> ## Documentation Index
> Fetch the complete documentation index at: https://docs.berachain.com/llms.txt
> Use this file to discover all available pages before exploring further.
# Valuing LP Tokens
> Calculate BEX LP token value: informational and on-chain methods.
## Overview
BEX LP tokens represent a share of a liquidity pool. Accurately valuing these tokens is essential for displaying balances, calculating rewards, and for on-chain operations like collateralization and liquidation. There are several methods to value LP tokens, each suited to different use cases.
## Methods of valuation
### Informational (sum of balances)
This calculation is for informational purposes only and should NOT be used on-chain as it can be
easily manipulated.
This method is suitable for off-chain, informational, or UI purposes. It is **not manipulation-resistant** and should not be used for on-chain or critical financial operations.
**Formula:**
$$
Price_{LP\ token} = \frac{\sum_i (Balance_i \times Price_i)}{Supply_{LP\ Tokens}}
$$
**Where:**
* **Balancei**: balance of token $i$ in the pool
* **Pricei**: market price of token $i$
* **SupplyLP\ Tokens**: total supply of LP tokens
**Example:**
Suppose a \$BERA/\$HONEY pool contains the following:
| Token | Balance | Price (USD) | Value (USD) |
| -------------------- | --------- | ----------- | ------------ |
| \$BERA | 1,000 | \$10 | \$10,000 |
| \$HONEY | 10,000 | \$1 | \$10,000 |
| **Total Pool Value** | | | **\$20,000** |
| **LP Token Supply** | **1,000** | | |
* **Pool Value:** 1000 \$BERA $\times$ 10 USD + 10000 \$HONEY $\times$ 1 USD = 20000 USD
* **LP Token Price:** 20000 USD $/$ 1000 \$LPTOKEN = 20 USD
***
### Weighted pools
Weighted pools use a constant product invariant with custom weights. This method is **manipulation-resistant** and is recommended for on-chain or robust off-chain use.
| Calculation Steps | Formula |
| ----------------------------------------------------------------- | --------------------------------------------------------------------------------------------- |
| **Step 1: Pool Invariant** where $\sum_i w_i = 1$ | $x_1^{w_1} x_2^{w_2} \cdots x_n^{w_n} = k$ |
| **Step 2: Token Weighted Values** | $\frac{p_1 x_1}{w_1} = \cdots = \frac{p_n x_n}{w_n} = \hat{k}$ |
| **Step 3: Calculate $\hat{k}$** | $\hat{k} = k \cdot \prod_i \left( \frac{p_i}{w_i} \right)^{w_i}$ |
| **Step 4: Final LP Token Price** where $s$ is the LP token supply | $p_{LP} = \frac{\hat{k}}{s} = \frac{k}{s} \cdot \prod_i \left( \frac{p_i}{w_i} \right)^{w_i}$ |
**Example**
Imagine an 80 \$BAL/20 \$WETH Pool with the following:
| Calculation Steps | Values |
| -------------------------------- | -------------------------------------------------------------------------------------------------------------- |
| **Step 1: Token Weights** | $w_1 = 0.8$ (\$BAL)
$w_2 = 0.2$ (\$WETH) |
| **Step 2: Oracle Prices** | $p_1 \approx$ \$4.53 (\$BAL)
$p_2 \approx$ \$1090.82 (\$WETH) |
| **Step 3: Pool Parameters** | $k \approx 2,852,257.5$ (from `pool.getInvariant()`)
$s \approx 5,628,392.26$ (from `pool.totalSupply()`) |
| **Step 4: Final LP Token Price** | $p_{LP} = \frac{k}{s} \cdot \prod_i \left( \frac{p_i}{w_i} \right)^{w_i} \approx$ \$11.34 |
***
### Stable pools
Stable pools are optimized for assets that trade at or near parity (e.g., stablecoins). They use the StableSwap invariant and often expose a `getRate()` function.
**StableSwap Invariant:**
$$
A \cdot n^n \cdot \sum_i x_i + D = A \cdot D \cdot n^n + \frac{D^{n+1}}{n^n \cdot \prod_i x_i}
$$
Where:
* $A$ is the amplification parameter
* $n$ is the number of tokens
* $x_i$ are token balances
* $D$ is the invariant
**LP Token Price (using getRate):**
Most stable pools expose a `getRate()` function, which returns the value of 1 LP token in terms of the pool's base asset (e.g., USD or a stablecoin):
$$
p_{LP} = \text{getRate()} \times \text{(price of base asset)}
$$
**Manual Calculation (if needed):**
$$
p_{LP} = \frac{\sum_i x_i \cdot p_i}{S}
$$
Where $S$ is the actual supply (use `getActualSupply()` for pre-minted pools).
**Example:**
Suppose a USDC/DAI/USDT pool with $getRate() = 1.01$ and USD as the base asset:
* **LP token price:** $p_{LP} = 1.01 \times 1 = 1.01$ USD per LP token
***
### Linear pools
Linear pools are designed for pairs where one token is a yield-bearing or wrapped version of the other. They use a simple linear invariant and expose a `getRate()` function.
**Linear Pool Invariant:**
$$
x_{main} + r \cdot x_{wrapped} = k
$$
Where $r$ is the rate between the wrapped and main token.
**LP Token Price (using getRate):**
$$
p_{LP} = \text{getRate()} \times \text{(price of main token)}
$$
**Manual Calculation (if needed):**
$$
p_{LP} = \frac{x_{main} \cdot p_{main} + x_{wrapped} \cdot p_{wrapped}}{S}
$$
Where $S$ is the virtual supply (use `getVirtualSupply()`).
**Example:**
Suppose a wstETH/ETH pool with $getRate() = 1.05$ and ETH at $2000$:
* **LP token price:** $p_{LP} = 1.05 \times 2000 = 2100$ USD per LP token
## Special considerations
* **Pre-minted Supply:** Some pools (especially stable pools) pre-mint the maximum possible LP tokens. Always use `getActualSupply()` or `getVirtualSupply()` as appropriate.
* **Protocol Fees:** Some pools accrue protocol fees, which may affect the actual value of LP tokens. Weighted and stable pools account for these in their supply functions.
* **Manipulation Resistance:** For on-chain or critical use, always use invariant-based or rate-based pricing, not simple sum-of-balances.
* **Re-entrancy Protection:** When evaluating on-chain, always check for Vault re-entrancy using `ensureNotInVaultContext(vault)`.
* **Staked LP Tokens:** If LP tokens are staked, include both wallet and staked balances in your calculations.
## References
* [Balancer: Valuing BPT](https://docs-v2.balancer.fi/concepts/advanced/valuing-bpt/valuing-bpt.html#overview)
* [Balancer: Stable Math](https://docs-v2.balancer.fi/concepts/math/stable-math.html)
* BEX Vault Contract
* [BEX Pool Types](/bex/learn/pools)
* [BEX SDK](/build/bex/sdk/overview)