DLMM is a concentrated liquidity AMM that uses a dynamic fee mechanism to adjust liquidity based on market conditions.

​

Price Calculation Formulas

​

Base Price Formula

$$\text{price} = \left(1 + \frac{\text{bin\_step}}{\text{BASIS\_POINT\_MAX}}\right)^{\text{active\_id}}$$ Where:

• BASIS_POINT_MAX = 10,000
• Uses Q64.64 fixed-point arithmetic
• Example: For bin_step = 10, price = (1.001)^active_id

​

Price Impact Formulas

Selling X for Y: $$\text{min\_price} = \text{spot\_price} \times \frac{\text{BASIS\_POINT\_MAX} - \text{max\_price\_impact\_bps}}{\text{BASIS\_POINT\_MAX}}$$ Selling Y for X: $$\text{min\_price} = \text{spot\_price} \times \frac{\text{BASIS\_POINT\_MAX}}{\text{BASIS\_POINT\_MAX} - \text{max\_price\_impact\_bps}}$$

​

Fee Calculation Formulas

​

Total Trading Fee

$$\text{total\_fee\_rate} = \min(\text{base\_fee\_rate} + \text{variable\_fee\_rate}, \text{MAX\_FEE\_RATE})$$

​

Base Fee Formula

$$\text{base\_fee\_rate} = \text{base\_factor} \times \text{bin\_step} \times 10^{\text{base\_fee\_power\_factor}}$$

​

Variable Fee Formula

$$\text{variable\_fee\_rate} = \frac{(\text{volatility\_accumulator} \times \text{bin\_step})^2 \times \text{variable\_fee\_control} + \text{OFFSET}}{\text{SCALE}}$$ Where:

• OFFSET = 99,999,999,999
• SCALE = 100,000,000,000

​

Composition Fee Formula

$$\text{composition\_fee} = \frac{\text{swap\_amount} \times \text{total\_fee\_rate} \times (1 + \text{total\_fee\_rate})}{\text{FEE\_PRECISION}^2}$$ Where:

• MAX_FEE_RATE = 100,000,000

​

Liquidity and Bin Math Formulas

​

Liquidity Formula (Constant Sum)

$$L = \text{price} \times x + y$$ Where:

• L is liquidity
• x and y are token amounts
• Price is in Q64.64 format

​

Liquidity Share Formula

$$\text{liquidity\_share} = \frac{\text{in\_liquidity} \times \text{liquidity\_supply}}{\text{bin\_liquidity}}$$