Version: 3.0.0

# Fetching Spot Prices

## Fetching Token Prices with the SDK​

This guide will teach you how to fetch the current market price of any token on Uniswap. First, you will learn how to call the getter methods token0Price and token1Price exposed on Pool instances. Then you will peek under the hood and learn how the SDK calculates these quantities from the sqrtPriceX96 value. Going through these calculations will hopefully provide the necessary context behind fixed-point numbers, square roots, and difficult-to-understand variable names like sqrtPriceX96.

### Calling the functions​

Similar to other examples, you first must set up your pool. If you’re unsure how to collect all the parameters necessary in creating a Pool instance see Creating a Pool Instance or look at this typescript example. The Pool class contains two getter methods token0Price and token1Price which will return the prices of each token respectively as a Price.

After constructing the pool, you can save the token prices as constants:

const DAI_USDC_POOL = new Pool(  DAI,  USDC,  immutables.fee,  state.sqrtPriceX96.toString(),  state.liquidity.toString(),  state.tick)const token0Price = DAI_USDC_POOL.token0Priceconst token1Price = DAI_USDC_POOL.token1Price

### Understanding sqrtPrice​

What is sqrtPriceX96?

In Uniswap V3, prices of tokens are stored in the 0th slot of the pool state. Storing the price values instead of deriving them allows pools to perform higher precision operations. In the actual implementation, prices are stored as square roots, hence the sqrt prefix. The price is stored as a square root because of the geometric nature of the core AMM algorithm, x*y=k. Essentially, the math works out well when working with the square root of the price.

In addition, you'll notice the X96 suffix at the end of the variable name. This X* naming convention is used throughout the Uniswap V3 codebase to indicate values that are encoded as binary fixed-point numbers. Fixed-point is excellent at representing fractions while maintaining consistent fidelity and high precision in integer-only environments like the EVM, making it a perfect fit for representing prices, which of course are ultimately fractions. The number after X indicates the number of fraction bits - 96 in this case - reserved for encoding the value after the decimal point. The number of integer bits can be trivially derived from the size of the variable and the number of fraction bits. In this case, sqrtPriceX96 is stored as a uint160, meaning that there are 160 - 96 = 64 integer bits.

##### note

sqrtPriceX96 and sqrtRatioX96 represent the same value, and are interchangeable.

Consider the following derivation, which formalizes the definitions above:

sqrtPriceX96 = sqrt(price) * 2 ** 96

Thus, to get a price from a sqrtPriceX96 value, you can execute the following operations:

sqrtPriceX96 = sqrt(price) * 2 ** 96# divide both sides by 2 ** 96sqrtPriceX96 / (2 ** 96) = sqrt(price)# square both sides(sqrtPriceX96 / (2 ** 96)) ** 2 = price# expand the squared fraction(sqrtPriceX96 ** 2) / ((2 ** 96) ** 2)  = price# multiply the exponents in the denominator to get the final expressionsqrtRatioX96 ** 2 / 2 ** 192 = price

You will see that the formula in the last step is how the SDK calculates the prices with the functions token0Price and token1Price.

### token0Price​

Let's apply the math derived above to the functions token0Price and token1Price. Note that sqrtRatioX96 is interchangeable with sqrtPriceX96.

  /**   * Returns the current mid-price of the pool in terms of token0, i.e. the ratio of token1 over token0   */  public get token0Price(): Price<Token, Token> {    return (      this._token0Price ??      (this._token0Price = new Price(        this.token0,        this.token1,        Q192,        JSBI.multiply(this.sqrtRatioX96, this.sqrtRatioX96)      ))    )  }

token0Price returns a new Price as the ratio of token1 over token0. Note that a Price is constructed by:

constructor(    baseToken: Token,    quoteToken: Token,    denominator: BigintIsh,    numerator: BigintIsh)

Let's break down the denominator and the numerator of the returned price and prove that it matches the math derived above. Recall that the expression achieved above is

price = sqrtRatioX96 ** 2 / 2 ** 192

#### The numerator​

It's worth noting that the numerator is misleadingly listed below the denominator in the constructor for a Price. In any case, you will see that the numerator of the fraction is JSBI.multiply(this.sqrtRatioX96, this.sqrtRatioX96) which nicely follows the math above: sqrtPriceX96 ** 2.

#### The denominator​

The denominator is Q192. To break this number down recall the following constants defined in the SDK:

export const Q96 = JSBI.exponentiate(JSBI.BigInt(2), JSBI.BigInt(96))export const Q192 = JSBI.exponentiate(Q96, JSBI.BigInt(2))

Thus, the denominator for the token0Price also matches the math derived above where Q192 is (2 ** 96) * (2 ** 96) which is the same as (2 ** 192).

### token1Price​

Recall that token0Price is the ratio of token1 over token0 and that token1Price is the ratio of token0 over token1. This means that the derivation for token1Price follows the same math except the numerator and denominator are flipped, implying the inverse.

price = sqrtRatioX96 ** 2 / 2 ** 192
 price =  2 ** 192 / sqrtRatioX96 ** 2
which is simply shown below in the function definition of token1Price :
  /**   * Returns the current mid-price of the pool in terms of token1, i.e. the ratio of token0 over token1   */  public get token1Price(): Price<Token, Token> {    return (      this._token1Price ??      (this._token1Price = new Price(        this.token1,        this.token0,        JSBI.multiply(this.sqrtRatioX96, this.sqrtRatioX96),        Q192      ))    )  }
You can see that in the function definition the numerator is now Q192 and the denominator is now JSBI.multiply(this.sqrtRatioX96, this.sqrtRatioX96), matching the expression above.