# Liquidity Amplification Factor

A ranged position with price range from 0.8 to 1.2 in the above example provides the liquidity only in the range. Since the ranged pool does not provide the liquidity outside of the range, its liquidity is concentrated in the range. Compared to the basic position with the same capital, the ranged position with \[0.8, 1.2] range provides liquidity 10 times greater than the basic position in the price range. This value of 10 is the liquidity amplification factor of the ranged position. The liquidity amplification factor depends on the price range. As it can be seen below, the liquidity amplification factor increases as the size of the range is getting smaller.

| Current Pool Price | Min Price | Max Price | Liquidity Amplification Factor |
| ------------------ | --------- | --------- | ------------------------------ |
| 1                  | 0.8       | 1.2       | 10.38                          |
| 1                  | 0.9       | 1.1       | 20.44                          |
| 1                  | 0.98      | 1.02      | 100.49                         |
| 1                  | 0.99      | 1.01      | 200.49                         |
| 1.079              | 1.063     | 1.15      | 51.54                          |

For a ranged pool with Pmin, Pmax and P as the minimum price, maximum price and current pool price, the amplication factor (AMP) can be calculated as

$$AMP=\frac{1}{1 - \frac{1}{2}\left(\sqrt{\frac{P\_{min}}{P}} + \sqrt{\frac{P}{P\_{max}}} \right)}$$

Note that $$P\_{min}≤P≤P\_{max}$$


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://docs.crescent.network/introduction/crescent-dex/ranged-liquidity/liquidity-amplification-factor.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.