> ## 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.

# Fee Market Cap Scheduler Math

There are two types of Fee Market Cap Schedulers:

1. **Linear** (Mode 3)
2. **Exponential** (Mode 4)

# Math Formula

## Step 1: Calculate Passed Periods

The number of periods passed is determined by how much the sqrt price has increased from the initial price:

<div style={{ fontSize: "0.9em" }}>
  ```math theme={"system"}
  \text{Passed Period} = \frac{(\text{Current Sqrt Price} - \text{Initial Sqrt Price}) \times {10,000}}{\text{Initial Sqrt Price} \times \text{Sqrt Price Step Bps}}
  ```
</div>

Where:

* `current_sqrt_price`: The current sqrt price of the pool
* `initial_sqrt_price`: The initial sqrt price when the pool was created
* `sqrt_price_step_bps`: The sqrt price increase (in bps) required to advance one period

## Step 2: Calculate Current Fee

There are two modes for fee calculation:

### Linear Fee Market Cap Scheduler (Mode 3)

<div style={{ fontSize: "0.9em" }}>
  ```math theme={"system"}
  \text{Current Fee} = \text{Cliff Fee Numerator} - (\text{Passed Period} \times \text{Reduction Factor})
  ```
</div>

The fee decreases by a constant amount (`reduction_factor`) for each period passed.

### Exponential Fee Market Cap Scheduler (Mode 4)

<div style={{ fontSize: "0.9em" }}>
  ```math theme={"system"}
  \text{Current Fee} = \text{Cliff Fee Numerator} \times \left(1 - \frac{\text{Reduction Factor}}{10,000}\right)^{\text{Passed Period}}
  ```
</div>

The fee decreases by a percentage of the current fee for each period passed.

# Scheduler Expiration

The scheduler has an expiration mechanism to ensure fees eventually reach the minimum:

```
Expiration Point = Activation Point + Scheduler Expiration Duration
```

* If `current_point > expiration_point`, the scheduler expires
* When expired, the fee defaults to the **minimum fee** (fee calculated at `number_of_period`)
* This prevents fees from staying high indefinitely if the price doesn't increase

# Edge Cases

| Condition                               | Behavior                                            |
| --------------------------------------- | --------------------------------------------------- |
| `current_sqrt_price <= init_sqrt_price` | `passed_period = 0` (fee stays at cliff fee)        |
| `passed_period > number_of_period`      | `passed_period = number_of_period` (fee at minimum) |
| Scheduler expired                       | Fee defaults to minimum fee                         |
| Alpha Vault buying (before activation)  | Fee at minimum fee                                  |

# Example Calculations

## Linear Mode Example

Given:

* `cliff_fee_numerator`: 500,000,000 (50% fee)
* `number_of_period`: 100
* `sqrt_price_step_bps`: 100 (1% sqrt price step)
* `reduction_factor`: 4,950,000
* `init_sqrt_price`: 1,000,000
* `current_sqrt_price`: 1,050,000 (5% increase)

**Step 1: Calculate passed period**

```
Passed Period = (1,050,000 - 1,000,000) × 10,000 / (1,000,000 × 100)
             = 50,000 × 10,000 / 100,000,000
             = 5 periods
```

**Step 2: Calculate fee**

```
Fee = 500,000,000 - (5 × 4,950,000)
    = 500,000,000 - 24,750,000
    = 475,250,000 (≈ 47.5% fee)
```

## Exponential Mode Example

Given:

* `cliff_fee_numerator`: 500,000,000 (50% fee)
* `number_of_period`: 100
* `sqrt_price_step_bps`: 100 (1% sqrt price step)
* `reduction_factor`: 390 (3.9% reduction per period)
* `init_sqrt_price`: 1,000,000
* `current_sqrt_price`: 1,050,000 (5% increase)

**Step 1: Calculate passed period**

```
Passed Period = 5 periods (same as above)
```

**Step 2: Calculate fee**

```
Fee = 500,000,000 × (1 - 390/10,000)^5
    = 500,000,000 × (0.961)^5
    = 500,000,000 × 0.8154
    = 407,700,000 (≈ 40.8% fee)
```

# Fee Numerator Conversion

To convert fee numerator to percentage:

```
Fee Percentage = Fee Numerator / 10,000,000
```

Examples:

* 500,000,000 = 50% fee
* 10,000,000 = 1% fee
* 100,000,000 = 10% fee