DBC Formulas

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%.

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Curve Segment Formula

Each DBC curve segment behaves like a constant-product price range. $$x \times y = k$$ 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.

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Base Tokens Sold Through a Segment

The amount of base token available across a curve segment is: $$\text{Base Amount} = L \times \left(\frac{1}{\sqrt{P_\text{lower}}} - \frac{1}{\sqrt{P_\text{upper}}}\right)$$ 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.

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Quote Tokens Collected Through a Segment

The amount of quote token needed to move through a segment is: $$\text{Quote Amount} = L \times (\sqrt{P_\text{upper}} - \sqrt{P_\text{lower}})$$ In product terms, this tells you how much buying demand is needed to move from one curve price to the next.

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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: $$\text{Migration Quote Threshold} = \sum_i L_i \times (\sqrt{P_i} - \sqrt{P_{i-1}})$$ The pool becomes migration-ready when: $$\text{Quote Reserve} \ge \text{Migration Quote Threshold}$$

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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. $$\text{Migration Price} = \left(\sqrt{P_\text{migration}}\right)^2$$ 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.

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Total Trading Fee

DBC trading fees have two layers: $$\text{Total Trading Fee} = \text{Base Fee} + \text{Dynamic Fee}$$ 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%.

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Base Fee

The base fee is the default trading fee behavior. DBC supports fee scheduler and rate limiter behavior: A fixed-fee launch can be represented as a scheduler that does not decay.

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Dynamic Fee

The dynamic fee responds to volatility. $$\text{Dynamic Fee} = \left\lceil \frac{(\text{Volatility Accumulator} \times \text{Bin Step})^2 \times \text{Variable Fee Control}}{100000000000} \right\rceil$$ In product terms, the dynamic fee rises when price movement becomes more intense and decays when trading calms down.

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Fee Split

DBC first splits the total trading fee into protocol and non-protocol portions. $$\text{Protocol Fee} = \text{Trading Fee} \times 20\%$$ If a referral is included, the referral receives a share of the protocol fee. $$\text{Referral Fee} = \text{Protocol Fee} \times 20\%$$ The remaining trading fee is shared between partner and creator according to the config. $$\text{Creator Fee} = \text{LP Fee} \times \text{Creator Trading Fee Percentage}$$ $$\text{Partner Fee} = \text{LP Fee} - \text{Creator Fee}$$

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Migration Fee

DBC can take a configured migration fee from the quote reserve at graduation. That fee can be split between partner and creator. $$\text{Creator Migration Fee} = \text{Migration Fee} \times \text{Creator Migration Fee Percentage}$$ $$\text{Partner Migration Fee} = \text{Migration Fee} - \text{Creator Migration Fee}$$ 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: $$\text{Migration Quote Amount} = \left\lceil \text{Migration Quote Threshold} \times \frac{100 - \text{Migration Fee Percentage}}{100} \right\rceil$$ $$\text{Migration Fee} = \text{Migration Quote Threshold} - \text{Migration Quote Amount}$$

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Pool Creation Fee

Partners can configure a pool creation fee that is paid when a creator launches from the config. $$\text{Protocol Pool Creation Fee} = \text{Pool Creation Fee} \times 10\%$$ $$\text{Partner Pool Creation Fee} = \text{Pool Creation Fee} - \text{Protocol Pool Creation Fee}$$ 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.

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Surplus

Surplus is extra quote reserve above the migration threshold. $$\text{Total Surplus} = \text{Quote Reserve} - \text{Migration Quote Threshold}$$ 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. $$\text{Partner and Creator Surplus} = \left\lfloor\text{Total Surplus} \times 80\%\right\rfloor$$ $$\text{Protocol Surplus} = \text{Total Surplus} - \left\lfloor\text{Total Surplus} \times 80\%\right\rfloor$$

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Leftover

Leftover applies to fixed-supply launches. $$\text{Leftover} = \text{Remaining Base Vault Amount} - \text{Protocol and Trading Base Fees} - \text{Protocol Migration Base Fee}$$ 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.

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Transfer Fees

A Token 2022 transfer fee is charged by the token program on the transfer. The curve and the DBC trading-fee numerator use the post-fee amount. On an exact-in swap, the curve input is the amount left after the input mint’s transfer fee. The amount the user receives is the curve output after the output mint’s transfer fee. On an exact-out swap, the curve output is grossed up so the user still receives the requested amount after the output mint’s fee, and the input is grossed up by the input mint’s fee. $$\text{Curve Input} = \text{Amount In} - \text{Input Transfer Fee}$$ $$\text{Amount Received} = \text{Curve Output} - \text{Output Transfer Fee}$$ A fee is zero when its basis points are 0 or its maximum fee is 0. The base mint fee is the config’s transfer_fee_basis_points with a maximum fee of u64::MAX. The quote mint fee is the TransferFeeConfig epoch fee. At migration, version 1 configs on the transfer-fee path deposit the transfer-fee-excluded amount of each mint. The side whose fee takes the larger fraction of its budget is deposited at that post-fee amount. The other side is scaled by the same ratio. Scaled base rounds up. Scaled quote rounds down. The liquidity that reaches DAMM v2 is lower by the larger of the two fees. The part of the scaled side that is not deposited is added to the protocol migration fee.