed, decrease linearly, or decrease exponentially by schedule. | | Rate limiter | Fee increases with buy size during the configured launch window. | A fixed-fee launch can be represented as a scheduler that does not decay. ## Dynamic Fee The dynamic fee responds to volatility. ```math theme={"system"} \text{Dynamic Fee} = \left\lceil \frac{(\text{Volatility Accumulator} \times \text{Bin Step})^2 \times \text{Variable Fee Control}}{100000000000} \right\rceil ``` In product terms, the dynamic fee rises when price movement becomes more intense and decays when trading calms down. ## Fee Split DBC first splits the total trading fee into protocol and non-protocol portions. ```math theme={"system"} \text{Protocol Fee} = \text{Trading Fee} \times 20\% ``` If a referral is included, the referral receives a share of the protocol fee. ```math theme={"system"} \text{Referral Fee} = \text{Protocol Fee} \times 20\% ``` The remaining trading fee is shared between partner and creator according to the config. ```math theme={"system"} \text{Creator Fee} = \text{LP Fee} \times \text{Creator Trading Fee Percentage} ``` ```math theme={"system"} \text{Partner Fee} = \text{LP Fee} - \text{Creator Fee} ``` ## Migration Fee DBC can take a configured migration fee from the quote reserve at graduation. That fee can be split between partner and creator. ```math theme={"system"} \text{Creator Migration Fee} = \text{Migration Fee} \times \text{Creator Migration Fee Percentage} ``` ```math theme={"system"} \text{Partner Migration Fee} = \text{Migration Fee} - \text{Creator Migration Fee} ``` Partner and creator migration-fee withdrawals are available after the curve is complete because the program can then confirm the launch reached its migration quote threshold. The quote amount used for migration is calculated by removing the configured migration fee from the migration threshold, rounded up: ```math theme={"system"} \text{Migration Quote Amount} = \left\lceil \text{Migration Quote Threshold} \times \frac{100 - \text{Migration Fee Percentage}}{100} \right\rceil ``` ```math theme={"system"} \text{Migration Fee} = \text{Migration Quote Threshold} - \text{Migration Quote Amount} ``` A fixed 0.2% protocol liquidity migration fee also applies during migration. It is separate from the configurable partner and creator migration fee, and it reduces the base and quote liquidity deposited into the migrated pool. ## Pool Creation Fee Partners can configure a pool creation fee that is paid when a creator launches from the config. ```math theme={"system"} \text{Protocol Pool Creation Fee} = \text{Pool Creation Fee} \times 10\% ``` ```math theme={"system"} \text{Partner Pool Creation Fee} = \text{Pool Creation Fee} - \text{Protocol Pool Creation Fee} ``` Pool creation fee claims are tied to virtual pool creation, not to curve completion or migration. If configured, the pool creation fee must be between `0.001 SOL` and `100 SOL`, denominated in lamports. ## Surplus Surplus is extra quote reserve above the migration threshold. ```math theme={"system"} \text{Total Surplus} = \text{Quote Reserve} - \text{Migration Quote Threshold} ``` DBC allocates 80% of surplus to partner and creator, then splits that share using the creator trading fee percentage. The remaining 20% is protocol surplus. ```math theme={"system"} \text{Partner and Creator Surplus} = \left\lfloor\text{Total Surplus} \times 80\%\right\rfloor ``` ```math theme={"system"} \text{Protocol Surplus} = \text{Total Surplus} - \left\lfloor\text{Total Surplus} \times 80\%\right\rfloor ``` ## Leftover Leftover applies to fixed-supply launches. ```math theme={"system"} \text{Leftover} = \text{Remaining Base Vault Amount} - \text{Protocol and Trading Base Fees} - \text{Protocol Migration Base Fee} ``` In product terms, leftover is the unused base token supply that remains after the migrated pool is created and claimable base-token fee balances are excluded.